Dr. Sheldon Horowitz (Moderator):
Good afternoon and welcome to LD Talk, the Web's only online discussion devoted to topics of interest to the learning disabilities community.
LD Talk is a service of the National Center for Learning Disabilities (NCLD). Funding for LD Talk is generously provided by SchwabLearning.org.
It’s a pleasure to welcome you all to the today’s chat - Thanks for joining us!
Today’s topic is about math difficulties and math disabilities. And we’re thrilled to have Dr. Nancy Jordan, a leading expert in this area of research and practice, with us to answer your questions.
Dr. Nancy C. Jordan is a Professor in the School of Education at the University of Delaware in Newark, Delaware (USA). Dr. Jordan completed her doctoral work in Education at Harvard University and completed a post doctoral fellowship at the University of Chicago.
Prior to her doctoral studies, Dr. Jordan taught children with learning disabilities. Since 1999, her research project on children's mathematics has been funded by the National Institute of Child Health and Human Development. Her studies have been published in Child Development, the Journal of Educational Psychology, the Journal of Learning Disabilities, and the Journal of Experimental Child Psychology. Dr. Jordan's most recent work is concerned with kindergarten predictors of math difficulties in primary school.
I am Dr. Sheldon Horowitz, Director of Professional Services at the National Center for Learning Disabilities, and I’ll be the moderator of today’s discussion.
To those of you who have submitted questions in advance of today’s chat, many thanks! As usual, we encourage everyone to send in questions and we’ll try to respond to those that are most closely related to our discussion topic and of the broadest interest to our audience. (If you have questions unrelated to this topic, please feel free to send them to NCLD’s Help Desk at This e-mail address is being protected from spam bots, you need JavaScript enabled to view it )
Let’s now begin the discussion.
Question from Dr. Sheldon Horowitz:
We know that almost twice as many boys are identified as having LD than are girls, yet the true incidence of LD in reading (based on research data) suggests that dyslexia occurs in just as many girls as in boys. What do we know about the prevalence of math LD among school age children and is the incidence different between boys and girls?
Dr. Nancy C. Jordan:
In a recently published study, Mayo Clinic researchers determined Math Learning Disorder (LD) is common among school-age children.
Results show that boys are more likely to have Math LD than girls. The research also indicates that although a child can have a Math LD and a reading LD, a substantial percentage of children have Math LD alone. In fact, the cumulative incidence of Math LD through age 19 ranges from 6% to as high as 14%, depending on the Math LD definition.
LD is used to describe the seemingly unexplained difficulty a person of at least average intelligence has in acquiring basic academic skills -- skills that are essential for success at school, work and for coping with life in general. The results appear in the September-October issue of Ambulatory Pediatrics.
Question from Teresa, Parent:
What is the difference between dyscaculia vs. dyslexia. My daughter is dyslexic and also has a very difficult time with math.
Dr. Nancy C. Jordan:
Hi Teresa. While "dyslexia" means word trouble, "dyscalulia" means number trouble. Children with dyscalculia have specific problems with number sense, such as counting, estimation and comparison of quantities and basic arithmetic. Quick retrieval of number facts and calculation fluency seem to be a key characteristics of children with dyscalculia. As I mentioned in the previous response, reading disabilities tend to co-occur with math weaknesses, especially in areas that have a verbal basis (e.g., solving word problems).
Question from Theresa Williingham, President, Learning is For Everyone, Inc. (www.LIFEofFlorida.org):
This may well be answered during the chat, but I'm wondering how to distinquish dyscaculia from math anxiety, or simple dislike (and consequent disinterest and lack of retention)? My teenage daughter has a long history of frustrating difficulties with math, and doesn't seem to retain information from one lesson to the next, including what I'd consider rather basic skills. Yet she loves science, especially biological sciences, and we're concerned (as is she) that her difficulties with math will compromise her ability to pursue a career in that area. Thank you for your help. Theresa Willingham
Dr. Nancy C. Jordan:
Hi Theresa, Math anxiety is a common problem that can be rooted in genuine difficulties or poor instruction. Moreover, many teenagers opt out of math because they do not see its relevance to their lives. If your daughter did not acquire basic skills and has trouble with retention of mathematical information, it makes sense that she would feel anxious in higher level math classes. You might want to screen for basic problems and then get her a tutor so she can aquire the skills she needs to compete in biology and other sciences. Special help may reduce her math anxiety. NCJ
Question from Naomi Weiss, parent, Board member Cherry Hill Special Education PTA, advocate, Cherry Hill School District:
Math deficiencies plaque NLD(Nonverbal learning Disorder) students, during their school careers; even when identified and recognized, these students do not receive appropriate math tutoring that coordinates with their lanquage skill strengths to create strategies to address their specific disability's math weaknesses. Are there specific math programs or teaching strategies and tools, that have research based success with NLD students, available to public schools, that should be known and utilized by public school districts to address the unique identifying math difficulties of NLD students?
Dr. Nancy C. Jordan:
You are correct that children can use their language strengths to compensate for weaknesses in math. In fact, our research has shown that the rate of math achievement for children with math LD only is faster than for children with both math and reading/language LD. I do not know of specific math programs for children with nonverbal learning disabilities. However, most of the programs being used in the schools do have a verbal component.
Assuming that the child with NLD has strong language skills, he or she should be encouraged to give verbal explanations for solving problems and to talk through their problem solving. The child also might do better with mental calculation than written work.
Mel Levine makes a number of good suggestions along these lines. See his Web site, All Kinds of Minds for more information.
Regarding research, teaching math to children with NLD certainly would be an important area for future investigation. In general, research in teaching math to children with LD lags behind research in the reading area. For more information on the state of research in MD, see the recent article by Dr. Sheldon Horowitz, Math & LD: Counting on Research for Answers.
Question from Patricia Pascale, Learning Disabilites Teacher Consultant:
Do you think that the standardized measures for identification of a specific learning disability in math which may include the Woodcock Johnson are an accurate assessment? What standardized measures would you suggest to be best practice? What would you suggest as a functional assessment?
Dr. Nancy C. Jordan:
The WJ-3 is a reliable and valid test. However, it assesses a relatively narrow set of skills and may need to be followed up with functional, curriculum-based measures.
For example, to get a better reading of a child's skill in word problems, the LDTC might want to take examples directly from the child's math curriculum.
Lynn Fuchs has written a lot about developing valid curriculum-based measures (CBM)and even has published a CBM instrument that can be adapted (Pro-Ed, I think).
With respect to other standardized tests, the new KTEA and WIAT also are good screening measures. The KeyMath, I believe, is due for a revision (the problems are getting out of date and the norms old). Same goes for the PIAT. For young children, the TEMA-3 can provide important information.
Most untimed measures should be supplemented with timed measures, if fluency is an issue. It is noteworthy that the newer versions of the WJ, WIAT, and KTEA include rate-based measures.
Question from Moira Laughlin, Greene County Educational Service Center, Parent Mentor:
How appropriate is encouraging a child as young as 3rd-4th grade (who is struggling with understanding arithmetic concepts and operations) to use a calculator for all math assignments? Child has difficulty understanding abstract language and concepts.
Dr. Nancy C. Jordan:
The issue of how and when to use calculators in math is important. First, the child would need to learn calculator skills. Some young children make more mistakes with a calculator than without one!
Second, young children should use calculators selectively, for example, on tasks where concepts rather than skills (such as word problems) are emphasized. In this way, the child could concentrate on the sructure of the problem without worrying about lower-level calculations.
However, I wouldn't recommend calculators for all math assignments in elementary school. Children should still work on mastery of basic skills, and too much calculator use could be counterproductive.
Question from Seymour Burack, School Psychologist, Sayreville New Jersey:
Do you have any opinions on the Dyscalculia Screener which was developed by Dr Brian Butterworth
Dr. Nancy C. Jordan:
Although I have not used the Dyscalculia Screener, I know it is based on sound theoretical principles. It is likely to pick up children with fundamental problems in number. However, a more thorough diagnostic work up would be needed to evaluate other areas of math (e.g., applications and problem solving).
More information about the Dyscalculia Screener is available here.
Question from Dr. Sheldon Horowitz:
Nancy: Are there any other valuable screening or assessment tools that can help identify young students at risk of math difficulities?
Dr. Nancy C. Jordan:
There are not as many validated screening tools in math as there are in reading.
However, we recently developed a "number sense" battery in our lab which is strongly predictive of first-grade math achievement. In particular, we look at counting and number knowledge (e.g., indicating which of 2 numbers is greater, estimating distances between numbers) as well as verbal and nonverbal calculation. The battery is described in detail in a publication that will be coming out in Child Development early in 2006 (Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M Development of Number Sense in Kindergartners).
Part of our battery is based on the Number Knowledge Test developed by Sharon Griffin and Robbie Case. Ben Clarke and folks in Oregon also are developing a tool along these lines. One unique feature of their work is the use of timed measures to assess number speed and fluency. A parallel reading test might be the DIBELS.
As I think I mentioned in another answer, the Test of Early Mathematics Abilities - 3 (Pro-Ed) is another good screening tool.
Michele Mazzocco recently published a paper on kindergarten predictors of MD (Mazzocco, M.M.M. & Thompson, R.E. 2005, Kindergarten Predictors of Math Learning Disability, Learning Disabilities Research and Practice, 20 (3), 142-155) and found particular areas of the TEMA-3 to be very predictive of MD in third grade. The areas included reading numbers. magnitude judgments of 1-digit numbers, and mental addition, all areas of basic number sense.
In general, cognitve skills directly related to number are more predictive of math achievement than are measures general verbal and spatial skills. Our kindergarten number sense battery predicts math achievement above and beyond IQ , working memory, and reading skill.
NCJ
Question from Judy Guillot, Resource, LSU Laboratory School:
Many of our elementary LD students have trouble memorizing multiplication facts. Should we continue to push them to memorize, or is that something they cannot do? At present we allow them to use a multiplication chart. Is that an acceptable accommodation?
Dr. Nancy C. Jordan:
Hi Judy, I think you should make every effort to help children master the multiplication tables but also allow them to use accommodations. An advantage of the multiplication chart is that children can see how all of the combinations are related. You might allow them to use charts or calculators on more complicated multistep problems but still spend 5 or 10 minutes a day practicing the facts. Although some children may never reach full mastery, partial fact knowledge will still help them.
Question from Dr. Sheldon Horowitz:
Nancy:
Can you tell us more about the number sense" battery you have developed? Specifically, when and how could people obtain the battery?
Dr. Nancy C. Jordan:
A complete description of our battery is described in an upcoming edition of Child Development. The manuscript is in press and is scheduled for 2/2006 publication. A copy of the manuscript can be obtained through the website of the Society for Research in Child Development (http://www.srcd.org) and the linking onto the journal. Then a PDF file can be obtained. But it will not be available until close to the publication date.
Question from RevDanaBeth Wells-Goodwin, Dynamic Learning Network, Denmark, Maine:
Does dyscaculia affect one's ability to learn to read music? (read notes and count note values; master keyboard techniques.) Are there strategies to help with retention in this area?
Dr. Nancy C. Jordan:
This is an interesting question, but I 'm afraid I don't know the answer. I'm not aware of any research looking at connections between dyscalculia and the ability to read music.
Question from Laura Ericson, parent:
My 14 yr old 8th grade son writes out each Algebra problem in laborious extra steps & detail and doesn't like or seem to understand shortcuts to quicker solutions. He has processing & other learning disabilities & I wonder if his insistence on extra steps reflects the way his brain processes & solves algebra? What can we do to help him?
Dr. Nancy C. Jordan:
Laura, It does sound like your child's learning disabilities may be affecting his approach to solving the algebra problems. Although you don't indicate the nature of his LD, algebra requires abstract thinking quantitative reasoning, and memory, among other things. Your son seems to understand algebra and can reach solutions to problems when he writes out all the steps. This is a good thing and can be used to help him be more efficient. Perhaps if he is given explicit help in short cuts, based on his own work, he will see how they can help. He also might need extended practice to master the new approaches. Of course, if shortcuts continue to be problematic, he should be given more time on exams.
Question from Kathy Laffin, Consultant for Specific Learning Disabilities, Wisconsin Dept of Public Instruction:
The newest math curriculum materials focus heavily on math vocabulary, problem solving and solutions to math problems that include written explanations. What are some methods to assist students with learning disabilities to work within this math curriculum framework?
Dr. Nancy C. Jordan:
Many of the newer "progessive" curricula do no provide direct instruction in basic skills. Students with LD, therefore, may need supplemental help with number combinations, written calculations, calculation fluency, etc. They also should be given lots of opportunities to talk about what they are doing or to make their thinking public. These activities would need to be very structured (e.g., summarize the problem in your own words, explain how you will solve the problem, describe an alternate way to solve the problem). Unfortunately, children with language difficulties can be penalized by some of the newer approaches but children with MD with language strengths might resonate with them.
Question from MaryLou, Mother of a learning disabled child:
Dr. Jordan, Our school system utilizes "Chicago Math". The constant change in concepts prior to mastering an idea has been a challenge and frustration for my child. Our struggle is with organization and processing. Do you have any suggestions on how to work within this framework and increase my child's success?
Dr. Nancy C. Jordan:
Hi MaryLou, I am assuming you mean the math program that was developed at the University of Chicago. Sometimes more "progressive" curricula, like this one, create problems for children with learning disabilities. They tend to empahisize problem solving and inductive reasoning over skill developent.
Research shows that many children with LD (and without LD!) need a more explicit approach to instruction, one that provides lots of opportunities for practice and mastery. I suggest you get your child a tutor to reinforce the skills he does not pick up in school. You also could get a copy of the math textbook to preview the material with him at home.
Question from Rosalind Pomerance, Learning Specialist, Ramaz Middle School:
If a students with a learning disability, needs to use a calculator for math exams, will his use of the calculator on a standardized test invalidate his scores? If he does not use a calculator will his score be representative of his true abilities?
Dr. Nancy C. Jordan:
This depends on the test and the school policies. Some tests provide for calculator use. Many children with LD are allowed to use calculators on standardized tests as a special accommodation. Or an alternative test could be given that would allow calculator use. This issue should be addressed in the student's IEP.
Dr. Sheldon Horowitz (Moderator):
Policies regarding accommodations used in district and state-wide assessments, such as those required by the No Child Left Behind Act (NCLB), vary greatly from state to state.
The National Center for Learning Disabilities recently released a Parent Advocacy Brief that provides important information for parents on making accommodation decisions.
The Parent Advocacy Brief is part of a series of informational products NCLD has created to help parents understand key provisions of No Child Left Behind.
All of the NCLB resources can be downloaded FREE of CHARGE here.
Question from Jeannie Madge, Homeschool Mother:
My 7yo daughter has dyslexia and memory issues. She cannot memorize the names of 6, 7, 8 or 9. She knows what they mean but cannot memorize the names. She cannot yet understand ones, tens, hundreds, etc. Is this a disability or her age? Jeannie
Dr. Nancy C. Jordan:
Hi Jeannie. Thank you for your question. Although there is a relation betweeen dyslexia and math difficulties, this is not always the case. Dyslexia is considered a risk factor, however. By 7 years of age, most children know the number names (which are picked up pretty readily through informal experiences) and have some understanding of tens and ones, etc. But it would be hard to know at this point if your daughter has a math disability. You would get more information by giving her a screening test, such as the Test of Early Mathematics - 3 (Pro-Ed). Best wishes. NCJ
More information on the Test of Early Mathematics is available here.
Question from John Rosenitsch, LD teacher, St. Luke Elementary:
How do I help with the language aspect of problem solving, in order to ease a child's understanding of written math?
Dr. Nancy C. Jordan:
Of course this is a pretty general question but it addresses an important area of concern. I assume by easing a child's "understanding of written math" you mean easing the reading and associated language requirements.
If a child is relatively strong in quantitative skills but weak in reading, he should be given support with written math instructions and word problem solving.
If the child has difficulties even when a problem is read to him, you might help him break the problem into steps and represent the steps with pictures or diagrams. He should practice thinking about what the problem is asking, making mental or physical representations, and talking through the steps.
Many state tests require children to give written verbal explanations for math problems, which conflates langauage and number skills. Children with language difficulites often have a hard time with this type of activity. But I think they can learn to give proficient explanations with very structured, explicit practice.
Question from James Dunderman, LDT-C:
Many students here, high school age LD, still have difficulty learning long division. Some are lagging behind in the prerequisite skills while others don't get the overall concept nor can follow the sequence of steps necessary to solving the problem. Word problems add another set of learning issues. Is there a well researched method or materials that would help them to learn these concepts. Thanks.
Dr. Nancy C. Jordan:
James,
I'm not sure that here is a "well researched" method out there but students with MD tend to benefit from explicit approaches that also provide lots of practice.
Long division is often problematic because it requires coordination of several skills. If the student can't recall the steps for solving long division problems, he or she might be given a model of a correctly solved problem. Each step could be highlighted. The model could be referred to during subsequent written work. The student also could be allowed to use a calculator for the compuation part (e.g., subtracting), if this is a problem.
Because your students are in high school and still having difficulty, the problems should probably be presented in meaningful, "real world" contexts. In the real world, people don't use long division all that much but simple problems that require remainders to be expressed as decimals or percentages are important.
Question from Nancy Clarke, Mother From Canada:
Could you please tell me why my daughter has trouble with single digits, yet when doing a problem that is multi-step she has not problems. 2+2=4 will stump her. But put that problem within a multi-step she will answer the question correctly. In geometry she is two years advance over her peers, yet basic abc's of math will stump her. Is there any suggestions or methods might be use to overcome this? I have discovered in the past year, that my daughter thinks of numbers, angles, squares and so forth in a third dismensional way. In her mind she sees the curves not a flat surface. Is this common and if it is, is there any information on it? The only thing I did was to tell my daughter to think the numbers and symbols in 3-D in her mind. Within two weeks she was picking up patterns, where before it was a struggle for her. She still takes special math to relearn her math basics, but her homeroom teacher will asked her to do geometry problems that the other children in her classroom are struggling with. She will do the problem in a much different way, and other children are getting it. I believe children who have learning disabilities think in a 3-D or 4-D method. Teaching methods are not considering the children who actually sees and thinks like this. Thanking you for your time Nancy Clarke Grand Bank, Newfoundland
Dr. Nancy C. Jordan:
Hi Nancy,
Your daughter's profile is very interesting, and it highlights how it is possible to be very strong in some areas of math but not in others.
With respect to the multi-step (I assume you also mean multi-digit)problems, usually the difficulty is the other way around, that is, the student can compute single digits but has trouble applying this knowledge with written, multidigit calculation problems.
You should try to figure out how she is compensating for her lack of "fact knowledge" on the multidigit tasks. It is possible that she has been taught to memorize the facts by rote (and thinks that she must approach the combinations this way) but can apply counting/calculation strategies on problems that may be more meaningful to her.
I also am wondering how efficiently she solves the multidigit problems -- does it take her a long time? If she is applying counting strategies, etc., her speed would probably be reduced.
It also would be interesting to know if she has the same type of problem with multiplication.
In any case, a more conceptual approach to teaching single digit number combinations would seem to be more appropriate than drill based on rote memory.
Your daughter is lucky she is good with geometry and that her teacher is willing to individualize her instruction accordingly. Geometry may tap some spatial abilities that are separate from number.
I have not seen any research on children with LD thinking in 3-D. But many children benefit from visualizing numbers and using mental representations.
Question from Lisa, parent:
What suggestions do you have for getting a child's processing to be more rapid? My child can perform math accurately, but the timing is quite slow. He understands the facts and processes that are needed.
Dr. Nancy C. Jordan:
Lisa:
Rapid retrieval of number facts or combinations is a common problem for children with math difficulties.
If your child understands the various operations, he may simply need extended practice. Many math programs in US schools move quickly from skill to skill and do not provide many practice/review activities.
If the problem is with addition and subtraction facts, he might benefit from explicit help in calculation "short cuts", such as getting a solution by thinking of a known fact (e.g., 3+3=6 so 3+4=7) or applying calculation principles (e.g., 3 + 4 and 4 + 3 both = 7).
The more children use mental calculation strategies, the more likely they are to learn the fact and answer quickly. If difficulty persists, despite extended practice, he might be allowed to use a calculator for basic calculations.
Research in our lab suggests that rapid fact retrieval deficits are pretty persistent throughout the elementary school years.
Question from Kristine Halleck, Mother:
My daughter was diagnosed with LD & ADD in 3rd grade, and exhibited some borderline tendancies for Aspergers Syndrome. She is now a sophmore in High School. Of the 9 potential trouble areas listed in this article, my daughter exhibits difficulty in 6 of them, some more pronounced than others. She is a quiet, hard-working student and has good grades in most other classes except for math. She wants to go to college so her Case Workers have always pushed for the tougher math classes. Last year she took Algebra and squeaked by with D for the year. Always does her homework, terrible on quizzes & tests. This year she is taking Geometry and has a D average and will be getting a tutor soon. My biggest worry isn't even these math classes. It's everything on your list...no concept of time, money or estimating. Doesn't play games at all, poor sense of direction, easily disoriented & definitely does not do well when her routine changes. These are my biggest concerns!! The school is happy because she passes math (after hours & hours of extra help). How do I get her tested for these major weaknesses and what should be done to help her? Over the years, her father & I have tried all the manipulatives & games to try to help her (flash cards, clocks with moveable hands, play money, blocks, you name it). Please help. I'm sorry I was not concise.
Dr. Nancy C. Jordan:
Hello, Given that your daughter has an IEP already, I'm surprised her math difficulties weren't already diagnosed and addressed. She would need to be tested in basic math as well as underlying number processes related to computation, estimation, time, etc. The school psychologist or LD specialist should be able to do this. The other option would be a private evaluator. Because she is already in higher- level math classes, it might be most beneficial to have a special educator work with her within the framework of these classes. But she could also work with a tutor on basic concepts that would be more relevant to her day to day life. You could also explore whether the high school has a practical math course that would meet her needs. In any case, it seems like there should be math goals in your daughter's IEP. Good luck! NCJ
Question from Barbara Powers, Reading Specialist and Adjunct Faculty, Ottawa University, Freelance Educator:
Children today are taught to count on their fingers or look at a chart and count squares. they are taught to count either going up or down without being taught to analyze whether they should count up or down, depending on which way is shorter. However, I teach children to see the picture of the numbers in their head by using manipulatives; then many children no longer are learning diabled in math. In fact, the way they teach math today caused LD problems in my opinion. What are your thoughts on this.
Dr. Nancy C. Jordan:
Hi Barbara, Your approach makes sense and certainly would help with smaller set sizes. Other approaches that are helpful include a number line and thinking about relations between combinations as well as between operations. For example, the commutativity principle allows children to know that 3 + 4 and 4 + 3 equal 7 and the inverse principle allows children to know that 7 - 4 = 3 and so forth. Children who can use mental number line and apply principles seem to master facts more quickly. My feeling is that fingers are ok to help children solve problems initially but they should be encouraged to shift to mental strategies as quickly as possible.
Although I'm not sure that teaching approaches actually cause LD some approaches clearly exacerbate them.
Question from Ms. Dell MacGregor, parent of son with Dyscaculia:
Our son, age 20, has been diagnosed with Dyscalculia and other LD/ADD issues. He lost a year in his educational track because he was unable to pass the Math portion (one of 5 tests) of the Georgia High School Graduation Test requirement and thus was denied a High School Diploma. That, in turn, stopped him from attending Andrew College. In the ensuing time period, he took the Math portion for the SEVENTH TIME and finally passed. Now he is at Andrew College, taking remedial math and, again, may not pass this course!! He has a real disability in math...right?! HOWEVER, he would like secondary education and a college degree. What can be done to allow individuals in his situation to earn higher education degrees- just not in math related fields? He needs practical mathematical skills to function in society - he does not need the math he is being forced to try to learn in order to get higher education in history, historic preservation, etc. where a lot of his interest lies. Should he be denied secondary educational degrees because he cannot function in the academic math world of today? At 60 years of age, with a college degree in biology from Emory University, I do not understand the Algebra or Geometry that my son needed to learn in high school. Have we gone too far with what we expect of those who are not mathematically oriented? Many, like my son, have already dropped out of the education process. Is this what we truly want?
Dr. Nancy C. Jordan:
Hello, I empathize with your son's situation. Because he has a diagnosed math disability, it seems like he should be eligible for accommodations on the tests and in his courses. Also, it can be important to select colleges that have reasonable math requirements for students with LD. At least he will be able to select a major that takes advantage of his strengths. I know states are getting more rigorous about their high school math requirements. I agree that some students with disabilities would be better served by more practical math classes.
Question from melisa wharton, parent , anchorage:
15 yr old daughter, honors classes except 2 yrs behind in Math.(Algebra 1, now) Strong reading comprehension skills.Very good memory for languages, music,etc... Advanced profiency on reading/ writing , and below profiency on MATH in standard testing. KEY CURRICULUM PRESS/ Keys to ALgebra is the very basic , nuts and bolts series that tutoring her on. Problem: She can understand Math concepts when all same kind of problem on one page,if concepts explained, and sample given. - however when presented with the mixed concepts /problems does poorly. She says she can't recognize what to do if mixed problems are on a page (algebra), because she can't remember which problem is which cncept? Poor memory of past concept? Would routine reviews of mixed problems help, or maybe having reference sheet with fornmulas, with sample problem available? any ideas? thanks, for your research!!
Dr. Nancy C. Jordan:
From the information you provide, it is hard to pinpoint your daughter's weakness exactly. It may be that she has learned basic math in a rote fashion and is then thrown off when different problems are presented. The weakness could be rooted in poor understanding of number concepts, poor memory, weak attention to detail, and/or poor use of learning strategies (or metacognition). It would be important to know whether your daughter had trouble with math concepts prior to learning Algebra. Seems like tutoring should focus on development of flexible strategies for solving problems and self-monitoring.
Question from Bob Follansbee, Education Development Center:
Hi Nancy. I know it's not exactly your area, but what particular issues do you consider significant in teacher preparation in math content for dealing with MD? How about preparation in math of special education teachers?
Dr. Nancy C. Jordan:
Hi Bob, Nice to hear from an old friend! Here at UD, we require preservice elementary special ed teachers to take a math foundations course, a regular ed math methods course, and a methods course for special educators. It is particulary important that teachers become comfortable with basic math content Many teachers readily admit that they are "not good at math" and thus teach by the text. We are a rather math phobic society. I also think it is helpful for teachers to have taken course in basic cognitive or human development, where they can learn how quantitative skills develop from infancy onward. In general, we are not as advanced with evidence-based methods for teaching math as we are in reading. Hope all is well. Nancy
Question from Anita Landoll, Teacher, Special Education, Halifax County Schools:
Would you please speak about this: I notice that many of my sped students are able to learn the math concepts when I present the infomation on a concrete level. They seem to truely understand whenever I have them do the work for themselves. Yet, because of NCLB, I am presently handing them calculators to use to solve the problems, so that we can show that they are mastering grade level learning objectives. How do the two ideas mesh?
Dr. Nancy C. Jordan:
This is one of the downsides of the high stakes tests. Concrete manipulatives should be used in the first three grades before the testing requirements ramp up. Then children could gradually shift from using concrete strategies to mental ones. It is not clear why you are giving them the calcuatores to show they are mastering learning objectives. Are calculators allowed on the tests? Children should work toward mastery of basic skills without calculators and only use them on tasks where problem solving is the goal, rather than basic calculation.
Dr. Sheldon Horowitz (Moderator):
And just to be clear about the issue of "high stakes". NCLB is a mandate that holds schools and districts accountable for student achievement. There are no high stakes requirments for individual students (i.e. grade promotion and/or graduation with a standard diploma). Some states, however, have added student stakes to performance on state assessments, including those required by NCLB. The use of any accommodation on state assessments (including a calculator) varies by state. For more information about No Child Left Behind please visit www.LD.org/NCLB.
Question from JoAnn Reeds, Consultant for Ohio Dept. of Education, Office for Exceptional Children:
Have you found any effective intermittent norm based evaulation tools which allow frequent testing - monitoring of learning progress across grade levels?
Dr. Nancy C. Jordan:
One measure that is good in this respect is Monitoring Basic Skills Progress (Fuchs, Hamlett, & Fuchs) published by Pro Ed. The tests are curriculum based and allow for frequent evaluations.
Question from Dr. Sheldon Horowitz:
Nancy... Parents and educators often contact NCLD and ask for information about games, materials and more and more frequently, software that can teach or reinforce math skills. With no endorsement intended, do you have any favorites, at different levels of instruction, that you'd like to share?
Dr. Nancy C. Jordan:
The editors of eSchool News have pubished the results of a survey of almost 900 educators who were asked to select their favorite (and by inference, most effective) mathematics software and teaching solutions. The findings included selections in the areas of math lieteracy, fractions, decimals, percents, algebra, geometry and more. Visit http://www.eschoolnews.com/resources/surveys/
editorial/rca/sms2005/pdf/RCAsms2005.pdf to access the results of this online survey.
Question from Mary Jo Kilgas, SLD Teacher, Victor Haen Elementary School, Kaukauna, WI:
What does research say about timings and math facts? I feel that students can learn their facts without making it a timed situation, but criteria in grade levels are so geared to how fast/accurate students can do facts. That is their basis as to whether the students have mastered them.
Dr. Nancy C. Jordan:
First of all, fluency with math facts seems to be a hallmark of math difficulties in children. I agree that facts can be mastered without always creating timed situations. Mastery can be built on understanding. For example, students should learn how facts are related to one another and how to use known facts to derive solutions to unknown ones. Timed situations should be brief and used to reinforce lessons. The goal is for children to perform lower-level skills effortlessly so they can concentrate on problem solving. For example, if a child takes a very long time to do basic subtraction or multiplication then long division will be very laborious. But if the child has learned facts by rote with little understanding, he may not have the foundations for learning more advanced math.
Dr. Sheldon Horowitz (Moderator):
We frequently receive questions from parents and educastors about where they might find idea for math activities to provide practie or, in an informal way, supplement math instruction. Here are just a few of the many online resources you might want to consider.
- Counting by 1s, 2s and tens,, learning coin values, adding and subtracting, place value, ordinal numbers, telling time, measurement and more (See http://www.internet4classrooms.com/skills_1st.htm)
Building math skills in grades K-8 (See: http://www.familyeducation.com/topic/front/0,1156,66-20869,00.html)
Here are 12 fun ways to introduce your child to the world of math. (See: http://parentcenter.babycenter.com/refcap/bigkid/glearning/66998.html)
Question from Israel G. Espinoza, Educational Consultant:
I keep seeing the word "explicit" in your answers. Do you think that "explicit" instruction such as the Saxon approach is what is most effective for kids struggling in math? Or do you favor conceptual exploration of mathematical ideas such as the CGI approach that is being studied at the University of Michigan?
Dr. Nancy C. Jordan:
What I mean by explicit is teaching skills and concepts directly as opposed to discovery learning. In general, children with math difficulties benefit from direct instruction in basic skills. Children need these skills to guide their exploration. Many children with LD need more help than what is provided in the exploration approaches. Of course, skills, such as calculation fluency, are necessary but not sufficient.
Dr. Sheldon Horowitz (Moderator):
We've gathered together links to many additional resources on Math. Be sure to check them out!
Dr. Sheldon Horowitz (Moderator):
The hour is up and we need to bring this LDTalk to a close. Thank you to everyone who submitted questions and to all who joined in and followed the discussion.
A very special thanks to Dr. Nancy Jordan for sharing her expertise with us. A transcript of today's chat will be available at www.LDTalk.org very soon.
Also be sure to visit NCLD’s Web site, www.LD.org for upcoming information about a Math & LD initiative that is now underway. A Research Roundtable was convened by NCLD in June 2005 and Dr. Jordan was one of the scientists who participated in this exciting new work. Look for more information about screening measures, critical skills and abilities, promising practices and intervention targets in the coming months.
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> Become a FRIEND of the National Center for Learning Disabilities to receive valuable benefits;
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Good afternoon and welcome to LD Talk, the Web's only online discussion devoted to topics of interest to the learning disabilities community.
LD Talk is a service of the National Center for Learning Disabilities (NCLD). Funding for LD Talk is generously provided by SchwabLearning.org.
It’s a pleasure to welcome you all to the today’s chat - Thanks for joining us!
Today’s topic is about math difficulties and math disabilities. And we’re thrilled to have Dr. Nancy Jordan, a leading expert in this area of research and practice, with us to answer your questions.
Dr. Nancy C. Jordan is a Professor in the School of Education at the University of Delaware in Newark, Delaware (USA). Dr. Jordan completed her doctoral work in Education at Harvard University and completed a post doctoral fellowship at the University of Chicago.
Prior to her doctoral studies, Dr. Jordan taught children with learning disabilities. Since 1999, her research project on children's mathematics has been funded by the National Institute of Child Health and Human Development. Her studies have been published in Child Development, the Journal of Educational Psychology, the Journal of Learning Disabilities, and the Journal of Experimental Child Psychology. Dr. Jordan's most recent work is concerned with kindergarten predictors of math difficulties in primary school.
I am Dr. Sheldon Horowitz, Director of Professional Services at the National Center for Learning Disabilities, and I’ll be the moderator of today’s discussion.
To those of you who have submitted questions in advance of today’s chat, many thanks! As usual, we encourage everyone to send in questions and we’ll try to respond to those that are most closely related to our discussion topic and of the broadest interest to our audience. (If you have questions unrelated to this topic, please feel free to send them to NCLD’s Help Desk at This e-mail address is being protected from spam bots, you need JavaScript enabled to view it )
Let’s now begin the discussion.
Question from Dr. Sheldon Horowitz:
We know that almost twice as many boys are identified as having LD than are girls, yet the true incidence of LD in reading (based on research data) suggests that dyslexia occurs in just as many girls as in boys. What do we know about the prevalence of math LD among school age children and is the incidence different between boys and girls?
Dr. Nancy C. Jordan:
In a recently published study, Mayo Clinic researchers determined Math Learning Disorder (LD) is common among school-age children.
Results show that boys are more likely to have Math LD than girls. The research also indicates that although a child can have a Math LD and a reading LD, a substantial percentage of children have Math LD alone. In fact, the cumulative incidence of Math LD through age 19 ranges from 6% to as high as 14%, depending on the Math LD definition.
LD is used to describe the seemingly unexplained difficulty a person of at least average intelligence has in acquiring basic academic skills -- skills that are essential for success at school, work and for coping with life in general. The results appear in the September-October issue of Ambulatory Pediatrics.
Question from Teresa, Parent:
What is the difference between dyscaculia vs. dyslexia. My daughter is dyslexic and also has a very difficult time with math.
Dr. Nancy C. Jordan:
Hi Teresa. While "dyslexia" means word trouble, "dyscalulia" means number trouble. Children with dyscalculia have specific problems with number sense, such as counting, estimation and comparison of quantities and basic arithmetic. Quick retrieval of number facts and calculation fluency seem to be a key characteristics of children with dyscalculia. As I mentioned in the previous response, reading disabilities tend to co-occur with math weaknesses, especially in areas that have a verbal basis (e.g., solving word problems).
Question from Theresa Williingham, President, Learning is For Everyone, Inc. (www.LIFEofFlorida.org):
This may well be answered during the chat, but I'm wondering how to distinquish dyscaculia from math anxiety, or simple dislike (and consequent disinterest and lack of retention)? My teenage daughter has a long history of frustrating difficulties with math, and doesn't seem to retain information from one lesson to the next, including what I'd consider rather basic skills. Yet she loves science, especially biological sciences, and we're concerned (as is she) that her difficulties with math will compromise her ability to pursue a career in that area. Thank you for your help. Theresa Willingham
Dr. Nancy C. Jordan:
Hi Theresa, Math anxiety is a common problem that can be rooted in genuine difficulties or poor instruction. Moreover, many teenagers opt out of math because they do not see its relevance to their lives. If your daughter did not acquire basic skills and has trouble with retention of mathematical information, it makes sense that she would feel anxious in higher level math classes. You might want to screen for basic problems and then get her a tutor so she can aquire the skills she needs to compete in biology and other sciences. Special help may reduce her math anxiety. NCJ
Question from Naomi Weiss, parent, Board member Cherry Hill Special Education PTA, advocate, Cherry Hill School District:
Math deficiencies plaque NLD(Nonverbal learning Disorder) students, during their school careers; even when identified and recognized, these students do not receive appropriate math tutoring that coordinates with their lanquage skill strengths to create strategies to address their specific disability's math weaknesses. Are there specific math programs or teaching strategies and tools, that have research based success with NLD students, available to public schools, that should be known and utilized by public school districts to address the unique identifying math difficulties of NLD students?
Dr. Nancy C. Jordan:
You are correct that children can use their language strengths to compensate for weaknesses in math. In fact, our research has shown that the rate of math achievement for children with math LD only is faster than for children with both math and reading/language LD. I do not know of specific math programs for children with nonverbal learning disabilities. However, most of the programs being used in the schools do have a verbal component.
Assuming that the child with NLD has strong language skills, he or she should be encouraged to give verbal explanations for solving problems and to talk through their problem solving. The child also might do better with mental calculation than written work.
Mel Levine makes a number of good suggestions along these lines. See his Web site, All Kinds of Minds for more information.
Regarding research, teaching math to children with NLD certainly would be an important area for future investigation. In general, research in teaching math to children with LD lags behind research in the reading area. For more information on the state of research in MD, see the recent article by Dr. Sheldon Horowitz, Math & LD: Counting on Research for Answers.
Question from Patricia Pascale, Learning Disabilites Teacher Consultant:
Do you think that the standardized measures for identification of a specific learning disability in math which may include the Woodcock Johnson are an accurate assessment? What standardized measures would you suggest to be best practice? What would you suggest as a functional assessment?
Dr. Nancy C. Jordan:
The WJ-3 is a reliable and valid test. However, it assesses a relatively narrow set of skills and may need to be followed up with functional, curriculum-based measures.
For example, to get a better reading of a child's skill in word problems, the LDTC might want to take examples directly from the child's math curriculum.
Lynn Fuchs has written a lot about developing valid curriculum-based measures (CBM)and even has published a CBM instrument that can be adapted (Pro-Ed, I think).
With respect to other standardized tests, the new KTEA and WIAT also are good screening measures. The KeyMath, I believe, is due for a revision (the problems are getting out of date and the norms old). Same goes for the PIAT. For young children, the TEMA-3 can provide important information.
Most untimed measures should be supplemented with timed measures, if fluency is an issue. It is noteworthy that the newer versions of the WJ, WIAT, and KTEA include rate-based measures.
Question from Moira Laughlin, Greene County Educational Service Center, Parent Mentor:
How appropriate is encouraging a child as young as 3rd-4th grade (who is struggling with understanding arithmetic concepts and operations) to use a calculator for all math assignments? Child has difficulty understanding abstract language and concepts.
Dr. Nancy C. Jordan:
The issue of how and when to use calculators in math is important. First, the child would need to learn calculator skills. Some young children make more mistakes with a calculator than without one!
Second, young children should use calculators selectively, for example, on tasks where concepts rather than skills (such as word problems) are emphasized. In this way, the child could concentrate on the sructure of the problem without worrying about lower-level calculations.
However, I wouldn't recommend calculators for all math assignments in elementary school. Children should still work on mastery of basic skills, and too much calculator use could be counterproductive.
Question from Seymour Burack, School Psychologist, Sayreville New Jersey:
Do you have any opinions on the Dyscalculia Screener which was developed by Dr Brian Butterworth
Dr. Nancy C. Jordan:
Although I have not used the Dyscalculia Screener, I know it is based on sound theoretical principles. It is likely to pick up children with fundamental problems in number. However, a more thorough diagnostic work up would be needed to evaluate other areas of math (e.g., applications and problem solving).
More information about the Dyscalculia Screener is available here.
Question from Dr. Sheldon Horowitz:
Nancy: Are there any other valuable screening or assessment tools that can help identify young students at risk of math difficulities?
Dr. Nancy C. Jordan:
There are not as many validated screening tools in math as there are in reading.
However, we recently developed a "number sense" battery in our lab which is strongly predictive of first-grade math achievement. In particular, we look at counting and number knowledge (e.g., indicating which of 2 numbers is greater, estimating distances between numbers) as well as verbal and nonverbal calculation. The battery is described in detail in a publication that will be coming out in Child Development early in 2006 (Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M Development of Number Sense in Kindergartners).
Part of our battery is based on the Number Knowledge Test developed by Sharon Griffin and Robbie Case. Ben Clarke and folks in Oregon also are developing a tool along these lines. One unique feature of their work is the use of timed measures to assess number speed and fluency. A parallel reading test might be the DIBELS.
As I think I mentioned in another answer, the Test of Early Mathematics Abilities - 3 (Pro-Ed) is another good screening tool.
Michele Mazzocco recently published a paper on kindergarten predictors of MD (Mazzocco, M.M.M. & Thompson, R.E. 2005, Kindergarten Predictors of Math Learning Disability, Learning Disabilities Research and Practice, 20 (3), 142-155) and found particular areas of the TEMA-3 to be very predictive of MD in third grade. The areas included reading numbers. magnitude judgments of 1-digit numbers, and mental addition, all areas of basic number sense.
In general, cognitve skills directly related to number are more predictive of math achievement than are measures general verbal and spatial skills. Our kindergarten number sense battery predicts math achievement above and beyond IQ , working memory, and reading skill.
NCJ
Question from Judy Guillot, Resource, LSU Laboratory School:
Many of our elementary LD students have trouble memorizing multiplication facts. Should we continue to push them to memorize, or is that something they cannot do? At present we allow them to use a multiplication chart. Is that an acceptable accommodation?
Dr. Nancy C. Jordan:
Hi Judy, I think you should make every effort to help children master the multiplication tables but also allow them to use accommodations. An advantage of the multiplication chart is that children can see how all of the combinations are related. You might allow them to use charts or calculators on more complicated multistep problems but still spend 5 or 10 minutes a day practicing the facts. Although some children may never reach full mastery, partial fact knowledge will still help them.
Question from Dr. Sheldon Horowitz:
Nancy:
Can you tell us more about the number sense" battery you have developed? Specifically, when and how could people obtain the battery?
Dr. Nancy C. Jordan:
A complete description of our battery is described in an upcoming edition of Child Development. The manuscript is in press and is scheduled for 2/2006 publication. A copy of the manuscript can be obtained through the website of the Society for Research in Child Development (http://www.srcd.org) and the linking onto the journal. Then a PDF file can be obtained. But it will not be available until close to the publication date.
Question from RevDanaBeth Wells-Goodwin, Dynamic Learning Network, Denmark, Maine:
Does dyscaculia affect one's ability to learn to read music? (read notes and count note values; master keyboard techniques.) Are there strategies to help with retention in this area?
Dr. Nancy C. Jordan:
This is an interesting question, but I 'm afraid I don't know the answer. I'm not aware of any research looking at connections between dyscalculia and the ability to read music.
Question from Laura Ericson, parent:
My 14 yr old 8th grade son writes out each Algebra problem in laborious extra steps & detail and doesn't like or seem to understand shortcuts to quicker solutions. He has processing & other learning disabilities & I wonder if his insistence on extra steps reflects the way his brain processes & solves algebra? What can we do to help him?
Dr. Nancy C. Jordan:
Laura, It does sound like your child's learning disabilities may be affecting his approach to solving the algebra problems. Although you don't indicate the nature of his LD, algebra requires abstract thinking quantitative reasoning, and memory, among other things. Your son seems to understand algebra and can reach solutions to problems when he writes out all the steps. This is a good thing and can be used to help him be more efficient. Perhaps if he is given explicit help in short cuts, based on his own work, he will see how they can help. He also might need extended practice to master the new approaches. Of course, if shortcuts continue to be problematic, he should be given more time on exams.
Question from Kathy Laffin, Consultant for Specific Learning Disabilities, Wisconsin Dept of Public Instruction:
The newest math curriculum materials focus heavily on math vocabulary, problem solving and solutions to math problems that include written explanations. What are some methods to assist students with learning disabilities to work within this math curriculum framework?
Dr. Nancy C. Jordan:
Many of the newer "progessive" curricula do no provide direct instruction in basic skills. Students with LD, therefore, may need supplemental help with number combinations, written calculations, calculation fluency, etc. They also should be given lots of opportunities to talk about what they are doing or to make their thinking public. These activities would need to be very structured (e.g., summarize the problem in your own words, explain how you will solve the problem, describe an alternate way to solve the problem). Unfortunately, children with language difficulties can be penalized by some of the newer approaches but children with MD with language strengths might resonate with them.
Question from MaryLou, Mother of a learning disabled child:
Dr. Jordan, Our school system utilizes "Chicago Math". The constant change in concepts prior to mastering an idea has been a challenge and frustration for my child. Our struggle is with organization and processing. Do you have any suggestions on how to work within this framework and increase my child's success?
Dr. Nancy C. Jordan:
Hi MaryLou, I am assuming you mean the math program that was developed at the University of Chicago. Sometimes more "progressive" curricula, like this one, create problems for children with learning disabilities. They tend to empahisize problem solving and inductive reasoning over skill developent.
Research shows that many children with LD (and without LD!) need a more explicit approach to instruction, one that provides lots of opportunities for practice and mastery. I suggest you get your child a tutor to reinforce the skills he does not pick up in school. You also could get a copy of the math textbook to preview the material with him at home.
Question from Rosalind Pomerance, Learning Specialist, Ramaz Middle School:
If a students with a learning disability, needs to use a calculator for math exams, will his use of the calculator on a standardized test invalidate his scores? If he does not use a calculator will his score be representative of his true abilities?
Dr. Nancy C. Jordan:
This depends on the test and the school policies. Some tests provide for calculator use. Many children with LD are allowed to use calculators on standardized tests as a special accommodation. Or an alternative test could be given that would allow calculator use. This issue should be addressed in the student's IEP.
Dr. Sheldon Horowitz (Moderator):
Policies regarding accommodations used in district and state-wide assessments, such as those required by the No Child Left Behind Act (NCLB), vary greatly from state to state.
The National Center for Learning Disabilities recently released a Parent Advocacy Brief that provides important information for parents on making accommodation decisions.
The Parent Advocacy Brief is part of a series of informational products NCLD has created to help parents understand key provisions of No Child Left Behind.
All of the NCLB resources can be downloaded FREE of CHARGE here.
Question from Jeannie Madge, Homeschool Mother:
My 7yo daughter has dyslexia and memory issues. She cannot memorize the names of 6, 7, 8 or 9. She knows what they mean but cannot memorize the names. She cannot yet understand ones, tens, hundreds, etc. Is this a disability or her age? Jeannie
Dr. Nancy C. Jordan:
Hi Jeannie. Thank you for your question. Although there is a relation betweeen dyslexia and math difficulties, this is not always the case. Dyslexia is considered a risk factor, however. By 7 years of age, most children know the number names (which are picked up pretty readily through informal experiences) and have some understanding of tens and ones, etc. But it would be hard to know at this point if your daughter has a math disability. You would get more information by giving her a screening test, such as the Test of Early Mathematics - 3 (Pro-Ed). Best wishes. NCJ
More information on the Test of Early Mathematics is available here.
Question from John Rosenitsch, LD teacher, St. Luke Elementary:
How do I help with the language aspect of problem solving, in order to ease a child's understanding of written math?
Dr. Nancy C. Jordan:
Of course this is a pretty general question but it addresses an important area of concern. I assume by easing a child's "understanding of written math" you mean easing the reading and associated language requirements.
If a child is relatively strong in quantitative skills but weak in reading, he should be given support with written math instructions and word problem solving.
If the child has difficulties even when a problem is read to him, you might help him break the problem into steps and represent the steps with pictures or diagrams. He should practice thinking about what the problem is asking, making mental or physical representations, and talking through the steps.
Many state tests require children to give written verbal explanations for math problems, which conflates langauage and number skills. Children with language difficulites often have a hard time with this type of activity. But I think they can learn to give proficient explanations with very structured, explicit practice.
Question from James Dunderman, LDT-C:
Many students here, high school age LD, still have difficulty learning long division. Some are lagging behind in the prerequisite skills while others don't get the overall concept nor can follow the sequence of steps necessary to solving the problem. Word problems add another set of learning issues. Is there a well researched method or materials that would help them to learn these concepts. Thanks.
Dr. Nancy C. Jordan:
James,
I'm not sure that here is a "well researched" method out there but students with MD tend to benefit from explicit approaches that also provide lots of practice.
Long division is often problematic because it requires coordination of several skills. If the student can't recall the steps for solving long division problems, he or she might be given a model of a correctly solved problem. Each step could be highlighted. The model could be referred to during subsequent written work. The student also could be allowed to use a calculator for the compuation part (e.g., subtracting), if this is a problem.
Because your students are in high school and still having difficulty, the problems should probably be presented in meaningful, "real world" contexts. In the real world, people don't use long division all that much but simple problems that require remainders to be expressed as decimals or percentages are important.
Question from Nancy Clarke, Mother From Canada:
Could you please tell me why my daughter has trouble with single digits, yet when doing a problem that is multi-step she has not problems. 2+2=4 will stump her. But put that problem within a multi-step she will answer the question correctly. In geometry she is two years advance over her peers, yet basic abc's of math will stump her. Is there any suggestions or methods might be use to overcome this? I have discovered in the past year, that my daughter thinks of numbers, angles, squares and so forth in a third dismensional way. In her mind she sees the curves not a flat surface. Is this common and if it is, is there any information on it? The only thing I did was to tell my daughter to think the numbers and symbols in 3-D in her mind. Within two weeks she was picking up patterns, where before it was a struggle for her. She still takes special math to relearn her math basics, but her homeroom teacher will asked her to do geometry problems that the other children in her classroom are struggling with. She will do the problem in a much different way, and other children are getting it. I believe children who have learning disabilities think in a 3-D or 4-D method. Teaching methods are not considering the children who actually sees and thinks like this. Thanking you for your time Nancy Clarke Grand Bank, Newfoundland
Dr. Nancy C. Jordan:
Hi Nancy,
Your daughter's profile is very interesting, and it highlights how it is possible to be very strong in some areas of math but not in others.
With respect to the multi-step (I assume you also mean multi-digit)problems, usually the difficulty is the other way around, that is, the student can compute single digits but has trouble applying this knowledge with written, multidigit calculation problems.
You should try to figure out how she is compensating for her lack of "fact knowledge" on the multidigit tasks. It is possible that she has been taught to memorize the facts by rote (and thinks that she must approach the combinations this way) but can apply counting/calculation strategies on problems that may be more meaningful to her.
I also am wondering how efficiently she solves the multidigit problems -- does it take her a long time? If she is applying counting strategies, etc., her speed would probably be reduced.
It also would be interesting to know if she has the same type of problem with multiplication.
In any case, a more conceptual approach to teaching single digit number combinations would seem to be more appropriate than drill based on rote memory.
Your daughter is lucky she is good with geometry and that her teacher is willing to individualize her instruction accordingly. Geometry may tap some spatial abilities that are separate from number.
I have not seen any research on children with LD thinking in 3-D. But many children benefit from visualizing numbers and using mental representations.
Question from Lisa, parent:
What suggestions do you have for getting a child's processing to be more rapid? My child can perform math accurately, but the timing is quite slow. He understands the facts and processes that are needed.
Dr. Nancy C. Jordan:
Lisa:
Rapid retrieval of number facts or combinations is a common problem for children with math difficulties.
If your child understands the various operations, he may simply need extended practice. Many math programs in US schools move quickly from skill to skill and do not provide many practice/review activities.
If the problem is with addition and subtraction facts, he might benefit from explicit help in calculation "short cuts", such as getting a solution by thinking of a known fact (e.g., 3+3=6 so 3+4=7) or applying calculation principles (e.g., 3 + 4 and 4 + 3 both = 7).
The more children use mental calculation strategies, the more likely they are to learn the fact and answer quickly. If difficulty persists, despite extended practice, he might be allowed to use a calculator for basic calculations.
Research in our lab suggests that rapid fact retrieval deficits are pretty persistent throughout the elementary school years.
Question from Kristine Halleck, Mother:
My daughter was diagnosed with LD & ADD in 3rd grade, and exhibited some borderline tendancies for Aspergers Syndrome. She is now a sophmore in High School. Of the 9 potential trouble areas listed in this article, my daughter exhibits difficulty in 6 of them, some more pronounced than others. She is a quiet, hard-working student and has good grades in most other classes except for math. She wants to go to college so her Case Workers have always pushed for the tougher math classes. Last year she took Algebra and squeaked by with D for the year. Always does her homework, terrible on quizzes & tests. This year she is taking Geometry and has a D average and will be getting a tutor soon. My biggest worry isn't even these math classes. It's everything on your list...no concept of time, money or estimating. Doesn't play games at all, poor sense of direction, easily disoriented & definitely does not do well when her routine changes. These are my biggest concerns!! The school is happy because she passes math (after hours & hours of extra help). How do I get her tested for these major weaknesses and what should be done to help her? Over the years, her father & I have tried all the manipulatives & games to try to help her (flash cards, clocks with moveable hands, play money, blocks, you name it). Please help. I'm sorry I was not concise.
Dr. Nancy C. Jordan:
Hello, Given that your daughter has an IEP already, I'm surprised her math difficulties weren't already diagnosed and addressed. She would need to be tested in basic math as well as underlying number processes related to computation, estimation, time, etc. The school psychologist or LD specialist should be able to do this. The other option would be a private evaluator. Because she is already in higher- level math classes, it might be most beneficial to have a special educator work with her within the framework of these classes. But she could also work with a tutor on basic concepts that would be more relevant to her day to day life. You could also explore whether the high school has a practical math course that would meet her needs. In any case, it seems like there should be math goals in your daughter's IEP. Good luck! NCJ
Question from Barbara Powers, Reading Specialist and Adjunct Faculty, Ottawa University, Freelance Educator:
Children today are taught to count on their fingers or look at a chart and count squares. they are taught to count either going up or down without being taught to analyze whether they should count up or down, depending on which way is shorter. However, I teach children to see the picture of the numbers in their head by using manipulatives; then many children no longer are learning diabled in math. In fact, the way they teach math today caused LD problems in my opinion. What are your thoughts on this.
Dr. Nancy C. Jordan:
Hi Barbara, Your approach makes sense and certainly would help with smaller set sizes. Other approaches that are helpful include a number line and thinking about relations between combinations as well as between operations. For example, the commutativity principle allows children to know that 3 + 4 and 4 + 3 equal 7 and the inverse principle allows children to know that 7 - 4 = 3 and so forth. Children who can use mental number line and apply principles seem to master facts more quickly. My feeling is that fingers are ok to help children solve problems initially but they should be encouraged to shift to mental strategies as quickly as possible.
Although I'm not sure that teaching approaches actually cause LD some approaches clearly exacerbate them.
Question from Ms. Dell MacGregor, parent of son with Dyscaculia:
Our son, age 20, has been diagnosed with Dyscalculia and other LD/ADD issues. He lost a year in his educational track because he was unable to pass the Math portion (one of 5 tests) of the Georgia High School Graduation Test requirement and thus was denied a High School Diploma. That, in turn, stopped him from attending Andrew College. In the ensuing time period, he took the Math portion for the SEVENTH TIME and finally passed. Now he is at Andrew College, taking remedial math and, again, may not pass this course!! He has a real disability in math...right?! HOWEVER, he would like secondary education and a college degree. What can be done to allow individuals in his situation to earn higher education degrees- just not in math related fields? He needs practical mathematical skills to function in society - he does not need the math he is being forced to try to learn in order to get higher education in history, historic preservation, etc. where a lot of his interest lies. Should he be denied secondary educational degrees because he cannot function in the academic math world of today? At 60 years of age, with a college degree in biology from Emory University, I do not understand the Algebra or Geometry that my son needed to learn in high school. Have we gone too far with what we expect of those who are not mathematically oriented? Many, like my son, have already dropped out of the education process. Is this what we truly want?
Dr. Nancy C. Jordan:
Hello, I empathize with your son's situation. Because he has a diagnosed math disability, it seems like he should be eligible for accommodations on the tests and in his courses. Also, it can be important to select colleges that have reasonable math requirements for students with LD. At least he will be able to select a major that takes advantage of his strengths. I know states are getting more rigorous about their high school math requirements. I agree that some students with disabilities would be better served by more practical math classes.
Question from melisa wharton, parent , anchorage:
15 yr old daughter, honors classes except 2 yrs behind in Math.(Algebra 1, now) Strong reading comprehension skills.Very good memory for languages, music,etc... Advanced profiency on reading/ writing , and below profiency on MATH in standard testing. KEY CURRICULUM PRESS/ Keys to ALgebra is the very basic , nuts and bolts series that tutoring her on. Problem: She can understand Math concepts when all same kind of problem on one page,if concepts explained, and sample given. - however when presented with the mixed concepts /problems does poorly. She says she can't recognize what to do if mixed problems are on a page (algebra), because she can't remember which problem is which cncept? Poor memory of past concept? Would routine reviews of mixed problems help, or maybe having reference sheet with fornmulas, with sample problem available? any ideas? thanks, for your research!!
Dr. Nancy C. Jordan:
From the information you provide, it is hard to pinpoint your daughter's weakness exactly. It may be that she has learned basic math in a rote fashion and is then thrown off when different problems are presented. The weakness could be rooted in poor understanding of number concepts, poor memory, weak attention to detail, and/or poor use of learning strategies (or metacognition). It would be important to know whether your daughter had trouble with math concepts prior to learning Algebra. Seems like tutoring should focus on development of flexible strategies for solving problems and self-monitoring.
Question from Bob Follansbee, Education Development Center:
Hi Nancy. I know it's not exactly your area, but what particular issues do you consider significant in teacher preparation in math content for dealing with MD? How about preparation in math of special education teachers?
Dr. Nancy C. Jordan:
Hi Bob, Nice to hear from an old friend! Here at UD, we require preservice elementary special ed teachers to take a math foundations course, a regular ed math methods course, and a methods course for special educators. It is particulary important that teachers become comfortable with basic math content Many teachers readily admit that they are "not good at math" and thus teach by the text. We are a rather math phobic society. I also think it is helpful for teachers to have taken course in basic cognitive or human development, where they can learn how quantitative skills develop from infancy onward. In general, we are not as advanced with evidence-based methods for teaching math as we are in reading. Hope all is well. Nancy
Question from Anita Landoll, Teacher, Special Education, Halifax County Schools:
Would you please speak about this: I notice that many of my sped students are able to learn the math concepts when I present the infomation on a concrete level. They seem to truely understand whenever I have them do the work for themselves. Yet, because of NCLB, I am presently handing them calculators to use to solve the problems, so that we can show that they are mastering grade level learning objectives. How do the two ideas mesh?
Dr. Nancy C. Jordan:
This is one of the downsides of the high stakes tests. Concrete manipulatives should be used in the first three grades before the testing requirements ramp up. Then children could gradually shift from using concrete strategies to mental ones. It is not clear why you are giving them the calcuatores to show they are mastering learning objectives. Are calculators allowed on the tests? Children should work toward mastery of basic skills without calculators and only use them on tasks where problem solving is the goal, rather than basic calculation.
Dr. Sheldon Horowitz (Moderator):
And just to be clear about the issue of "high stakes". NCLB is a mandate that holds schools and districts accountable for student achievement. There are no high stakes requirments for individual students (i.e. grade promotion and/or graduation with a standard diploma). Some states, however, have added student stakes to performance on state assessments, including those required by NCLB. The use of any accommodation on state assessments (including a calculator) varies by state. For more information about No Child Left Behind please visit www.LD.org/NCLB.
Question from JoAnn Reeds, Consultant for Ohio Dept. of Education, Office for Exceptional Children:
Have you found any effective intermittent norm based evaulation tools which allow frequent testing - monitoring of learning progress across grade levels?
Dr. Nancy C. Jordan:
One measure that is good in this respect is Monitoring Basic Skills Progress (Fuchs, Hamlett, & Fuchs) published by Pro Ed. The tests are curriculum based and allow for frequent evaluations.
Question from Dr. Sheldon Horowitz:
Nancy... Parents and educators often contact NCLD and ask for information about games, materials and more and more frequently, software that can teach or reinforce math skills. With no endorsement intended, do you have any favorites, at different levels of instruction, that you'd like to share?
Dr. Nancy C. Jordan:
The editors of eSchool News have pubished the results of a survey of almost 900 educators who were asked to select their favorite (and by inference, most effective) mathematics software and teaching solutions. The findings included selections in the areas of math lieteracy, fractions, decimals, percents, algebra, geometry and more. Visit http://www.eschoolnews.com/resources/surveys/
editorial/rca/sms2005/pdf/RCAsms2005.pdf to access the results of this online survey.
Question from Mary Jo Kilgas, SLD Teacher, Victor Haen Elementary School, Kaukauna, WI:
What does research say about timings and math facts? I feel that students can learn their facts without making it a timed situation, but criteria in grade levels are so geared to how fast/accurate students can do facts. That is their basis as to whether the students have mastered them.
Dr. Nancy C. Jordan:
First of all, fluency with math facts seems to be a hallmark of math difficulties in children. I agree that facts can be mastered without always creating timed situations. Mastery can be built on understanding. For example, students should learn how facts are related to one another and how to use known facts to derive solutions to unknown ones. Timed situations should be brief and used to reinforce lessons. The goal is for children to perform lower-level skills effortlessly so they can concentrate on problem solving. For example, if a child takes a very long time to do basic subtraction or multiplication then long division will be very laborious. But if the child has learned facts by rote with little understanding, he may not have the foundations for learning more advanced math.
Dr. Sheldon Horowitz (Moderator):
We frequently receive questions from parents and educastors about where they might find idea for math activities to provide practie or, in an informal way, supplement math instruction. Here are just a few of the many online resources you might want to consider.
- Counting by 1s, 2s and tens,, learning coin values, adding and subtracting, place value, ordinal numbers, telling time, measurement and more (See http://www.internet4classrooms.com/skills_1st.htm)
Building math skills in grades K-8 (See: http://www.familyeducation.com/topic/front/0,1156,66-20869,00.html)
Here are 12 fun ways to introduce your child to the world of math. (See: http://parentcenter.babycenter.com/refcap/bigkid/glearning/66998.html)
Question from Israel G. Espinoza, Educational Consultant:
I keep seeing the word "explicit" in your answers. Do you think that "explicit" instruction such as the Saxon approach is what is most effective for kids struggling in math? Or do you favor conceptual exploration of mathematical ideas such as the CGI approach that is being studied at the University of Michigan?
Dr. Nancy C. Jordan:
What I mean by explicit is teaching skills and concepts directly as opposed to discovery learning. In general, children with math difficulties benefit from direct instruction in basic skills. Children need these skills to guide their exploration. Many children with LD need more help than what is provided in the exploration approaches. Of course, skills, such as calculation fluency, are necessary but not sufficient.
Dr. Sheldon Horowitz (Moderator):
We've gathered together links to many additional resources on Math. Be sure to check them out!
Dr. Sheldon Horowitz (Moderator):
The hour is up and we need to bring this LDTalk to a close. Thank you to everyone who submitted questions and to all who joined in and followed the discussion.
A very special thanks to Dr. Nancy Jordan for sharing her expertise with us. A transcript of today's chat will be available at www.LDTalk.org very soon.
Also be sure to visit NCLD’s Web site, www.LD.org for upcoming information about a Math & LD initiative that is now underway. A Research Roundtable was convened by NCLD in June 2005 and Dr. Jordan was one of the scientists who participated in this exciting new work. Look for more information about screening measures, critical skills and abilities, promising practices and intervention targets in the coming months.
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> Become a FRIEND of the National Center for Learning Disabilities to receive valuable benefits;
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