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When students struggle in math class, it can be for many reasons. Learning disabilities (LDs) that impact mathematics learning are diverse, and may take many different forms. The most important consideration when choosing an intervention for math LDs is to pick an intervention that matches the problems the student is experiencing.
Broadly speaking, students might run into trouble when trying to complete their math homework if they lack the necessary conceptual, declarative, or procedural knowledge. Conceptual knowledge involves a deep understanding of the meaning of mathematics and the connections among concepts. If a student does not have a strong grasp of the mathematical concept the class is focussing on, he or she may need to be retaught the concept in a different way.
Declarative Knowledge is the information that students retrieve from memory or know “at a glance”, like addition or multiplication facts. Tools like flashcards may help students memorize math facts and handouts like addition, multiplication, and fraction charts can help to bridge the gap until students can reliably remember math facts. Click here to download free math charts, from the website Teachers Pay Teachers.
Procedural knowledge is the ability to follow a set of sequential steps to solve computation problems, word problems, or real-world tasks. When students lack procedural knowledge, they may know what they need to do to solve a math problem, but they struggle with the “how”. If a student is struggling with the procedure of a math problem, for example not knowing where to start or forgetting the order of steps to solve a problem, then a heuristic may be helpful.
What Are Heuristics?
At its most basic, a heuristic is a shortcut in problem-solving that reduces the amount of information that needs to be processed (Gray, 1994, p. 395) or a plan to break down a big problem into smaller parts. Heuristics are best used with students who understand the mathematical concept, but who have trouble remembering the steps in completing a problem (Burns, 2011; Snyder, 1988).
Sometimes heuristics are taught by teachers, and sometimes students come across them on their own. Some examples of heuristics include using a rule of thumb, an educated guess, an intuitive judgement, stereotyping, or common sense. The most basic heuristic is considered to be trial and error (“Heuristics”, 2014).
Below are some examples of heuristics that can help your child tackle their math work:
Key-Word Strategy
The “key-word” strategy involves associating common words with the operation they represent. For example, students might associate “gave away” to mean the question involves subtraction. In the following word problem, this strategy would work:
Amy had 10 pencils. She gave away 4 to Meaghan. How many pencils does Amy have left?
While this heuristic is helpful for students with math LDs, it may not work for all word problems. For example, the word problem:
Amy gave away 4 pencils to Meaghan. She gave away 6 pencils to Mino. How many pencils did Amy give away?
This word problem does not involve subtraction and actually requires addition to get the correct answer.
As this heuristic only works some of the time, it should be taught as a last resort if no other strategy works.
Underlining Important Information
Word problems often include extraneous information that can cause students to become confused or overwhelmed. This heuristic has students underline or highlight the important information, allowing them to simplify the question, as shown below:
Monkeys like to live in trees and eat bananas. If a monkey picks three bananas in the morning and three in the afternoon, and then his friend gives him five bananas, how many bananas does the monkey have to eat?
Your child may not know how to use this strategy independently yet, so it is important to start by doing several word problems together, underlining the important information, and discussing why certain parts were highlighted and certain parts were not.
Visualization
When using the visualization strategy, students use drawings, diagrams, or charts to solve problems. Visual representations can help students record information, understand what the question is asking, and later, evaluate their solution. However, just like the underlining strategy mentioned above, this strategy requires students to be able to identify the important information in a word problem, and parents or teachers may have to provide guidance when first using this strategy.
Click here to access the article Visual Representation in Mathematics.
Click here to access the article Helping Students with LDs Learn to Diagram Math Problems.
Mnemonic Devices
Mnemonic devices use visual and auditory clues to help students remember important information. The most familiar mnemonics use acronyms, which are words that are formed from the first letter of the words in a phrase. For example, HOMES for the Great Lakes: Huron, Ontario, Michigan, Erie, Superior.
Many students with LDs struggle with weak short term memory; mnemonics can help students of all ages to remember important information that they may otherwise have difficulty retrieving. Mnemonic instruction has been shown to significantly aid in recall, retention, and understanding (Scruggs & Mastropieri, 2000).
You may remember two common mnemonic devices from your own time in the math classroom:
1. BEDMAS (brackets, exponents, division, multiplication, addition, subtraction), is used when solving an equation with multiple operations.
Click here to access LD@school’s template for the BEDMAS mnemonic
2. FOIL (first, outside, inside, last), is used when expanding algebraic expressions.
Click here to access LD@school’s template for the FOIL mnemonic
These two are not the only examples of mnemonic devices; researchers have developed many others to help students with learning disabilities succeed in math. Review the mnemonic devices listed below and print or download the template(s) that you feel matches the problems your child is experiencing. Having these mnemonic devices printed and on hand while completing math work can lower the demand on your child’s working memory and allow him or her to focus on finding the correct answer.
For simple math facts, such as 6 x 8, use DRAW or SOLVE (Miller and Mercer, 1993).
Click here to access LD@school’s template for the DRAW mnemonic
Click here to access LD@school’s template for the SOLVE mnemonic
If your child is having trouble with using SOLVE or DRAW, SIGNS may provide enough extra cues to solve the problem (Watanabe, 1991).
Click here to access LD@school’s template for the SIGNS mnemonic
If your child can read and understand word problems, but has difficulty developing an equation to solve them, use RIDGES (Snyder, 1988).
Click here to access LD@school’s template for the RIDGES mnemonic
When the focus moves from math facts to more complex word problems, a mnemonic like FAST DRAW can help (Miller and Mercer, 1993).
Click here to access LD@school’s template for the FAST DRAW mnemonic
Remember, just like all the other heuristics listed in this article, the use of mnemonics must first be modeled. Once you’ve chosen a mnemonic you think might help, sit with your child and work through a few math problems together. Once your child is able to reliably follow all the steps of the mnemonic, he or she is ready to work independently.
The use of heuristics, or self-strategies, in mathematics can have a profound impact on a student’s ability to quickly and accurately solve a math fact or word problem. Students with LDs (whether math specific or not) will especially benefit from the structure and sequence a heuristic provides.
References
Burns, M. K. (2011). Matching math interventions to students’ skill deficits: A preliminary investigation of a conceptual and procedural heuristic. Assessment for Effective Intervention, 36, 210–218.
Gray, P. (1994). Psychology (2nd ed.). New York, NY: Worth Publishers.
Heuristics. (n.d.). In Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Heuristic
Miller, S. P., & Mercer, C. D. (1993). Mnemonics: Enhancing the math performance of student with learning disabilities. Intervention in School and Clinic, 29, 78–82.
Scruggs, T., & Mastropieri, M. (2000). Students with learning and behavior problems: An update and research synthesis. Journal of Behavioral Education, 10(2/3), 163-173.
Snyder, K. (1988). RIDGES: A problem-solving math strategy. Academic Therapy, 23, 262–263.
Watanabe, A. (1991). The effects of a mathematical word problem solving strategy on problem solving performance by middle school students with mild disabilities. Unpublished doctoral dissertation, University of Florida, Gainesville.
