LEARNING DISABILITIES IMPACTING MATHEMATICS

Ann Morrison, Ph.D.

Your Own Experience

Think back to when you were in elementary, middle, and high school. What was your experience learning mathematics? Was it easy for you? Was it difficult? Is remembering your experiences learning math making you happy or anxious at all?

Table Discussion

What is the difference between people who are just “bad” at math and people with dyscalculia?

Share anything you want about your own experience learning math

Dyscalculia

Recognizing numbers Fluidity and flexibility Visualizing Counting Estimating Measurement Manipulation of numbers Patterns Spatial relations Rules

CO Prepared Graduate Competencies in Mathematics, 1st half

The prepared graduate competencies are the preschool through twelfth-grade concepts and skills that all students who complete the Colorado education system must master to ensure their success in a postsecondary and workforce setting.

Prepared graduates in mathematics: Understand the structure and properties of our number system. At their most

basic level numbers are abstract symbols that represent real-world quantities Understand quantity through estimation, precision, order of magnitude, and

comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

Make both relative (multiplicative) and absolute (arithmetic) comparisons between quantities. Multiplicative thinking underlies proportional reasoning

Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts

CO Prepared Graduate Competencies in Mathematics, 2nd half

Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

Apply transformation to numbers, shapes, functional representations, and data

Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

Communicate effective logical arguments using mathematical justification and proof. Mathematical argumentation involves making and testing conjectures, drawing valid conclusions, and justifying thinking

Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions

Factors Complicating Mathematics Education

Sometimes parents can help, sometimes they can’t

Bottom-up versus top-down approaches oftentimes don’t match with students’ learning

Skills for algebra are different than for geometry

“Minute math” – timed computation Inflexible teachers Teachers for whom math came very

easily

Learning Disabilities Including Dyscalculia

Typically stem from challenges in one of the following cognitive processes: attention language visualization metacognition memory, storage and retrieval

Language for Mathematics

Difficulties with language can be caused by challenges with: phonological awareness which slows

decoding, particularly of multisyllabic words.

connecting language with imagery, which impacts language comprehension.

memory storage and retrieval, which slows the speed at which words can be read and understood.

Language for Mathematics

Functions presented as expressions can model many important phenomena. Two important families of functions characterized by laws of growth are linear functions, which grow at a constant rate, and exponential functions, which grow at a constant percent rate. Linear functions with a constant term of zero describe proportional relationships.

Colorado Common State Standards for Mathematics, 2009

Visualization and Mathematics Mathematics often requires students to

create a mental model based on partial visual models that are provided or entirely on language.

Solve the problem on the next page. While you do, stay aware of how you use visualization to solve it.

Visualization and Mathematics

Visualization and Mathematics How did you use visualization strategies

to solve the previous problem?

Metacognition and Mathematics Metacognition is a skill that includes:

Before completing a task: Planning an approach or strategy for how to complete

the task Deciding how you will know whether you completed the

task successfully While completing the task:

Evaluating how well the approach or strategy is working Changing to another approach or strategy if the first one

isn’t working After completing the task:

Deciding whether you completed the task successfully If the task wasn’t completed successfully, deciding how

to approach it differently on the next attempt

Metacognition and Mathematics The next slide has a math problem on it. Use metacognitive skills in solving it.

Metacognition and Mathematics

Metacognition and Mathematics How did you use metacognitive skills in

solving the previous problem? Before solving it? While solving it? After solving it?

More

con

crete

More

A

bst

ract

Symbolic

Iconic

Enactivehttps://voicethread.com/new/share/5911079/

The image provided on the previous slide is iconic in the symbolic, iconic, and enactive model

Create an enactive model Create a symbolic model There are many ways to do both, no one

answer

How Can You Represent the Dots?