MODULE 4 MATH DIFFICULTIES AND DISABILITIES
Far more students suffer with math difficulties than with a math disability. Approximately 26% of students with learning disabilities exhibit problems in the area of math and about 6% of the overall population with a math disability (Lerner & Johns, 2009). The principles of effective mathematic instruction have been shown to be effective in helping students with math difficulties and disabilities. Effective mathematic instruction includes early number learning, progressing from the concrete to the abstract, providing opportunity for practice and review, generalizing the concepts and skills that have been learned and teaching mathematics vocabulary.
Lerner, J.W., & Johns, B.H., (2009). Math difficulties. Learning disabilities and related mild disabilities (pp. 446-483). Belmont: Wadsworth, Cengage Learning.
Math Vids Videos
I looked at several videos on the website mathvids.com. The videos included adding negative numbers, introduction to geometry proofs, graphing linear equations in algebra I and tutorials on the basic functions of a T-84 calculator. In comparing the videos to the effective principles of mathematic instruction I found a lot lacking. Most of the videos were for higher level math that are past the basics of number learning and used little concrete to abstract learning. The video on adding negative numbers was the best in providing an example in the concrete and the abstract together. It also provided practice and review on several different problems and repeatedly used the vocabulary needed for this lesson. I would have liked to have seen the vocabulary written as well as verbally presented. One algebra video did show two ways to do the same problems. While most videos only demonstrated doing one problem the videos can be replayed until you understand all of the steps. Many of our math teachers use the videos that are provided with the e-books our students use. The head of the math department also video tapes his lesson on his smart board and places it on Edline for the students to access from home in case they have questions when doing their homework or are out sick for the day. He will also color code the different steps. I find I use websites such as mathvids.com for a tutorial when helping students in the lab.
Math Vids Videos retrieved on April 1, 2001 from http://www.mathvids.com/
IRIS
1. High-Quality Math Instruction
The components of high-quality math instruction include a standard-based curriculum and evidence-based instructional strategies. A standard-based curriculum must contain the content skills believed important for students to learn. The National Council of Teacher of Mathematics (NCTM) has set the principles and standards for schools in mathematics in the United States. There is a national movement to use the Common Core State Standards that are easier to use for daily lesson planning and assessment. Texas presently does not use the Common Core State Standards.
Evidenced-based instructional strategies are strategies proven though research to be effective in teaching students math skills and concepts. Both standard-based curriculum and evidenced-based instructional strategies should be implemented with fidelity to be successful.
2. NCTM Standards
The NCTM standards are focused on essential mathematical concepts that are organized and integrated. These concepts build knowledge and understanding across grade levels.
The standard concepts or the knowledge we hope to acquire, include numbers and operations, algebra, geometry, measurement, and data analysis and probability. Process standards are the way we learn and use knowledge such as problem solving, reasoning and proof, communication, connections, and representations. All five content and process standards should be taught at each grade level but the emphasis will vary across grade levels.
Video Analysis
Evidenced based teaching strategies include explicit or direct instruction, peer tutoring and cooperative learning. In the video the students are using a cooperative learning strategy. Cooperative learning involves working in small mixed ability groups. Cooperative learning shows greater motivation, increased time on task, and improved self-esteem. Effective teaching practices in the video included student discussions on how to find the area. The students presented and compared multiple solutions. The students were also using a manipulative by having the design on the board. The teacher came over and then assesses their understanding by letting them discuss their solutions and how they got them. Student discussions and compared multiple solutions give students an output to verbalize their thinking processes in understanding a concept. The board manipulative gives a concrete element to an abstract problem and the teacher assessing their understanding by asking questions all help to build conceptual understanding.
While I do not teach a math class I do coordinate with the two teachers who teach our basic math courses for students with math difficulties and disabilities, I coordinate with them by sharing information, strategies, and resources. These are also principles, concepts and strategies I can use in the resource room.
The Iris Center for Training Enhancement (2010). High quality math instruction: what teachers should know. Retrieved April 1, 2011from http://Iris.peabody.vanderbilt.edu/math/chalcycle.htm
Dyscalculia: Readings for Module 4
Language of Math by Marilyn Burns (Burns, 2006): I was very interested in reading this article. Many of my middle school and high school students struggle with the vocabulary of math. It is vocabulary they do not use every day and it is used in isolation. Students often know how to do the problems once they are given an example, but when they just read the directions incorporating math terms without an example they are often lost. Burns gave some great points in teaching mathematic vocabulary. First students must understand the concepts before they can understand the language. Student need to see vocabulary written so classrooms should display charts and students should keep their own list at home. Teacher need to associate the symbol to the words by pointing to the symbol and saying the word. When students discuss and present ideas they need to use the appropriate vocabulary.
Burns, M. (2006). Language of math. Instructor, 41-43.
In Redoing the Numbers: Secondary Math for a Postsecondary Work World (Woodward, 1999), Woodward states “Students need to learn how to manage information, communicate with others, and use technology appropriately. They need to know math, but they need to know much more.” Through the Workplace Literacy Project students were freed from the traditional paper-and-pencil-skills involving worksheets and their efforts were placed on conceptual understanding, application, and written and oral communication. The students used technology such as fraction calculators and excel spreadsheets, to do a lot of the tasks. I personally loved this article. I would like to see an upper level math class for students to collect data, analyze it, and present their results. Real life mathematics!
Woodward, J. (1999). Redoing the numbers: secondary math for a postsecondary work world. The Counsel for Exceptional Children, 31, 74-79.
In Teaching Students Math Problem-Solving through Graphic Representations, Asha Jitendra uses problem schemata identification and representation instruction to help students with math learning difficulties become effective problem solvers. First by using diagrams, students identify the story (word problem), the situation of change, and the group or compare situations. Phase two involves selecting and applying the appropriate math operation, by first identifying the whole or total. Students then memorize the rules using self-instruction sheets by scaffolding until they become independent. Schemata diagrams are also removed once students are proficient. While I have color coded and used mnemonics and arrows I have not used diagrams in math except in geometry. It is something worth trying especially with the middle school students.
Jitendra, A. (2022). Teaching students with math problem-solving through graphic representations. Council for Exceptional Children, 34, 34-38.
Learning Estimation and Other Advanced Mathematics Concepts in an Inclusive Class by Kathleen Mittag and Anthony Van Reusen and Connecting Math and Science for All Students by John Cawley give wonder ways of teaching math concepts through classroom activities. These activities are hand-on, systematic, linked to prior learning, and real-life problems that have been shown to be highly effective. While these are activities I would not be using in the resource room I will give them to math teachers for additional strategies and teaching techniques.
Mittag, K.C., & Van Reusen, A. K. (1999). Learning estimation and other advanced mathematics concepts in an inclusive class. Teaching Exceptional Children, 31, 66-72.
