first steps in that process: 1) make sure students are receiving instruction that covers and connects basic foundational math skills, 2) build cause and effect background knowledge with models and exploration opportunities using math tools and strategies present in the lesson, 3) support problem solving with concrete objects, 4) show concrete objects and lesson materials in two or three choices as a way for students to communicate, 5) expand cause and effect by asking questions with well-planned choices and 6) support students’ collaboration and risk-taking by accepting each answer to a question, then check and discuss. 1. Make sure students are receiving instruction that cov- ers and connects basic foundational math skills by providing math curriculum that is connected meaningfully across all math content areas, such as those recommended by the NCTM: Num- bers and Operations, Geometry, Algebra, Data and Probability and Measurement. (It is worth noting that other sources, such as Common Core State Standards, show different configurations of content areas. However, the same math content is covered in each source, just sorted differently.) Typically, the idea of con- nected math across all math content areas has been ignored in traditional special education math programs, especially those described as functional math. When you consider that we all learn by connecting new information to relevant known infor- mation, the idea of pre-requisite skills becomes monumentally important. As we learned from Equals math curriculum data, students with disabilities learn very well with general educa- tion math instruction methodologies that are based on brain and learning research, including making connections in learn- ing, as long as access, appropriate pacing and adaptations are provided. When you think about it, isn’t teaching math connect- ed within and between all math content areas an example of promoting generalization that we have embraced as proof of a learned concept? Why, then, have we been teaching in function- al math silos for so long, with limited scope in math content and no connections between concepts? In talking with many educators over the years across the United States, I found that the principles of math instruction ne- glected in pre-service teacher education tend to play a role in teachers clinging to long-held, ineffective practices in math. Es- sentially, students with moderate or significant disabilities have been left without quality math instruction altogether, result- ing in special education teachers improvising. Unless teachers have had some background in curriculum or the good fortune to be handed an appropriate curriculum for their students, they wouldn’t have necessarily known what was missing. Now that we know what is missing, it is essential to look for a math curriculum that is robust, connected and complete, deftly utilizing quality math instruction based on best practice princi- ples of learning and brain research with access that is necessary for optimal engagement and understanding.
tage of countless cause and effect experiences needed to solve math problems? Students with significant disabilities may not have had those experiences. So, it makes sense to arm students with information about how our physical world works, whatever the impact may be. Given that students with significant disabilities typically come to school with less free-flowing or independent explora- tion in their play, less access to use of toys and tools, and few- er hands-on experiences overall compared to same-age peers without disabilities, it makes sense to turn to the answer that lies within math itself: teach cause and effect that is present in math concepts and use of math tools in the process of problem solving. Using tools and strategies with learned, identified (and adapted) actions to solve problems makes problem solving more concrete. Consider the concept of addition from the National Council of Teachers of Mathematics (NCTM) math content area Numbers and Operations, for example, which easily comes to mind when thinking about cause and effect: add two sets (cause) which re- sults in one larger set (effect). All four operations are excellent examples of cause and effect, however, there are more examples from each remaining NCTM math content area: Data Analysis and Probability: When you compile data and graph it (cause), a visual comparison is displayed (effect). Geometry: Drawing two intersecting lines (cause) shows an angle (effect). Measurement: Place a bag of apples on a dial scale (cause) and the pressure makes the needle move on the dial (effect). Algebra: Write and multiply input amounts: 1, 2, 3 and 4 times 2 on an input/output table (cause) to reveal a pattern: 2, 4, 6 and 8 (effect). By modeling and providing hands-on experiences with math tools and actions, students have firsthand views of cause and ef- fect. With access to language, students can talk about what hap- pened. This, in turn, can be used when problem solving. When students are familiar with an action and its effect, they are more likely to choose that action when it makes sense in solving a par- ticular problem. For example, if I know adding means to join two sets together for a total, I will think of it when I solve a problem with two sets that are put together. Teachers must make cause and effect experiences accessible for students with disabilities by modeling and adapting actions with math tools and materials so students can understand and have as much hands-on experience and independence as possi- ble. With access to language, students can then talk about what is happening or what has happened right in front of them. These ideas fit nicely with the math community’s persistence that hands-on math is very valuable, especially when paired with models, exploration, and discussion. For students with disabil- ities, there are steps to take to provide access so they, too, can watch, do and talk about it, specifically with concrete objects and actions that make clear what is happening. Here are basic
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