few or no prerequisite skills taught, students learn a lot less math than their potential suggests they can learn. The collective knowledge gained in the last decade regarding how we learn, how our brains work and what children with disabilities can do has had a very positive impact. Take-aways from that knowledge have influenced teachers in general and special education in how to think about math instruction and students with disabilities. Here are a few examples: 1. Math is connected within and between content areas in a comprehensive view. 2. When we make connections, we learn. 3. Multi-sensory, hands-on math instruction increases active learning and builds understanding. 4. Having language supports and influences thought. 5. Students with disabilities can and do learn math. 1. Math is connected. When you carefully look at the National Council of Teachers of Mathematics (NCTM) Content Areas in mathematics (numbers and operations, geometry, measurement, algebra, and data and probability) it quickly becomes apparent that math content areas are connected. This is important because learning the system of numbers acts as a support for math learners and their under- standing of mathematics across math content.
learning, their past experiences with new experiences, their math knowledge with real-world examples and known vocab- ulary with a new application of a learned vocabulary word. When lesson objectives are ordered specifically to support subsequent skills, the idea of making connections is utilized to support students by providing necessary pre-requisite skills and connecting them to new knowledge. This is the very reason a well-constructed curriculum is useful and effective. We learn math over time, not in a vacuum specific to single skills requiring mastery. When a comprehensive curriculum is present, students build and learn math knowledge across lessons within and between content areas with specific, connected lesson objectives. 3. Multi-sensory, hands-on active learning is essential. Multi-sensory instruction is very useful for many reasons. Students are more engaged when they use a variety of tools, manipulatives, and points of view. Learning is experienced in multiple ways by increasing the modes of learning, positively affecting memory and recall. Hands-on instruction in math allows students to visualize a problem and move objects around to make sense of it and try ways to solve it. Representations provided, such as concrete, semi-concrete, and abstract materials, are recommended for all students regardless of ability or age. In the learning sequence from concrete to abstract, students are shown, and then use, a concrete view with manipulatives, a semi-concrete view with drawings, picture symbols, photos, or cards and an abstract view with numerals and symbols. It is a commonly accepted practice in general education mathematics to utilize these representa- tions to deepen understanding and assist in problem solving. These opportunities move students from passive learning to active learning experiences, which help anchor students in their understanding of math concepts. 4. Having language supports and influences thought. Language plays a large role in how and what we think. It is a significant part of learning when students begin to form thoughts about what is being learned. Emphasizing acquisition and the means of language access is a clear priority for students with disabilities, for both receptive and expressive language. Learning and understanding vocabulary is a staple of education as it has been proven to increase achievement. To take advantage of this connection to learning, students need to have access to express their ideas, thoughts and answers about what is happening in math class. Many students also require a substantial reduction in the amount of language used
On a basic level, for example,
• I can make sense of a dial scale and a ruler (measurement) or a graph (data) more easily if I understand number order and comparisons (numbers and operations) • When I solve a missing addend equation (numbers and operations), I can’t help but think about an unknown repre- sented by a letter in an equation (algebra). • I can multiply amounts (numbers and operations) in an in- put-output table and find a number pattern (algebra) • When I measure perimeter or area, I am applying skills I learned in measurement and geometry. • I determine which shape is a hexagon and which is an octa- gon (geometry) when I know how to count the number of sides (numbers and operations) It is important to note these connections within a curriculum are maximized when all math content areas are complete, with skills placed in a sensible order and pre-requisites included. 2. When we make connections, we learn. Making connections matter in new learning and memory as it allows students to use math flexibly in their real-world expe- riences. Students connect what they know with what they are
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