See It, Do It, Imagine It The Power of Cause and Effect in..

2. Build cause and effect background knowledge with models and exploration opportunities using math tools and strategies present in the lesson prior to problem solving. This is a must in good instruction and should be part of the math curriculum itself. Background knowledge, with an eye towards cause and effect, must include structure for students to rely on, such as familiar vocabulary, a related game, and concepts brought forward from past lessons. Modeled use of tools and strategies paired with math concepts and action words, e.g. add, place, sort, etc. help students see what is happening. When they have access to those same materials to explore, they can experience cause and effect firsthand. In Equals math, the Ac- tion Dictionary provides access by way of multiple adaptation suggestions for each action present in the lessons. Teachers choose which adaptation works best for a student and tweaks it to fit, or perhaps comes up with a new idea inspired by the adaptation ideas. Whichever is chosen, the idea is to basically provide enough support so students are able to watch, do and talk about what is happening as independently as possible. It may be necessary to show explicitly what the problem or the cause and effect relationship is about so students know what you are talking about, even if it feels like you are ‘giving away the answer’. It doesn’t matter, however, because if a student doesn’t know what you are getting at, wildly guessing the answer has no significance or merit. 3. Support problem solving with concrete objects. Through the process of problem solving, we usually think about several things, in varied order, such as naming the facts in the problem, choosing an action to take, identifying what the out- come might look like and which tool and strategy to use. Stu- dents with significant disabilities typically require concrete ma- terials for understanding this way of thinking, one step at a time. (This is not to say that students with significant disabilities never see semi-concrete and abstract representation. They require ex- posure to these as well, since numerals, operations symbols, pic- tures and X’s on a graph or array are a part of our world). Problem solving in a story format makes good sense for its relationship to the real world. However, the story can become a barrier when trying to navigate a math problem buried in a ton of words. This is where concrete objects cut through to the essence and in- crease interest as well. Well-placed objects fastened to the prob- lem above matching key words can assist students in focusing on the facts. Reducing the language down to basic facts and concepts of the problem is also helpful as long as math terms are maintained and the essence of the problem is preserved. When it comes to math terms, concrete representations of vocabulary, as seen in Equals math, support the meaning in the problem. The pic-symbol supported and demonstrated action words embedded in Equals lessons as background knowledge re- emerge when students are asked, “What do you do?” to solve

the problem. Making an estimate about an amount or a predic- tion of an outcome can be shown in a display of possible out- comes as depicted by objects. For example, in a problem adding three insects and two insects, I can ask my students to estimate how many total insects there will be when I add them, giving three choices displayed with insect counters: two insects, six insects or one insect. The students can estimate, comparing the insect sets of three and two attached to the problem to the three choices in the display. When solving a problem, students are asked to choose a tool or strategy. Often, the strategy can be linked to a tool or counter so the question has concrete answer choices. Using tools/strategies that were previously explored is key. In Equals math, you will find problem solving hinges on a well-planned exploration of background concepts, vocabulary and lesson objects and materials that are carried into the prob- lem-solving process. Choosing a tool and strategy, then, is easy to provide as the students already have had experience with them in the beginning of the lesson. 4. Show concrete objects and lesson materials in two or three choices to narrow the field after asking a question or expecting students to comment. Providing choices for stu- dents who do not have access to a communication device pro- grammed to represent what is happening in math at the mo- ment is a necessary support. Of course, students need access to their own communication systems at all times. However, in math class, students also need to have relevant choices to answer questions about the problem at hand. Providing two or three choices will give students power in the process while limiting the scope of possibilities from all the math tools in the world to just the math tools on the table. It gives the student a chance to focus on and use familiar objects that were explored earlier in the lesson to answer a new question. Students have access to a display by eye gaze, point or touch. If a student requires a different response, recording “That’s the one I want,” on a Step- by-Step communicator, placing it near the student, and pointing to each choice works well. 5. Expand cause and effect by asking questions with well- planned choices. By expanding on questions about the lesson concept and what happened in the problem, students have an opportunity to engage in basic reasoning with materials they know. For ex- ample, students learned about using three dimensional shapes (cubes) to make a new three-dimensional shape (rectangular prism tower). Three objects are placed in a display: a butter- fly counter, a cube and a hexagon with piles of each object on the table nearby. The teacher asks, “What do you use to make a tower?” When a student chooses, the teacher follows through and demonstrates building a tower with the chosen object, ask- ing students to assist or build it themselves (with adaptations to support students building a tower as needed). Discuss what

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