It is important to realize that we must not force a tool on a student nor expect everyone to use the same tool or to solve the problem in the same way. If we do this, we have procedural zed the use of manipulatives that allows some students to go into automatic pilot. Using tools in the classroom is a balancing act. Given too much guidance takes away the thinking, given too little guidance can cause confusion and possibly never advance the thinking of the student. This is what makes teaching an art versus a science. In this blog I will attempt to describe a procedure to use in the classroom to create that perfect balance.
Step #1 - Choose the tool(s) to support the lessons' objectives. Just remember, sometimes students' will use appropriate tools that you will never have thought of using. So be careful that you don't limit the tools. I once saw a student solve a decimal problem using the tens frames. I would have never in my wildest dreams thought to use the tens frames, but it makes a lot of sense in the way he used it to solve the problems.
Step #2 - Introduce new tools to students. If it is a tool students have not used before, give free time to explore. Students need opportunity to become familiar with the tools before expected to solve problems using the tool. Once the "free time" has been provided it is important to make certain students understand it is now a math tool in which to solve problems. Ask students to brainstorm how might the tool be used. Record their ideas onto the sign (see attached files below) and then hang these tools on a board to remind students of the math tools they have at their disposal.
Step # 3- Consider the children when planning your lesson. Are they tactile, visual, etc? Just remember the tools that are effective for one child may not be effective for another. It takes each child different amounts of time to move from the concrete to the representational to the abstract. Time varies from child to child, but it is the ultimate goal to move students through these phases.
Step #4 - Communication about the use of the tools is at the heart of the effectiveness of using the tools. Ask appropriate questions frequently. Questions, such as:
"What does the blocks represent?"
"What number did you start with?"
"Why did you put those blocks into those groups?"
"Why did you put those blocks into those groups?"
"How did you know that three groups of five was 15?"
Students should discuss their work using their own words. This helps them to clarify, perfect, and organize their thinking. Using their own words students should: talk, write, and discuss their mathematical ideas.
Step # 5 - Connect the strategies and the thinking of the students. The ultimate goal is to move students from concrete to pictorial to abstract (mental math). Students will not always naturally progress without the careful questioning and guidance of teachers. Teachers need to help children to move through these phases.
Math tools do not guarantee success. Sometimes students learn to use manipulatives (tools) in a rote manner. As teachers, we need to reflect on the role of the tools and how they connect to mathematical ideas. It math tools are not the silver bullet, what makes a perfect equation to insure mathematical success? Well here is my idea:
Math Tools + Student Discussion + Engagement + Questioning + Reflection + Cooperative Learning + Perseverance + Exploratory and Deductive Activities = Students Deepened Understanding and Love for Math. My ultimate goal!!
For more ideas on how to make this vision a reality see Classroom Sneak Peek - Mathematical Practice # 5
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