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Learning to Love Math -Chapter 2 continued

Chapter 2 - Understanding and Planning Achievable Challenge

Differentiating instruction is the key to creating  achievable challenges for students, through instruction, homework, multimedia support, etc.

In order to differentiate instruction, students' learning strengths must be understood, and Willis shares two general categories for students: Map Readers and Explorers. According to Willis, Map Readers like to work independently, and are most comfortable when they have specific instructions or procedures to follow. Map Readers have characteristics of the linguistic and logical-mathematical intelligence groups proposed by Gardner (1983), as well as learning styles of auditory, sequential, and analytic learners. They prefer problems with definite answers and procedures, they prefer new skills to be modeled by the teacher, process information in “parts-to-whole,” are comfortable with logical, orderly, structured approaches, and are good at using words to understand information, but may prefer written responses. They want to practice before sharing ideas and answers, appreciate early and frequent feedback, enjoy working independently and do not usually respond well to mixed-ability groupings. Map Readers take more time and work deliberately, showing all their work on homework and taking detailed notes.

Explorers are learners that want to skip instructions and jump into figuring things out with trial and error. Explorers share characteristics of spatial and bodily-kinesthetic groups and Gardner’s learning styles of global, big-picture, exploratory learners. They want to use their imagination, prefer discovery and exploratory learning where they can experiment, create, construct, and explore topics before there is direct instruction or modeling. These learners process information best when it’s introduced as “big picture” and then broken down; they use visualization memory strategies, enjoy choice and opportunities for innovation, find it helpful to draw diagrams, use graphic organizers, or make models and then add their own elaborations. Explorers recognize a pattern and then find thematic and cross-curricular links beyond math; they relate to inquiry projects that are open-ended.  Explorers work well in various groupings, and respond well to models or manipulatives that help see direction of instruction; they construct mental patterns to connect prior learning with new knowledge.

Using students learning strengths
To help find students' strengths and interests, Willis suggests introducing each new unit by offering the different categories of learners (Map Readers and Explorers) at least one, specific, targeted activity. You can then observe what elicits their interest and participation. She also suggests using interviews and written inventories to determine students’ interests and strengths.
Willis suggests using multisensory input - rather than lecturing and writing on the board, she suggests playing music at some point during the day, drawing diagrams, graphs, or sketches, and showing pictures or video clips, as well as offering hands-on experiences with manipulatives and using students to demonstrate concepts. For younger students, she suggests varying the presentation of information by stimulating several senses, like speaking in a rhythmic cadence, rhyme, or rap key phrase.

In attempting to differentiate instruction, it's important to avoid boredom. To avoid the stress of boredom,Willis states that teachers should limit excessive repetition once mastery is clear. For those students that finish quickly and correctly, teachers should have appropriately challenging or higher-level conceptual problems ready for them. This idea of too much repetition should be applied to homework as well – it is a turnoff and a stressor. Willis suggests individualizing students' math homework.
To help gifted math students show work (which is often difficult because they do it so quickly in their heads), give them more challenging problems that will require them to show the work in order to figure out the answer.

It is clearly difficult to individualize for all students and all lessons, so Willis suggests that teachers find their own achievable challenge in terms of differentiating for their students. Start by focusing on individualizing for just one or two students, or focus on trying one unit that engages students according to their learning strengths and interests. By doing so, she states that you will “stimulate and strengthen your own neuronal network for differentiating and planning for achievable challenge, and these approaches will become more and more automatic.”


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