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    Math Tools: Research-Based Practices for Differentiating Instruction and Raising Achievement in Mathematics

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    Mathematical Styles and Strategies for Differentiating Instruction and Increasing Student Engagement

    Our thoughtful questions

    Why do some students succeed in mathematics while others do not? Is it a matter of skill or will?

    How can we use research-based teaching tools and strategies to address

    the styles of all learners so they succeed in mathematics?

    Our workshop is based on the following assumptions What teachers do and the instructional decisions they make have a

    significant impact on what students learn and how they learn to think.

    Different students approach mathematics using different learning styles and need different things from their teachers to achieve in mathematics.

    Style-based mathematics instruction is more than a way to invite a greater

    number of students into the teaching and learning process; it is, plain and simple, good mathbalanced, rigorous, and diverse.

    In this workshop, you will learn:

    The characteristics of the four basic mathematical learning styles (Mastery, Understanding, Self-Expressive, and Interpersonal).

    How to use a variety of mathematical teaching tools to differentiate instruction and increase student engagement.

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    Numbers play an important role in our life experiences, from a persons age to important dates, to birth order, to college GPA, and so on.

    1. Select five numbers that are meaningful to you and that will help someone learn a little bit more about you.

    2. Write a sentence or question for each number, leaving a blank line where the

    number should go (e.g. Thenumberofpeopleinmyfamilyis__). Share your numbers with a neighbor. See if your neighbor can match the right number to your sentence.

    Sentence Answer






    3. Meet with two other pairs (to form a group of six) and write each of your

    numbers on a sticky note. Place all of your numbers on your table and see how many groups you can make that share a common characteristic (e.g. 2,12,32numbersthathave2intheonescolumn).

    4. Visit another table and try to guess the reason for their groupings.

    5. Return to your table and discuss how you might use some of the parts of this activity with your students.

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    The three things I remember most from learning mathematics are 1. 2. 3.

    I learn mathematics best when I can:

    Mathematics is Because

    Which of these terms best describe you as a learner of mathematics? Circle all that apply.

    variable cubical spherical

    irrational equilateral congruent

    infinite finite rational

    point acute factorial

    parabolic minimum constant

    exponential divisible square

    maximum obtuse transformation

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    Complete the first (Before Workshop) and last columns (After Workshop) by placing an A for Agree or a D for Disagree in each box. Share your thoughts with your group and give one or two reasons to support your position. Before After Workshop Workshop

    1. Most mathematics teachers use a variety of teaching tools and strategies to teach mathematics.

    2. Differences in mathematical teaching styles account for 65% of the reason that students are not successful in mathematics.

    3. There is an inverse correlation between writing in mathematics and mathematical achievement.

    4. Success in mathematics has more to do with feeling than with thinking.

    5. Cooperative learning is a highly effective strategy for learning mathematics.

    6. Proficiency in mathematical procedures is more important than understanding mathematical concepts (procedure vs. content).

    7. In the United States, teachers of mathematics cover more content in a year than their counterparts in other countries whose students score higher on international tests of mathematical achievement.

    8. Access to high-level concepts in mathematics is an important equity issue.

    9. Mathematical achievement has little to do with career success.

    10. Divergent thinking and creativity are more important to learning in the humanities than they are to learning in mathematics.

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    Range Finder Note:Afulldescriptionofthistoolcanbefoundonpages208211ofMathTools,Grades312:64WaystoDifferentiateInstructionandIncreaseStudentEngagement.

    Examine the three sets of mathematical problems A, B, and C below. Complete the one set that you feel most comfortable solving in five minutes.

    Set A 1) 28 + 32 + 51 2) 3 x 37 3) 225 114 Set B 1) 4(20) + 31 2) 3(52)+ 62 3) 10(26 15) + 1 Set C 1) Solve for x: 3x 133 = 200 2) Find the LCM of 3 and 37 3) Evaluate: 2a + 4b + c when a = 50, b = 5, and c = 9.

    Reflection Reflect upon the level you chose and answer the questions below. Then meet with a partner and share your responses. Why did you select the set you did? What makes Set B more challenging than Set A? What makes Set C more challenging than Set B? How well do you believe your mathematics education has provided you with the skills you need in life?

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    Yes, But Why?


    Work with a partner. Write down the last two digits of the year you were born. Add that number to the age you will be on your birthday this calendar year. Compare your answer with your partners. What did you discover? Work with your partner to develop an explanation for why you both had the same answer. Neat Trick

    My Numbers My Partners Numbers Last two digits of

    the year I was born

    Age for this calendar year


    Yes, the answers are the same but why? 3-D Approach


    Use a 3-D approach to explain your reasoning for the Neat Trick above. How would you represent your answer algebraically, graphically, numerically, with a diagram, or through writing?

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    Create Your Own How could you modify this Neat Trick to make it more remarkable? Use your understanding of this Neat Trick to create your own mathematical trick. Explain the steps in your new trick below.

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    What Is Mathematical Literacy?

    Mastery of procedural and

    conceptual knowledge.


    A language to communicate ideas and

    solve real-world problems.


    Understanding of logical reasoning to

    explain and prove a solution.


    Application of strategies to formulate

    and solve problems.


    What percentage of your classroom practice in mathematics would you estimate you spend in each of these areas? (Write your percentage on the line in each box above) How does your classroom practice compare with the NAEP data?

    NAEP data shows that proficiency in these four areas has developed unevenly. In many classrooms, students are able to mimic rules and procedures demonstrated by their teacher: however, students often acquire these skills with little depth of understanding or the ability to use them to solve complex problems (Kowley & Wearing 2000).

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    WHAT KIND OF PROBLEM SOLVER ARE YOU? Math is all about problem solving. But not all students and not all mathematicians solve problems in the same way. In fact, even though your textbook might tell you otherwise, there are many different ways to solve math problems. Your own preferences as a problem solver can tell you a lot about how your mind works and how you learn best. So, how do you go about solving problems in mathematic? Lets conduct