WEEK 6--DIFFRENTIATION---MISSING SECTION

1.

Your responses to each of these questions

· Grade 7 and grade 8 students benefit greatly when they a comprehensive understanding of fractions and their respective decimal and percent equivalences. With this in mind, which of the fractions to decimal and percent equivalences would you consider fit into the categories:

· Autofacts

· Stratofacts

· Clueless facts

You might think about autofacts as being those fractions to decimals to percents that your students already know. Stratofacts can be described as those facts that your students can figure out slowly using an idiosyncratic strategy. This just means a strategy your students can use to figure out the conversion. Clueless facts are those facts that your students just cannot recall at all. They are completely unknown.

· What are some strategies you can use with your students who are clueless when it comes to identifying the fraction to decimals for the eighths? sixths?

· How might you move your students from the Stratofacts to the Autofacts category? Or, is it important to do so? Justify your response.

· How might you move your students from the Clueless category to the Stratofacts category? Or, is it important to do so? Justify your reponse.

As we move into the 21st century we keep hearing that there are basic facts that all students should know. These facts have obviously changed over the past 50 years since cheap $2 calculators can do most of the simple computations that were considered “basic facts” in the 1950s, 1960s, 1970s and 1980s. More is expected of the children we teach than what we were trained to teach…what is the more? Is it at the expense of what used to be crucial? Have we changed what and how we do things to accommodate the expectations that exist for the future? What are some mathematical facts that you believe are crucial for all students to know and be able to do by grade 8 and…more importantly…how are you going to help all students achieve those expectations?

2

· Applications

Examine the following problem. It is designed for grade 7 or grade 8 students. Since most of us teach in heterogeneous classes we recognize that this may be a great challenge for some of our students. That being said, the problem embraces the learning objectives and expectations for grade 8 students in the NAEP frameworks. How might you differentiate this problem so that all students have opportunity to access the situation and work on a grade 7 or grade 8 level mathematically? Be sure to justify your thinking and post your “redo” of the problem.

You are given the total cost of $2,589.96 for one iPad and three IPad2’s and a total cost of $2,659.95 for two iPad 2’s and three IPad’s. a. What is the price of one IPad? b. What is the price of one iPad 2? Be sure to explain your answers.

As we noted earlier, differentiating instruction means providing rigorous mathematics, presented in ways that include all students in grade appropriate mathematics. Based upon the fact that all students will be asked to solve this problem in one form or another take some time to develop a rubric on a scale from 1 – 4 that is inclusive of both the original problem and the revised problem. As you develop the rubric consider the different representations that are appropriate for this problem. Think about the evidence of understanding you will be looking for as you analyze what each student knows and is able to do. Be sure to post your rubric. Discuss with your peers, the rubric you developed, the rubrics they developed and how you can all come to consensus and provide one rubric that is appropriate for the problem situation and all students.

3.

· Reflect on the Following Accomodations and Article

“It is a wise man who once said that there is no greater inequality than the equal treatment of unequals.” -Felix Frankfurter, Supreme Court Justice Read and reflect on the following accommodations that are sometimes used for all students in a mathematics classroom. Indicate on a scale of 1 – 5 with 5 being “I strongly agree” how you feel about their implementation in a heterogeneous classroom. Include a brief justification of how you rated each accommodation.

· Read the attached Article: Write your thoughts on this.

1. All students should be allowed extended time to complete quizzes and tests. Strongly disagree / disagree / agree / strongly agree

2. I provide all my students the opportunity to retake a quiz or test and count the corrections towards the quiz or test grade. Strongly disagree / disagree / agree / strongly agree

3. I provide multiple-model assessments for all students. Strongly disagree / disagree / agree / strongly agree

4. I build into my classroom teaching and assessing routines that are always followed. Strongly disagree / disagree / agree / strongly agree

5. I count my student’s homework for no more than 5% of their term grade. Strongly disagree / disagree / agree / strongly agree

6. I use mathematics strategy notebooks developed in class and used for class problem solving for part of the term grade. Strongly disagree / disagree / agree / strongly agree

7. I allow my students some control over the difficulty level of their classwork and homework. Strongly disagree / disagree / agree / strongly agree