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Instructor: Anita Johnston        office: JM 250
phone: 517.796.8504    email: JohnstoAnitaM@jccmi.edu

TEACHING INVESTIGATION - WRITING ASSIGNMENT...
 

The purpose of this task is for you to investigate some alternative methods for teaching a particular mathematics topic in depth.  You will also become familiar with some of the teaching resources available to you.

 

I suggest that you begin by looking at some of the article(s) from Teaching Children Mathematics magazine, available in the JCC library.  Keep in mind that this is intended as a starting point; you may also search for additional resources from other publications and/or web sites. 

 

This paper should be typed (double-spaced) and have a professional appearance. The paper should have a title page and should include a reference page. The paper should be approximately 3 – 5 pages in length.  Please send it via an email attachment saved as a “rtf” file.

 

1. As you begin to organize and synthesize the information you find into a paper, keep in mind the guiding questions listed with your topic.  All papers should address the following questions in some depth:

2. Begin with an overview of your topic area, and the goal that is intended to be accomplished.

3. Which of the NCTM standards is being addressed?  Pick two to four of the most relevant, and discuss.

4. Compare and contrast traditional methods used to teach this topic with the methods you found in your research.

5. Each topic is accessible, at some level, to most if not all elementary age groups.  Address how the topic would be integrated throughout the K – 5 grade years, and be sure you describe activities appropriate for each age range.

6. Your paper should combine aspects of several resources, as well as ideas of your own. You will need to give credit to your resources, using end notes in your paper.  Use a minimum of four resources.

 

On August 29 we will assign topics.  If you have identified a topic area and found at least one resource in Teaching Children Mathematics then you will have “first choice” of the topic…depending on the number of students requesting the same topic. 

 

Topics List for MTH 210 Teaching Investigation – Writing Assignment

 

1.  Number Sense; Operation Sense

            What is Number Sense?

            How do students develop it?

            What manipulatives enhance number sense development?

            What activities promote number sense development?

            What is Operation Sense?

            How can teachers help students develop good operation sense?

 

2.  Fractions

            How can fractions be made meaningful for very young students?

            How can students’ understanding of fractions be developed as they mature?

            What manipulatives or activities can be used to promote understanding of fractions? (Initially)

            What activities can be used to reinforce and practice fraction concepts?

            What activities are available to help students perform operations on fractions?

            What real world connections to fractions can be made?

 

3.  Concepts of the Arithmetic Operations + - x ¸

            How do students learn to connect real world situations with certain arithmetic operations?

            How does this understanding develop throughout the school years?

            What activities or manipulatives promote conceptual thinking about arithmetic operations, rather than drilling algorithms?

            We tend to concentrate on younger children with concept, and do more drill as students get older; what are some activities appropriate for older students to get at the concepts again?

 

4.  Number Theory

            How can we encourage kids to generalize their mathematical thinking?

            What are some activities that promote this type of thinking?

            One element of number theory is prime numbers; what are some ways of helping students understand primes and prime factorizations?

 

5.  Place Value and Number Base

            Why must children begin to understand the concept of place value at an early age?

            What are some ways to introduce children to place value?

            What understanding of number base is appropriate for a young student? 

            We usually teach place value to young students; in what ways can the concepts of place value and number base be made appropriate for activities in upper elementary classrooms?

 

6.  Basic Arithmetic Facts

            Beyond sheer memorization, what are some ways for students to learn their basic facts?

            What manipulatives and activities can teachers provide to begin to help students learn their facts?  (initially)

            What activities could be used for basic fact practice?

            Why is learning basic facts essential?  What value might learning basic facts in the ways you outline be to the student later on?

 

7.  Ratio and Proportion

            How can young children be introduced to the concept of ratio?

            What activities and manipulatives might be appropriate in early elementary grades

            As students become more mathematically sophisticated, what are some ways to refine their understanding of ratio?

            What are some real activities that could be used in upper elementary grades?

            What are some activities with real world connections involving ratio and proportion?

 

8.  Fraction, Decimal and Percent

            Why is it important that these ideas be connected for students?

            What are some ways of making these connections?

            What are some activities or manipulatives that help in the teaching of  fractions, decimals, and percents?

            What real world ideas can be connected with the study of fractions, decimals and percents?

            How can the above be accomplished at varying ages?

 

9.  Patterns

            Why is the study of patterns essential to students’ mathematical development?  What foundations does it lay?

            We often think of patterns as appropriate math for younger students; what are some activities that are appropriate for older students as well?

            Where are patterns found in the real world?

            One famous pattern is the Fibonacci pattern.  Where is this pattern found in nature?  What other ideas are related to this pattern?

 

10.  Problem Solving

            What place does problem solving have in elementary education?

            How can teachers help students learn to problem solve?

            What are some specific ideas for activities that promote problem solving?

            What are some differences between problem solving at various ages?