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ETAP 623 Fall 2012

Purpose of the Mini-Course

  • Mathematics: the group of sciences dealing with quantities, magnitudes, and forms, and their relationships and attributes by the use of numbers and symbols.
  • Literacy: the state or quality of being able to read and write.
    Guralnik, D. B. (1970). Webster's New World dictionary of the American language (2d college ed.). New York: World Pub. Co..

Through this mini-course, I hope that you will begin to view Mathematics in a new light! Far too often, Math, for students, is presented as a "you get it" or "you don't." There is an over-emphasis on automaticity in the process and knowledge of algorithms. When, what students really need, is a balance of automaticity, fluency, and understanding. Mathematical Literacy is just one attempt at encouraging students to develop a 'voice' in their study of Mathematics. By adding both the written component and speaking components, students can become literate in Mathematical talk. I hope that by the end of this mini-course you can add just one more tool to your belt, while also developing an interest in Mathematical Literacy as well.

Needs Assessment

Intent Statement: Through this mini-course, I hope that the learner will be able to expand their knowledge on the importance of Mathematical Literacy and techniques for creating, developing, and utilizing one type of Mathematical Literacy: Math Journals. This course will help to provide strategies for using Math Journals as more than just writing opportunities, but also as a means to guide mathematical instruction and gauge students deep understanding of important mathematical concepts. As school districts push for more literacy in math and for teachers to adhere to some of the new math literacy concepts included within the Common Core, I think that a foundational understanding will help teachers to grow in this area. Additionally, once understood, Mathematical Literacy, can help to break the old ways of teaching math as solely rote memorization and automaticity in facts, in order to replace that style with fluency and understanding of mathematical processes and problem solving.


Learner Analysis: The learners for this mini-course in Mathematical Literacy will be students in either MS or PhD programs taking the Systematic Design of Instruction course. These students will come from mixed backgrounds, all having previously attained a Bachelor's degree in some capacity. Most, if not all, will have been exposed to the ideas of Common Core and NCTM Process Standards that guide the development and need for Math Literacy. Learners will have some interest and background in instructional design and developing instructional activities.


Content Analysis:

Content Overview:

  • Mathematical Literacy: What is mathematical literacy? What does it look like?
  • Importance of Mathematical Literacy: Why do we need mathematically literate students?
  • Developing Math Journals: How are math journals created?
  • Utilizing Math Journals: How can math journals be utilized to inform instruction and develop deep student understanding?

Context:

NYS P-12 Common Core Standards for Mathematics:
[Attend to Precision] Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
NCTM Process Standards: Instructional programs from prekindergarten through grade 12 should enable all students to
[Communication] Organize and consolidate their mathematical thinking through communication.
[Communication] Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
[Communication] Use the language of mathematics to express mathematical ideas precisely.
[Representation] Create and use representations to organize, record, and communicate mathematical ideas.


Goals:

1. To develop an understanding and interest in mathematical literacy.

2. To make instructors aware of a modern, relevant need for mathematical literacy.

3. To introduce one technique for teaching math literacy to students.

Learning Outcomes

  • The learner will become familiar with the discussion of Mathematical Literacy.
  • The learner will develop a rationale for the development of Mathematical LIteracy.
  • The learner will distinguish the important component and uses of Student Math Journals.
  • The learner will evaluate the usages of Student Math Journals for student success and guiding teacher instruction.

Performance Objectives

1. Given a question about grade level mathematics instruction, the learner will state the characteristics of good mathematical practice in writing.

2. When asked to explain the importance of mathematical literacy, the learner will classify math literacy, in writing, by describing the types of mathematical tasks and assessments.

3. Given a question about mathematical literacy, the learner will generate ideas about the development of math journals as a form of math literacy in writing.

4. Given a set of questions about math journals and math literacy, the learner will generate ideas about the development and utilization of math journals as a a form of math literacy, in writing, including a supporting rationale for the importance.

Instructional Curriculum Map

  • Essential Prerequisites
1. Knowledge of mathematical language and vocabulary.
2. Understanding of instructional design and methodology.
3. Understanding of assessment design.
4. Ability to interpret assessment results for purpose of informing instruction and student progress.
  • Supportive Prerequisites
1. Experience with mathematical literacy.
2. Familiarity with development of valid instructional tools.
3. Instructional experience.
4. Positive attitude towards mathematical instruction

Instructional Map:
Media: Mathematical_Literacy_Instructional_Map.pdf

Resources and References

  1. Clarke, D. (1997). Constructive assessment in mathematics: practical steps for classroom teachers. Berkley, CA: Key Curriculum Press.
  2. Mathematics Cartoons. (n.d.). Home. Retrieved November 16, 2012, from http:// simonsingh.net/books/fermats-last-theorem/wacky-fermat-stuff/mathematics-cartoons/