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Strategies for Enhancing Conceptual Understanding in the Mathematics Classroom

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Strategies for Enhancing Conceptual Understanding in the Mathematics Classroom

Lamont Holifield, M. Ed.

CICS-Ellison High School

Imathination Conference 2012

Saturday, January 21,2012

- Rationale for Discussion/Connection to Common Core
- Tool You Can Use
- Integrating Literature into Mathematics
- Writing in the Mathematics Classroom
- Debate and Critique

- Part of the challenge of teaching reading in Mathematics stems from the confusion over what “reading mathematics” actually means.
- Is it being able to read expressions with mathematical symbols?
- Is it being able to comprehend printed numerical data?
- Is it being able to comprehend worded mathematical passages in, say, a mathematics textbook?

- First and foremost, it is paramount to meeting at least three of the Standards for Mathematics Practice listed in the New Common Core Standards:
- Students must be able to make sense of problems and persevere in solving them.
- Students must be able to reason abstractly and quantitatively.
- Students must be able to construct viable arguments and critique the reasoning of others. Hence, the necessity of using principles of academic debate and argumentative reasoning skills.

- Secondly, it requires unique knowledge and skills not taught in other content areas.
- Typically students are taught to read from left to right. This holds true in mathematics with several exceptions.
- In addition, they must know how to read from right to left. For example, when reading an integer number line.
- They must know how to read from top to bottom. For example, when analyzing a table of data.
- They must also know how to read diagonally. For example, when reading a graph.

- Typically students are taught to read from left to right. This holds true in mathematics with several exceptions.

- Thirdly, mathematics text contain more concepts per word, per sentence, per paragraph than any other kind of text.
- In addition, the concepts are abstract making it difficult for readers to visualize their meaning.
- Fourth, authors typically write in terse and compact style. Each sentence contains a lot of information and there is a little redundancy. Students tackle the text, at time, like a short story and miss significant details, explanations and the underlying logic.

- Complexities of teaching mathematics in ways we did not experience as students
- Discomfort with our own mathematics knowledge
- Lack of sustained professional development opportunities like Imathination
- Greater requirement for facilitation skills and attention to classroom dynamics
- Lack of time, especially in face of curricular demands

- Secrets, Lies and Algebra (Algebra I, II Classroom) by Wendy Lichtman
- A Gebra Named Al (Algebra I, Chemistry) by Wendy Isdell
- Flatland, A Romance of Many Dimensions (Geometry, Pre-Calc) by E. A. Abbott
- The Numbers behind Numb3rs: Solving Crimes with Mathematics (Statistics/AP Stats) by Keith Devlin
- A Certain Ambiguity (Pre Calc or Higher Mathematics) by Gaurav Suri

- Students can make connections to text and engage in learning mathematical terminology without realizing that they are doing so.
- It allows students to experience mathematics in a non-intimidating manner. Consider the student who has only had negative experiences with mathematics and finally gets to experience it in a context he/she can enjoy.

- Based upon what you have heard, what can potentially be the value added to students?
- How can incorporating the reading of novels and other text potentially engage students in the learning?
- What challenges do you perceive?
Visit the Website below for other titles in mathematical

fiction:

http://kasmana.people.cofc.edu/MATHFICT/

Quote from: Maggie Johnston, 9th Grade Math Teacher, Denver, CO

“Writing in mathematics gives me a window into my students’ thoughts that I don’t normally get when they just compute problems. It shows me their roadblocks, and also gives me as a teacher, a road map.”

- What does the statement mean to you, personally?
- In the statement, I have underlined a couple of words. Answer the following questions:
- What is the purpose of a window?
- Why is students’ thinking important?
- What is a roadblock? What is the danger of not seeing a roadblock? What could potentially happen if a roadblock is simply ignored?
- What is the value of a road map?

- “The Journalists’ Questions”
- Biography and Autobiography (Mathography)
- Learning Logs, Blogs and Journals
- Summaries (Venn Diagrams, Concept Maps)
- Magnet Summaries
- Explicitly Teaching Relevant Vocabulary
- Creative Writing in Trigonometry (can be integrated into other mathematical subjects)

A Potential Transformative Model of the Math Classroom

Math Classroom functions as a community where thinking, talking, agreeing and disagreeing are encouraged. The teacher provides students with powerful math problems to solve together and students are expected to justify and explain their solutions. The primary goal is to extend one’s own thinking as well as that of others.

- What is your initial reaction to this model?
- Currently, how does this model fit as a description of your classroom?
- What are some challenges to adopting this type of model?

- Discourse Time! (What is It?/How does it work?)
- Debate in the Mathematics Class (Solving a System of Linear Equation Methodology Debate)
- Error Analysis Work (Looking at Work/Listening at Peers)
- Moving from Teacher Driven to Student-Led Discussion

For more information on any and all strategies introduced, contact me at:

Lamont Holifield

CICS-Ralph Ellison High School

1817 W. 80th Street

Chicago, IL 60620

(773) 307-0734