Starting Your Day Off Write: Writing to Learn Mathematics

Starting Your Day Off Write:

Writing to Learn Mathematics

Michael McComas

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Target audience:          All content areas:  Pre-K to College

Writing Process:          journaling, informal writing, reflective writing

Assessment:                self-assessment, peer assessment, and informal teacher assessment

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Introduction:
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While this will be an introductory lesson on solving linear equations in one-variable for students enrolled in developmental algebra at the college level, this technique could be used as an opening lesson for many content areas and different grade levels.  This lesson demonstrates an instructional cycle consisting of:  entry, construction, negotiation, practice, and reflection. There will be an entry into the lesson which provides opportunities to make connections with what they already know, student construction of knowledge through inductive reasoning, social negotiation where students actively participate in the creation of mathematics materials, practice, and reflection on the whole process from the opening journal write to completion of an assignment.Â

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Students often think or feel that mathematics is a long list of unrelated rules that they memorize for each class or exam; this type of instructional cycle requires students to make their own rules and connections and allows them to be active participants in the teaching and learning process.

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The Process:
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1.         Entry.  This instructional strategy will be journal writing:   “The primary purposes of the entry are to focus students’ attention on the learning activity, prepare them for what they are going to learn and encourage them to get involved” (Kindsvatter,   Wilen, & Isher, 1988, p.103).  Research shows that students learn more when they can make connections between learned material and new material (Smilkstein, 1991, p.13).   I want to give students the opportunity to make those connections before I introduce on new rules or processes.Â

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Students will view a set of equations and write a journal entry on the material in response to various prompts.   Journal prompts include:  Have you seen these types of problems?  When?  Where?  Are there similarities and/or differences?  How many can you solve?  If you can’t, where would you go look to help solve them?

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2.         Construction.  This instructional strategy will be inductive reasoning, a technique requiring active participation by learners.  According to J. Countryman, “Math is an active process, you will never know if you sit and wait for the teacher to tell you” (as cited in Zinsser, 1988, p. 152).  Students, working together in pairs, will go to www.mgmccomas.net , click on A National Library of Virtual Manipulatives , and then click on Algebra Balance Scales – Negatives.  I will demonstrate use of the website by completing an example and then ask students to practice their own problems.  After a period of play, I will ask student pairs to develop rules for solving linear equations in one-variable.  Through this active learning, students will construct new knowledge (Smilkstein, 1991).   Students will be given the opportunity to put this learning into practice by solving several linear equations and creating some equations for their partner to complete.Â

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3.         Negotiation.  As a whole group the class will share the rules developed in pairs and from those develop one set of rules for solving equations.  This is the point in the instructional cycle where the teacher must use his/her skills in incorporating the various individual or small group rules into one set of rules or guidelines to solve linear equations.  This represents the application of Vygotsky’s zone of proximal development, or the point at which learners require assistance to complete task (Gallagher, 1999).Â

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4.         Practice.  Students would complete a homework set solving linear equations.  It is very important for students to practice; math often looks easy when others are working the problems.  Brophy and Goode state that “academic success is influenced by the amount of time that students spend on appropriate tasks” (as cited in Cohen, 1995, p.15).

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5.         Reflection.  Write a reflective piece on the activity and the homework assignment.  Prompts could include:  are the homework problems related to classroom activity?  What did you learn?  What did you already know?  What are you missing? These journal entries could be shared to start the next day and get everyone quickly focused on the lesson (Hirt, 1999).

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Writing allows the student to explore their own thought process and find out what they do and don’t know about a particular process (Countryman, 1992). Journaling is an active learning process that continues outside the classroom.Â

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Applications
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This is an exercise that is useful to introduce new concepts for any content course.  As a pre-test, teachers will learn much more about student knowledge than possible with an objective test.  With this learning activity multiply standards can be met, here are examples of AMAYTC standards that can be met by this activity.   Â

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Standard P-2:  Teaching with Technology

Mathematics faculty will model the use of appropriate technology in the teaching of mathematics so that students can benefit from the opportunities it presents as a medium of instruction (Cohen, 1995, p.15).

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Standard P-2:  Interactive and Collaborative Learning

Mathematics faculty will foster interactive learning through student writing, reading, speaking, and collaborative activities so that students can learn to work effectively in groups and communicate about mathematics both orally and in writing (Cohen, 1995, p.16).

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Conclusion
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You now have a quick and easy method for starting new units.Â

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1.                  Journaling to make connections to previous material, allowing the student and teacher to view the connection process and making students stop and think.

2.                  Use active learning manipulatives to develop concepts.

3.                  Use of small groups promotes active learning.

4.                  Practice.

5.                  Reflective writing to provide informal assessment for the student and the teacher.

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References
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Cohen, D. (Ed.). (1995). Crossroads in mathematics:  Standards for introductory college mathematics before calculus.  Memphis, TN:  American Mathematical Association of Two-Year Colleges.

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Countryman, J.  (1992). Writing to Learn Mathematics. New Hampshire, MA., Heinemann.

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Gallagher, C.  (1999).  Lev Semyonovich Vygotsky. Retrieved July 9, 2006, from http://www.muskingum.edu/~psych/psycweb/history/vygotsky.htm#Theory

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Kindsvatter, R., Wilen, W., & Isher, M., (1988). Dynamics of effective teaching.  New York & London: Longman.

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Smilkstein, R. (1991).  A natural teaching method based on learning theory.  Gamut, p.12-15, 36.

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Zinsser, W. (1989).  Writing to Learn.  New York, NY.  Harper & Row Publishers.

Other Resources
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Goswami, D. & Stillman, P. (Eds.). (1987) Reclaiming the classroom:  Teacher research as an agency for change.  Portsmouth, NH:  Heinemann.

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Hester, J. (1994).  Teaching for thinking:  A program for school improvement through teaching critical thinking across the curriculum. Durham, NC: Carolina Academic Press.

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Hirt, D. (1999). Encouraging Active learning: Adding a journal to engineering lecture course. In S. Gardner & T. Fulwiler(Eds.). The journal book. (pp. 42-50).  Portsmouth, NH: Boynton/Cook Publishers.

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Smilkstein, R. (1989).  The natural process of learning and critical thinking.  Gamut,  26-29, 38.

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Smilkstein, R. (1993).  Acquiring knowledge and using it.  Gamut, 16-17, 41-43.

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Smith, C. (1991).  A commitment to critical thinking.  Bloomington, IN:  Grayson Bernard Publishers.

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Electronic Library
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Collaborative Learning. (2000). Digital Library for Earth System Education.  DLESE Workshop.  Retrieved from the World Wide Web July 9, 2006. http://www.dlese.org/annualmtg/AnnualMtg2000/sessionwreport.html

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Mathcast. (2006) Mathcasts are screencasts (screen movies of writing with voice) that focus on mathematics.  Retrieved from the World Wide Web July 9, 2006.  http://www.mathcasts.org/index.php?title=Main_Page
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Principles and Standards for School Mathematics. (2006)  National Council of Teachers of Mathematics.  Retrieved from World Wide Web July 8, 2006. http://standards.nctm.org/

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Social Constructivism. (2006) Graduate Student Teaching & Resource Center.  Retrieved from the World Wide Web July 9, 2006. http://gsi.berkeley.edu/resources/learning/social.html

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Social Development Theory  (L. Vygotsky).  (  ) Theory into Practice.  Retrieved from the World Wide Web July 9, 2006. http://tip.psychology.org/vygotsky.html

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Vygotsky and Social Cognition. (2001) Funderstanding.  Retrieved from World Wide Web July 9, 2006.  http://www.funderstanding.com/vygotsky.cfm