Journal Writing in the Mathematics Classroom: A ... - Oncourse

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environment. Tasks that declined in the level of cognitive demand, the tasks declined intoprocedures without connection to meaning, unsystematic exploration ornonmathematical activity.Ch. 1 and 2 of Principles and Standards for School Mathematics by NCTMDecisions made by teachers, school administrators and other education professionals about thecontent and character of school mathematics have important consequences both for students andfor society. The Principles of equity, curriculum, teaching, learning, assessment and technologyprovide guidance on describing particular features of high-quality mathematics education.Ch. 8: Using Algebra Tiles to Multiply Monomials and BinomialsMonique’s goal for her students is that they should understand the concepts underlying thecommon algorithm for multiply monomials and binomials. Monique wants her students to buildtheir understanding of algebraic operations using algebra tiles. However, she succumbs to thepressure of an upcoming district test and tries to expedite the students’ learning process by firstshowing them a shortcut algorithm (FOIL) for multiplying binomials prior to their experienceswith the manipulatives. At the end of the lesson, Monique wonders whether the students weremaking the connections she hoped they would.Developing Understanding through Problem Solving by James Hiebert and Diana WearneValuing deep understanding of mathematics is an important goal for students. Problem solvingleads to understanding. Thus, one way to support students’ efforts to understand is to allowmathematics to be problematic for them. Struggling, in a healthy sense and on the right kinds ofproblems for an appropriate amount of time, prepares students to make sense of relevantinformation, to piece together things in new ways and to see the benefits of bettermethods of solution.Mathematics as Sense Making by Jeremy A. Kahan and Terrence R. WybergTeaching math through problem solving begins by identifying the important mathematics that thestudents are to learn. We value students’ mathematical understanding resulting from teachingthrough problem solving. By making sense of and solving well-chosen problems with gentleguidance from an effective teacher, students encounter mathematics, making connections andmathematical thinking that are useful and important as well as rich and beautiful. Finally,problems should be accessible and engaging to students.The Sound of Problem Solving by Mark DriscollIn engaging students as they learn mathematics through problem solving a teacher should listenwith the intention of understanding students’ thinking. In addition, this article suggests that theterm student work should include what we hear as well as what we see. Arguably, goodmathematics teachers do all kinds of listening at different times for different purposes. Questionscan help shape the kinds of responses the teacher will hear and will help create a purpose forlistening. The impact of consistent, purposeful listening, especially in a problem-basedclassroom, can be a powerful way to elicit and understand students’ mathematical thinking.
Using Bloom’s Taxonomy as a Framework for Classroom Assessment by Signe E. KastbergThe author of this article used Bloom’s Taxonomy as a framework for classroom assessment.The framework is based on the content that she teaches and the processes that she believes arenecessary to demonstrate a mastery of that content. She used a content-by-process matrix tomake sure what she taught and assessed matched. Each cell in the matrix represents importantmathematics content and processes that students might use with the content.Making the NCTM’s Standards Work for Emergent English Speakers by Leslie GarrisonThis article describes how teachers can include elements of bilingual instruction to bolstermathematics instruction. These elements, such as working in groups, teaching appropriatevocabulary, encouraging students to express their thoughts in writing developing a meaningfulcontext, and challenging students’ reasoning skills, are also the benefit of good instruction; theyalso benefit all students. These elements promote the NCTM’s principles of mathematicsas problem-solving, mathematics as communication, mathematics as reasoningand mathematical connections.Changing Assessment Practices in an Algebra Class, or “Will This Be on the Test?”by Tricia MurphyWhen Tricia Murphy began teaching college algebra at her high school she realized that thiscourse in its traditional form was a filter: rote skills, symbol manipulation, little or noapplication- preparation for doing well in the “next class.” She began asking her students tofigure things out on their own, to make connections and to make sense of the mathematics thatthey were learning. However, the students were only worried about the problems on the test, sothey asked, “Will this be on the test?” She realized that she needed to change her assessments sothat the assessments matched instruction. She replaced her traditional assessment rather than addalternative assessments.
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Journal Writing in the Mathematics Classroom: A ... - Oncourse

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