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

Journal Writing in the Mathematics Classroom: A Beginner’s Approach by Nancy B.Williams and Brian D. WynneAssessing a student's understanding of mathematics should include more than just grades on atest. Journal writing will allow teachers to give and get feedback on a student's understandingwhile allowing them to explain in writing their thoughts. The topics for journals can be alternatedto include mathematical responses and affective responses. All procedures should be described ina syllabus.Thinking About Being a Mathematics TeacherAs future mathematics teachers, we should look at the reasons why we have chosen to go intothis profession. Chances are, there are many reasons that factor into our decision. This all stemsfrom our view of mathematics, and we should look at the possible views of math becauseeveryone is different. Some view mathematics as a communicative process, some believe it to bemainly about reasoning. Still, others view math as purely problem solving or about makingconnections. Everyone has his or her own opinion of math, which stems from cultural diversity.As math teachers we should keep in mind that what we teach and assess typically reflects ourview of math and what the students will learn.Introducing the Critical Features of ClassroomsThe unclear nature of the changing world requires that students be able to understand math.There are two cognitive processes that are key in students’ efforts to understand math- reflectionand communication. There are five dimensions that play a prominent role in defining classroomsin terms of the kind of learning that they afford. All five dimensions- the nature of classroomtasks, the role of the teacher, the social culture of the classroom, math tools as learning supports,and equity and accessibility- and the critical features within each are needed for thesystem to work.The Nature of Classroom TasksIf teachers would like students to understand, then be sure they are reflecting on what they aredoing and communicating about it to others. Tasks are key. When deciding whether a task isappropriate, it is helpful to look at the way in which goals students set. These goals will shapethe task and the kind of mathematical understandings that are likely to be left behind, or residue.Students should also see ways to begin the task using the tools they already possess. Students candevelop their own methods for problem solving as well.Ch. 1: Analyzing Mathematics Instructional TasksIn this article, tasks are examined in terms of their cognitive demands. There are different levelsof cognitive demand, in which it is important to vary tasks with respect to these levels.Determining the level of cognitive demand is important, although sometimes difficult. A tasksortingactivity considers how and why tasks differ and how these differences can impactopportunities for student learning can be helpful.Ch. 2: Using Cognitively Complex Tasks in the ClassroomSimply selecting and beginning a lesson with a high level task did not guarantee that studentwould actually think and reason in cognitively complex ways. If tasks maintained a high level ofcognitive demand on students, five support factors were typically seen in the classroom

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.