Strategies to Promote Motivation in the Mathematics Classroom
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1 Strategies to Promote Motivation in the Mathematics Classroom TASEL-M August Institute 2006
2 Motivation in the Math Classroom In pairs discuss:What, ideally, does student involvement in learning mathematics look and feel like from…your perspective as a teacher?the perspective of your students?
3 Research on Motivation Guiding question: What factors promote (or discourage) students’ involvement in thinking about and developing an understanding of math?“Involvement” is more than being physically on-taskFocused concentration and care about things making senseIntrinsically motivated to persistCognitively engaged and challengedTwo areas of focus:Cognitive Demand of Mathematical TasksDiscourse StrategiesReferencesHenningsen & Stein (1997). Mathematical tasks and student cognition. Journal for Research in Mathematics Education, 28(5),Turner et al. (1998). Creating contexts for involvement in mathematics. Journal of Educational Psychology, 90(4),
4 Mathematical Tasks What is cognitive demand? Focus is on the sort of student thinking required.Kinds of thinking required:MemorizationProcedures without ConnectionsRequires little or no understanding of concepts or relationships.Procedures with ConnectionsRequires some understanding of the “how” or “why” of the procedure.Doing MathematicsLower levelHigher level
5 Examples of Mathematical Tasks (1) MemorizationWhich of these shows the identity property of multiplication?A) a x b = b x aB) a x 1 = aC) a + 0 = aProcedures without ConnectionsWrite and solve a proportion for each of these:A) 17 is what percent of 68?B) 21 is 30% of what number?Too much of a focus on lower level tasks discourages student “involvement” in learning mathematics.
6 Examples of Mathematical Tasks (2) Procedures with ConnectionsSolve by factoring: x2 – 7x + 12 = 0Explain how the factors of the equation relate to the roots of the equation. Use this information to draw a sketch of the graph of the function f(x) = x2 – 7x + 12.Doing MathematicsDescribe a situation that could be modeled with the equation y = 2x + 5, then make a graph to represent the model. Explain how the situation, equation, and graph are interrelated.Higher level tasks, when well-implemented, promote “involvement” in learning mathematics.
7 Characteristics of Higher-Level Mathematical Tasks Higher-level tasks require students to…do more than computation.extend prior knowledge to explore unfamiliar tasks and situations.use a variety of means (models, drawings, graphs, concrete materials, etc…) to represent phenomena.look for patterns and relationships and check their results against existing knowledge.make predictions, estimations and/or hypotheses and devise means for testing them.demonstrate and deepen their understanding of mathematical concepts and relationships.
8 The Border ProblemWithout counting 1-by-1 and without writing anything down, calculate the number of shaded squares in the 10 by 10 grid shown.Determine a general rule for finding the number of shaded squares in any similar n by n grid.
9 Video Case: Building on Student Ideas The Border ProblemWhat might be the lesson’s goals and objectives?What is the cognitive demand of the task (as designed)?As you watch, consider:Who is doing most of the thinking?How does the teacher support student “involvement”?After watching, think about:What sort of planning would this lesson require?From: Boaler & Humphreys (2006). Connecting mathematical ideas. Portsmouth, NH: Heinemann.
10 Discourse Strategies (less involvement): I-R-E Initiation-Response-Evaluation (I-R-E)Ask a known-answer questionEvaluate a student response as right or wrongMinimize student interaction through prescribed “turn taking”Establish the authority of the text and teacherExamplesWhat is the answer to #5?What are you supposed to do next?What is the reciprocal of 3/5? 5/3. Very good!That is exactly what the book says.
11 Discourse Strategies (less involvement): Procedures Give directionsImplement proceduresTell students how to think and actExamplesListen to what I say and write it down.Take out your books and turn to page 45.
12 Discourse Strategies (less involvement): Extrinsic Support Superficial statements of praise (focus is not on the learning goals and objectives)Threats to gain complianceExamplesYou have such neat handwriting.These scores are terrible. I was really shocked.If you don’t finish up you will stay after class.
13 Discourse Strategies (more involvement): Intrinsic Support View challenge/risk taking as desirableRespond to errors constructivelyComment on students’ progress toward the learning goals and objectivesEvoke students’ curiosity and interestExamplesThat's great! Do you see what she did for #5?This may seem difficult, but if you stay with it you'll figure it out.Good. You figured out the y-intercept. How might we determine the slope here?
14 Discourse Strategies (more involvement): Negotiation Adjust instruction in response to studentsModel strategies students might useGuide students to deeper understandingExamplesWhat information is needed to solve this problem?Try to break the problem into smaller parts.Here is an example of how I might approach a similar problem.
15 Discourse Strategies (more involvement): Transfer Responsibility Support development of strategic thinkingEncourage autonomous learningHold students accountable for understandingExamplesExplain the strategy you used to get that answer.You need to have a rule to justify your statement.Why does Norma’s method work?
16 Reflecting on Instructional Practices: Creating a Self-Inventory Rubric How you can strengthen the ways student involvement and motivation are promoted and supported in your classes?Write 3-5 statements about specific strategies you’d like to work to improve this year.Draw ideas from On Common Ground, TARGET TiPS, motivation data, and Motivation in the Classroom presentationExamples:“I give students tasks that require them to think about mathematical relationships and concepts.”“I provide feedback to students that promotes further thinking and improved understanding.”“I allow opportunities for students to be an authority in mathematics.”Identify where you are now and where you want to be.