Mathematics Achievement Academy, Problem Solving And Discourse, Grade 2 .
MATHEMATICS ACHIEVEMENTACADEMY: PROBLEM SOLVING ANDDISCOURSE, GRADE 2Day 1: Problem Solving andMathematical ReasoningAcademy CelebrationsShare a student success story based on aMathematics Achievement Academy activity,strategy, or tool.1
Welcome! Intended outcomes Learning intentionsand success criteriaResources and MaterialsTexas Gatewayhttp://www.texasgateway.org/ Mathematics TEKS: Supporting Information Vertical Alignment ChartsNormsParticipationDiscourseMathematics2
NormsNorms How will we hold each otheraccountable for the norms? What is a cue we can use toremind each other of the normsif a norm is broken?Academic VocabularyHeuristicProblem-Solving Model: Analyzing given information Formulating a plan Determining a solution Justifying the solution Evaluating the problem-solving process and thereasonableness of the solutionMathematics TEKS 3(1)(B)3
Academy Pre-AssessmentProblem SolvingThe Classroom ChallengeYou have been given a teaching assignmentwhere you can request only five items to usein your classroom.What five items would you choose?Surprise!Problem SolvingProblem Solving in Everyday Life4
Problem SolvingProblem solving means engaging in a taskfor which the solution method is not knownin advance. In order to find a solution,students must draw on their knowledge, andthrough this process, they will often developnew mathematical understandings. Solvingproblems is not only a goal of learningmathematics, but also a major means ofdoing so.NCTM, 2000, p. 52Proficient Problem SolversWhat actions are completed by proficientproblem solvers?Proficient Problem SolversStudents who can both develop and carry outa plan to solve a mathematical problem areexhibiting knowledge that is much deeper andmore useful than simply carrying out acomputation. Unless students can solveproblems, the facts, the concepts, andprocedures they know are of little use.NCTM, 2000, p. 1825
What is Problem Solving?What are heuristics?What is Problem Solving?2(1)(B) The student is expected to use aproblem-solving model that incorporatesanalyzing given information, formulating aplan or strategy, determining a solution,justifying the solution, and evaluating theproblem-solving process and thereasonableness of the solution.What is Problem Solving? What experiences with problem solving doyour students bring to school? Why is it important to be aware of theseexperiences?6
Jack’s Garden Does this situation have more than one solution?How do you know? When did you realize that more than one correctand appropriate solution was possible? Once you determined the number of bean plants,how did you determine the number of tomatoplants? Was more than one number of tomato plantspossible at this point? Why or why not?Jack’s GardenWhat actions of a proficient problem solverdo you see reflected in each of these worksamples?Connecting to aProblem-Solving Model2(1)(B) The student is expectedto use a problem-solving modelthat incorporates analyzinggiven information, formulating aplan or strategy, determining asolution, justifying the solutionand evaluating the problemsolving process and thereasonableness of the solution.7
Connecting to aProblem-Solving ModelStudents are expected to use this process ina grade-appropriate manner when solvingproblems that can be considered difficultrelative to mathematical maturity.TEA, 2018BreakConnecting to aProblem-Solving Model Analyzing word problems Representing word problems Solving word problems8
Party Line102Analyzing Given InformationWhat does it mean toanalyze giveninformation?What questions mightyou ask to promptstudents to analyzegiven information?Formulating a Plan or StrategyWhat does it mean toformulate a plan orstrategy?What questions might youask to prompt students toformulate a plan orstrategy?9
Determining the SolutionWhat does it mean todetermine a solution?What questions might you askto prompt students todetermine a solution?What questions might you askto prompt students todetermine if a solution isreasonable?Justifying the Solution and Evaluating theProblem-Solving ProcessWhat does it mean tojustify a solution andevaluate a problem-solvingprocess?What questions might youask to prompt students tojustify a solution andevaluate a problem-solvingprocess?Connecting to aProblem-Solving Model10
Connecting to theProblem-Solving ModelConnecting to theProblem-Solving ModelActivity for Sense Making Read the problem. Draw a representationthat can be used tosolve the problem.11
Activity for Sense MakingShare your representations andengage in questions that promotesense making in problem solving. How does this representationshow the relationships in theproblem? I agree/disagree with yourrepresentation because . . .Activity for Sense Making Choose a representation. Record your representationon chart paper. Add clarifying information.Activity for Sense MakingShare representations andengage in sense making inproblem solving.12
Activity for Sense MakingUse a representation tosolve the problem.Sense MakingHow might studying several representationshelp students make sense of problems?How might studying several representationshelp students when formulating a plan orstrategy as part of a problem-solvingheuristic?Promoting Sense Making in ProblemSolving13
Promoting Sense Making in ProblemSolvingClarifying Student UnderstandingsClarifying Student Understandings of Classmates’ ThinkingGradesK-1Grade2Verifying Student UnderstandingsVerifying Student Understandings of Classmates’ ThinkingCharacteristics of ProblemsWhat common characteristics do younotice?Exercise Versus ProblemAn exercise asks a student to practice afamiliar skill.A problem involves the application ofpreviously learned mathematical skills,concepts, and/or procedures to a situationwhere a solution process is not immediatelyapparent.14
Exercise Versus ProblemOnline Professional LearningOnline Professional Learning15
Exit Slip: Success Criteria16
What is Problem Solving? 2(1)(B) The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. What is Problem Solving?
can use problem solving to teach the skills of mathematics, and how prob-lem solving should be presented to their students. They must understand that problem solving can be thought of in three different ways: 1. Problem solving is a subject for study in and of itself. 2. Problem solving is
3.3 Problem solving strategies 26 3.4 Theory-informed field problem solving 28 3.5 The application domain of design-oriented and theory-informed problem solving 30 3.6 The nature of field problem solving projects 31 3.7 The basic set-up of a field problem solving project 37 3.8 Characteristics o
1. explain the roles of mathematics problem solving in primary school, 2. classify mathematical problems, 3. explain the steps of mathematics problem solving, 4. explain and use certain heuristics or strategies to solve certain mathematical problem, 5. explain the concept of problem -based learning, and 6. make a lesson plan for problem-based .
Combating Problem Solving that Avoids Physics 27 How Context-rich Problems Help Students Engage in Real Problem Solving 28 The Relationship Between Students' Problem Solving Difficulties and the Design of Context-Rich Problems 31 . are solving problems. Part 4. Personalizing a Problem solving Framework and Problems.
THREE PERSPECTIVES Problem solving as a goal: Learn about how to problem solve. Problem solving as a process: Extend and learn math concepts through solving selected problems. Problem solving as a tool for applications and modelling: Apply math to real-world or word problems, and use mathematics to model the situations in these problems.
The Problem Solving Inventory (PSI) [8] is a 35-item instrument (3 filler items) that measures the individual's perceptions regarding one's problem-solving abilities and problem-solving style in the everyday life. As such, it measures a person's appraisals of one's problem-solving abilities rather than the person's actual problem .
Problem solving ability is one of the cognit. ive abilities that must. be possessed by students. In addition, the problem-solving ability is one of the general goals of mathematics and is even known as the heart of mathematics. Problem solving skills are also basic skills in learning mathematics.
English/Language Arts 4. Grade Level i. Ninth grade 5. Length of Class Time i. 90 minute class 6. Length of Time to Complete Unit Plan th i. The unit on Non-fiction began on March 8 and was competed on March th 30 . The class had instruction on the topic everyday of the week. Student population Contextual/Environmental Factors Source Implications for Instruction and Assessment Rural School .
