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    Problem solving powerpoint no narration Problem solving powerpoint no narration Presentation Transcript

    • Susan Hewett MAED 5040
      • The process of overcoming difficulties that possibly interfere with the attainment of a goal.
      • Originally, I had planned to focus on the difficulties with problem solving
      • However, I narrowed the information down to open ended problems and problem based learning
      • A problem with multiple ways to solve
      • A problem with multiple solutions
      • A scenario is given to students who use reasoning, questioning, and critical thinking to determine a solution (Cerezo, 2004)
      • Small groups receive a scenario with multiple solutions; together they must determine the solution and defend their answer (Belland, 2010)
      • An approach where students apply textbook knowledge to case study situations (Chamberlin & Moon, 2008)
      • 273 7 th grade students
      • Students presented with problem:
      • “ There are 3 jugs, A, B, and C. Find the best way of measuring out a given quantity of water using these jugs.
      • Many looked for and used a pattern within answers
      • A second problem about a circle with an inscribed hexagon was presented.
      • Students were asked to “write as many ideas as …[possible] about the figure”
      • Statements scored based on 3 criteria
      • Students who did not use the same pattern for the first problem did better on the second problem.
      • Students who avoid a pattern are able to develop original ideas in an open ended problem in mathematics
      • 90 4 th graders
      • Compares multiple choice and open ended problems
      • Data analyzed through use of written and verbal responses from students
      • Some students received multiple choice first, some open ended first
      • Problems were based on those that are given on state assessment every year
      • Multiple choice leads to focus on choices, not answer to question in problem
      • Open ended questions do not usually rely on learned algorithms and shortcuts that can apply and usually work
      • Students more likely to solve problem when open ended
      • 14 at risk females in grades 6-8
      • Attended various schools within the same system
      • Currently using problem based learning in classes
      • Selected because they are at risk, but like using problem based learning
      • Presented math or science situation to solve.
      • Collaboration in small group, followed by group presentation
      • Students willing to participate in group work and in presentation
      • Students interviewed about problem based learning
      • Problem based learning:
      • -enhances self-confidence
      • -leads to better organization
      • -increased student's attention
      • -students better able to process information
      • -real life applications
      • -more willing to participate
      • Small sample size
      • already using problem based learning
      • Selected students liked problem based learning
      • 12 7 th grade students, taught in French
      • Looked at thinking of students
      • As students worked, they were asked to talk through their reasoning and explanations
      • Only a few students solved problem correctly
      • Students preferred informal strategies to formal algebraic ones
      • Main strategy chosen was Trial and Error
      • Most students solved the problem using non-algebraic techniques
      • Strategies used:
      • Estimation and guess and check
      • Trial and error
      • Forward operations
      • Work backwards
      • Write a numerical sentence
      • Write an algebraic equation
      • Small sample size
      • Analyzing thinking is very subjective
      • Presence of researcher as students work problems
      • Not a true research study
      • Presents information comparing problem based learning and model eliciting approach
      • Apply textbook knowledge to real life situations
      • Discusses pros and cons of problem based learning
      • Realistic
      • Leads to creativity
      • Higher order thinking
      • Teacher as facilitator
      • Learn via discovery
      • Self-directed learning
      • Interconnectedness
      • Collaboration
      • Self-assessment
      • Time
      • Don’t focus on single discipline
      • Mathematical models may or may not be used
      • Must be used regularly
      • 164 5 th graders
      • Problems were presented via Internet, but work was done in classroom supervised by homeroom teacher
      • Students were given the following problem:
      • Which of the following numbers: 15, 20, 23, 25 does not belong? Explain why.
      • Open ended problem breaks away from stereotype that there is only one solution
      • The variety of solutions and the reasons were studied
      • 24 6 th grade students
      • Low achieving students
      • Involved after school program
      • Used manipulatives
      • Students worked in groups on given problems
      • Each small group developed their own arguments and justifications
      • Students were eager to share findings
      • Students corrected one another
      • Small sample size
      • Setting
      • Participants
      • 79 7 th grade students
      • Use of computer technology and scaffolding
      • Study not related to math classes
      • Specifically focused on the development of arguments
      • More beneficial to low and average achievers
      • Scaffolding kept groups organized
      • Students stayed focused
      • Involved graduate students and 9 th and 10 th grade students
      • Focused on how to teach problem solving
      • Used individual teacher’s lessons and observations
      • The teachers did not always hear the reasoning of students when an alternative solution was given
      • Teachers were unable to select problems that conveyed what they wanted
      • There must be a connection between different topics
      • At the end of the study, the problems were no longer a means of memorizing and applying a formula, but became a tool for investigation by students.
      • Saturday
      • Graduate students
      • 48 10 th grade females
      • Control and experimental groups were determined on basis of pre-test scores
      • 2 teachers
      • Primary grades usually use expository teaching methods for math
      • Problem solving techniques leads to students integrating the content
      • Problem solving methods have become the “norm” in math classes
      • Experimental group showed larger gains
      • Interesting side note : experimental group was actually a combination of expository and problem-solving
      • Reasons : -students lacked basic math skills
      • -caused students to have difficulty
      • Small sample size
      • Location of school in Pakistan
      • Lack of basic skills prior to study
      • Students hesitant to change how they learn
      • 110 3 rd graders, placed in 2 groups
      • Pre-test
      • 7 weeks
      • Computer software
      • Motivated students
      • All students solve problems
      • Use regularly with non-routine problems
      • Justify explanations
      • Work collaboratively
      • Multiple solutions or methods
      • Time to implement
      • Greater achievement
      • Real life applications
      • Belland, B. (2010). Portraits of middle school students constructing evidence-based arguments during problem-based learning: the impact of computer-based scaffolds. Educational Technology Research & Development , 58 (3), 285-309. doi:10.1007/s11423-009-9139-4.
      • Cerezo, N. (2004). Problem-based learning in the middle school: A research case study of the perceptions of at-risk females. Research in Middle Level Education Online , 27 (1), 20-42. Retrieved from Education Research Complete database.
      • Chamberlin, S. A. , & Moon, S. M. (2008). How does the problem based learning approach compare to the model-eliciting activity approach in mathematics?. International Journal for Mathematics Teaching and Learning , Nov 28 . Retrieved from
      • Imai, T. (2000). The influence of overcoming fixation in mathematics towards divergent thinking… International Journal of mathematical Education in Science and Technology , 31(2), 187 – 193. Retrieved from Education Research Complete database.
      • Karp, A. (2010). Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction. Journal of Mathematics Teacher Education , 13 (2), 121-139. doi:10.1007/s10857-009-9127-y.
      • Kazemi, E. (2002). Exploring test performance in mathematics: the questions children’s answers raise. Journal of Mathematical Behavior , 21 (2), 203. Retrieved from Education Research Complete database.
      • Klavir, R., & Hershkovitch, S. (2008). Teaching and evaluating ‘open-ended’ problems. International Journal for Mathematics Teaching and Learning , May 20 . Retrieved from
      • Mueller, M., & Masher, C. (2009). Learning to Reason in an Informal Math After-School Program. Mathematics Education Research Journal , 21 (3), 7-35. Retrieved from Education Research Complete database
      • Osta, I., & Labban, S. (2007). Seventh graders' prealgebraic problem solving strategies: geometric, arithmetic, and algebraic interplay. International Journal for Mathematics Teaching and Learning , Nov 28 . Retrieved from
      • Perveen, K. (2010). Effect Of The Problem-Solving Approach On Academic Achievement Of Students In Mathematics At The Secondary Level. Contemporary Issues in Education Research , 3 (3), 9-13. Retrieved from Education Research Complete database.
      • Schoppek, W., & Tulis, M. (2010). Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice. Journal of Educational Research , 103 (4), 239-252. Retrieved from Education Research Complete database