Problem solving powerpoint


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a description of different research on problem solving

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Problem solving powerpoint

  1. 1. Susan Hewett MAED 5040
  2. 2. <ul><li>The process of overcoming difficulties that possibly interfere with the attainment of a goal. </li></ul>
  3. 3. <ul><li>Originally, I had planned to focus on the difficulties with problem solving </li></ul><ul><li>However, I narrowed the information down to open ended problems and problem based learning </li></ul>
  4. 4. <ul><li>A problem with multiple ways to solve </li></ul><ul><li>A problem with multiple solutions </li></ul>
  5. 5. <ul><li>A scenario is given to students who use reasoning, questioning, and critical thinking to determine a solution (Cerezo, 2004) </li></ul><ul><li>Small groups receive a scenario with multiple solutions; together they must determine the solution and defend their answer (Belland, 2010) </li></ul><ul><li>An approach where students apply textbook knowledge to case study situations (Chamberlin & Moon, 2008) </li></ul>
  6. 6.
  7. 7. <ul><li>273 7 th grade students </li></ul><ul><li>Students presented with problem: </li></ul><ul><li>“ There are 3 jugs, A, B, and C. Find the best way of measuring out a given quantity of water using these jugs. </li></ul><ul><li>Many looked for and used a pattern within answers </li></ul>
  8. 8. <ul><li>A second problem about a circle with an inscribed hexagon was presented. </li></ul><ul><li>Students were asked to “write as many ideas as …[possible] about the figure” </li></ul><ul><li>Statements scored based on 3 criteria </li></ul><ul><li>Students who did not use the same pattern for the first problem did better on the second problem. </li></ul>
  9. 9. <ul><li>Students who avoid a pattern are able to develop original ideas in an open ended problem in mathematics </li></ul>
  10. 10. <ul><li>90 4 th graders </li></ul><ul><li>Compares multiple choice and open ended problems </li></ul><ul><li>Data analyzed through use of written and verbal responses from students </li></ul>
  11. 11. <ul><li>Some students received multiple choice first, some open ended first </li></ul><ul><li>Problems were based on those that are given on state assessment every year </li></ul>
  12. 12. <ul><li>Multiple choice leads to focus on choices, not answer to question in problem </li></ul><ul><li>Open ended questions do not usually rely on learned algorithms and shortcuts that can apply and usually work </li></ul><ul><li>Students more likely to solve problem when open ended </li></ul>
  13. 13. <ul><li>14 at risk females in grades 6-8 </li></ul><ul><li>Attended various schools within the same system </li></ul><ul><li>Currently using problem based learning in classes </li></ul><ul><li>Selected because they are at risk, but like using problem based learning </li></ul>
  14. 14. <ul><li>Presented math or science situation to solve. </li></ul><ul><li>Collaboration in small group, followed by group presentation </li></ul><ul><li>Students willing to participate in group work and in presentation </li></ul><ul><li>Students interviewed about problem based learning </li></ul>
  15. 15. <ul><li>Problem based learning: </li></ul><ul><li>-enhances self-confidence </li></ul><ul><li>-leads to better organization </li></ul><ul><li>-increased student's attention </li></ul><ul><li>-students better able to process information </li></ul><ul><li>-real life applications </li></ul><ul><li>-more willing to participate </li></ul>
  16. 16. <ul><li>Small sample size </li></ul><ul><li>already using problem based learning </li></ul><ul><li>Selected students liked problem based learning </li></ul>
  17. 17. <ul><li>12 7 th grade students, taught in French </li></ul><ul><li>Looked at thinking of students </li></ul><ul><li>As students worked, they were asked to talk through their reasoning and explanations </li></ul>
  18. 18. <ul><li>Only a few students solved problem correctly </li></ul><ul><li>Students preferred informal strategies to formal algebraic ones </li></ul><ul><li>Main strategy chosen was Trial and Error </li></ul>
  19. 19. <ul><li>Most students solved the problem using non-algebraic techniques </li></ul><ul><li>Strategies used: </li></ul><ul><li>Estimation and guess and check </li></ul><ul><li>Trial and error </li></ul><ul><li>Forward operations </li></ul><ul><li>Work backwards </li></ul><ul><li>Write a numerical sentence </li></ul><ul><li>Write an algebraic equation </li></ul>
  20. 20. <ul><li>Small sample size </li></ul><ul><li>Analyzing thinking is very subjective </li></ul><ul><li>Presence of researcher as students work problems </li></ul>
  21. 21. <ul><li>Not a true research study </li></ul><ul><li>Presents information comparing problem based learning and model eliciting approach </li></ul><ul><li>Apply textbook knowledge to real life situations </li></ul><ul><li>Discusses pros and cons of problem based learning </li></ul>
  22. 22. <ul><li>Realistic </li></ul><ul><li>Leads to creativity </li></ul><ul><li>Higher order thinking </li></ul><ul><li>Teacher as facilitator </li></ul><ul><li>Learn via discovery </li></ul><ul><li>Self-directed learning </li></ul><ul><li>Interconnectedness </li></ul><ul><li>Collaboration </li></ul><ul><li>Self-assessment </li></ul>
  23. 23. <ul><li>Time </li></ul><ul><li>Don’t focus on single discipline </li></ul><ul><li>Mathematical models may or may not be used </li></ul><ul><li>Must be used regularly </li></ul>
  24. 24. <ul><li>164 5 th graders </li></ul><ul><li>Problems were presented via Internet, but work was done in classroom supervised by homeroom teacher </li></ul>
  25. 25. <ul><li>Students were given the following problem: </li></ul><ul><li>Which of the following numbers: 15, 20, 23, 25 does not belong? Explain why. </li></ul><ul><li>Open ended problem breaks away from stereotype that there is only one solution </li></ul><ul><li>The variety of solutions and the reasons were studied </li></ul>
  26. 26. <ul><li>24 6 th grade students </li></ul><ul><li>Low achieving students </li></ul><ul><li>Involved after school program </li></ul><ul><li>Used manipulatives </li></ul>
  27. 27. <ul><li>Students worked in groups on given problems </li></ul><ul><li>Each small group developed their own arguments and justifications </li></ul><ul><li>Students were eager to share findings </li></ul><ul><li>Students corrected one another </li></ul>
  28. 28. <ul><li>Small sample size </li></ul><ul><li>Setting </li></ul><ul><li>Participants </li></ul>
  29. 29. <ul><li>79 7 th grade students </li></ul><ul><li>Use of computer technology and scaffolding </li></ul><ul><li>Study not related to math classes </li></ul><ul><li>Specifically focused on the development of arguments </li></ul>
  30. 30. <ul><li>More beneficial to low and average achievers </li></ul><ul><li>Scaffolding kept groups organized </li></ul><ul><li>Students stayed focused </li></ul>
  31. 31. <ul><li>Involved graduate students and 9 th and 10 th grade students </li></ul><ul><li>Focused on how to teach problem solving </li></ul><ul><li>Used individual teacher’s lessons and observations </li></ul>
  32. 32. <ul><li>The teachers did not always hear the reasoning of students when an alternative solution was given </li></ul><ul><li>Teachers were unable to select problems that conveyed what they wanted </li></ul><ul><li>There must be a connection between different topics </li></ul><ul><li>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. </li></ul>
  33. 33. <ul><li>Saturday </li></ul><ul><li>Graduate students </li></ul>
  34. 34. <ul><li>48 10 th grade females </li></ul><ul><li>Control and experimental groups were determined on basis of pre-test scores </li></ul><ul><li>2 teachers </li></ul>
  35. 35. <ul><li>Primary grades usually use expository teaching methods for math </li></ul><ul><li>Problem solving techniques leads to students integrating the content </li></ul><ul><li>Problem solving methods have become the “norm” in math classes </li></ul>
  36. 36. <ul><li>Experimental group showed larger gains </li></ul><ul><li>Interesting side note : experimental group was actually a combination of expository and problem-solving </li></ul><ul><li>Reasons : -students lacked basic math skills </li></ul><ul><li> -caused students to have difficulty </li></ul>
  37. 37. <ul><li>Small sample size </li></ul><ul><li>Location of school in Pakistan </li></ul><ul><li>Lack of basic skills prior to study </li></ul><ul><li>Students hesitant to change how they learn </li></ul>
  38. 38. <ul><li>110 3 rd graders, placed in 2 groups </li></ul><ul><li>Pre-test </li></ul><ul><li>7 weeks </li></ul><ul><li>Computer software </li></ul>
  39. 39. <ul><li>Motivated students </li></ul><ul><li>All students solve problems </li></ul>
  40. 40. <ul><li>Use regularly with non-routine problems </li></ul><ul><li>Justify explanations </li></ul><ul><li>Work collaboratively </li></ul><ul><li>Multiple solutions or methods </li></ul><ul><li>Time to implement </li></ul><ul><li>Greater achievement </li></ul><ul><li>Real life applications </li></ul>
  41. 41. <ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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 </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>Klavir, R., & Hershkovitch, S. (2008). Teaching and evaluating ‘open-ended’ problems. International Journal for Mathematics Teaching and Learning , May 20 . Retrieved from </li></ul>
  42. 42. <ul><li>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 </li></ul><ul><li>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 </li></ul><ul><li>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. </li></ul><ul><li>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 </li></ul>