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# Problem solving powerpoint no narration

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## Problem solving powerpoint no narrationPresentation 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
• 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
• -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
• 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
• 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
• 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 http://www.cimt.plymouth.ac.uk/journal/chamberlin.pdf
• 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 http://www.cimt.plymouth.ac.uk/journal/klavir.pdf
• 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 http://www.cimt.plymouth.ac.uk/journal/osta.pdf
• 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