Susan HewettMAED 5040

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The process of overcoming difficulties that possibly interfere with the attainment of a goal.

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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

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A problem with multiple ways to solve

A problem with multiple solutions

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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)

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273 7th 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

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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.

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Students who avoid a pattern are able to develop original ideas in an open ended problem in mathematics

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90 4th graders

Compares multiple choice and open ended problems

Data analyzed through use of written and verbal responses from students

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Some students received multiple choice first, some open ended first

Problems were based on those that are given on state assessment every year

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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

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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

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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

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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

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Small sample size

already using problem based learning

Selected students liked problem based learning

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12 7th grade students, taught in French

Looked at thinking of students

As students worked, they were asked to talk through their reasoning and explanations

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Only a few students solved problem correctly

Students preferred informal strategies to formal algebraic ones

Main strategy chosen was Trial and Error

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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

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Small sample size

Analyzing thinking is very subjective

Presence of researcher as students work problems

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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

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Realistic Leads to creativity Higher order thinking Teacher as facilitator Learn via discovery Self-directed learning Interconnectedness Collaboration Self-assessment

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Time

Don’t focus on single discipline

Mathematical models may or may not be used

Must be used regularly

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164 5th graders

Problems were presented via Internet, but work was done in classroom supervised by homeroom teacher

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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

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24 6th grade students

Low achieving students

Involved after school program

Used manipulatives

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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

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Small sample size

Setting

Participants

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79 7th grade students

Use of computer technology and scaffolding

Study not related to math classes

Specifically focused on the development of arguments

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More beneficial to low and average achievers

Scaffolding kept groups organized

Students stayed focused

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Involved graduate students and 9th and 10th grade students

Focused on how to teach problem solving

Used individual teacher’s lessons and observations

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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.

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Saturday

Graduate students

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48 10th grade females

Control and experimental groups were determined on basis of pre-test scores

2 teachers

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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

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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

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Small sample size

Location of school in Pakistan

Lack of basic skills prior to study

Students hesitant to change how they learn

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110 3rd graders, placed in 2 groups

Pre-test

7 weeks

Computer software

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Motivated students

All students solve problems

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Use regularly with non-routine problems Justify explanations Work collaboratively Multiple solutions or methods Time to implement Greater achievement Real life applications

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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

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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

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