Download - Problem solving powerpoint
![Page 1: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/1.jpg)
Susan HewettMAED 5040
1
![Page 2: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/2.jpg)
The process of overcoming difficulties that possibly interfere with the attainment of a goal.
2
![Page 3: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/3.jpg)
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
3
![Page 4: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/4.jpg)
A problem with multiple ways to solve
A problem with multiple solutions
4
![Page 5: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/5.jpg)
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)
5
![Page 6: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/6.jpg)
6
![Page 7: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/7.jpg)
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
7
![Page 8: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/8.jpg)
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.
8
![Page 9: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/9.jpg)
Students who avoid a pattern are able to develop original ideas in an open ended problem in mathematics
9
![Page 10: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/10.jpg)
90 4th graders
Compares multiple choice and open ended problems
Data analyzed through use of written and verbal responses from students
10
![Page 11: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/11.jpg)
Some students received multiple choice first, some open ended first
Problems were based on those that are given on state assessment every year
11
![Page 12: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/12.jpg)
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
12
![Page 13: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/13.jpg)
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
13
![Page 14: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/14.jpg)
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
14
![Page 15: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/15.jpg)
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
15
![Page 16: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/16.jpg)
Small sample size
already using problem based learning
Selected students liked problem based learning
16
![Page 17: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/17.jpg)
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
17
![Page 18: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/18.jpg)
Only a few students solved problem correctly
Students preferred informal strategies to formal algebraic ones
Main strategy chosen was Trial and Error
18
![Page 19: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/19.jpg)
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
19
![Page 20: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/20.jpg)
Small sample size
Analyzing thinking is very subjective
Presence of researcher as students work problems
20
![Page 21: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/21.jpg)
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
21
![Page 22: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/22.jpg)
Realistic Leads to creativity Higher order thinking Teacher as facilitator Learn via discovery Self-directed learning Interconnectedness Collaboration Self-assessment
22
![Page 23: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/23.jpg)
Time
Don’t focus on single discipline
Mathematical models may or may not be used
Must be used regularly
23
![Page 24: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/24.jpg)
164 5th graders
Problems were presented via Internet, but work was done in classroom supervised by homeroom teacher
24
![Page 25: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/25.jpg)
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
25
![Page 26: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/26.jpg)
24 6th grade students
Low achieving students
Involved after school program
Used manipulatives
26
![Page 27: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/27.jpg)
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
27
![Page 28: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/28.jpg)
Small sample size
Setting
Participants
28
![Page 29: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/29.jpg)
79 7th grade students
Use of computer technology and scaffolding
Study not related to math classes
Specifically focused on the development of arguments
29
![Page 30: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/30.jpg)
More beneficial to low and average achievers
Scaffolding kept groups organized
Students stayed focused
30
![Page 31: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/31.jpg)
Involved graduate students and 9th and 10th grade students
Focused on how to teach problem solving
Used individual teacher’s lessons and observations
31
![Page 32: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/32.jpg)
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.
32
![Page 33: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/33.jpg)
Saturday
Graduate students
33
![Page 34: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/34.jpg)
48 10th grade females
Control and experimental groups were determined on basis of pre-test scores
2 teachers
34
![Page 35: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/35.jpg)
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
35
![Page 36: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/36.jpg)
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
36
![Page 37: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/37.jpg)
Small sample size
Location of school in Pakistan
Lack of basic skills prior to study
Students hesitant to change how they learn
37
![Page 38: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/38.jpg)
110 3rd graders, placed in 2 groups
Pre-test
7 weeks
Computer software
38
![Page 39: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/39.jpg)
Motivated students
All students solve problems
39
![Page 40: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/40.jpg)
Use regularly with non-routine problems Justify explanations Work collaboratively Multiple solutions or methods Time to implement Greater achievement Real life applications
40
![Page 41: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/41.jpg)
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
41
![Page 42: Problem solving powerpoint](https://reader035.vdocument.in/reader035/viewer/2022062704/5557c1c0d8b42a696c8b543e/html5/thumbnails/42.jpg)
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
42