Problem Solving
This bar graph indicates the scores earned on the pre and post problem solving test for all 19 of my students. I chose to demonstrate the results of all of my students, because it was not just the 7 students who needed the intervention most that received these instructional strategies. Therefore, this data demonstrates the positive results from the implementation of math journals and math talks, even for average or above average students. All, besides student 3, 14, and 16, earned either the same or a higher score on the post-test than on the pre-test.
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This line graph displays the average progress on the problem solving math journals completed by the seven students who needed intervention most. Seven journal entries were collected from the entire class and graded over time. I chose to only display the average score of these 7 students, as I focused my analysis more closely on them and took the time to conference with these specific students who needed the most instruction to grow. The journal entry scores indicated an improvement in problem solving accuracy and explanation. Specifically, the average score started at about 4 out of 6 points and concluded at about 5.5 out of 6 points.
To view the journals and rubric utilized, please click here.
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T-Test Results
A paired-sample t-test was conducted to determine the impact of journals and math talks on problem solving.
T-Test for Problem Solving
A paired-samples t-test was conducted to determine the effect of the use of math journals with math talks on students’ ability to accurately solve word problems. There was a significant difference in the scores prior to implementing summarizing strategies (M=7.47, SD=6.14) and after implementing (M=9.37, SD=3.39) math journals with math talks; t(19)= 3.28, p = 0.002. The observed standardized effect size is large, (0.75). This indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that the use of math journals with math talks had a positive effect on students’ ability to accurately solve word problems. Specifically, the results suggest that the use of math journals with math talks increased achievement in problem solving.
Though four students did not improve on the problem solving post test from the pretest, they proved to enhance their problem solving skills through their daily math journals. Additionally, two of those students were able to test out of the math support they were receiving, as well as improve and/or pass the Problem Solving District Common Assessment that they were required to retake,
Remaining Questions:
- What additional support can I provide for above average students to further enhance their learning?
- Would the use of math journals from the start to end of the school year generate a larger effect?
- How can I further assist students in finding the hidden questions of multi-step word problems?
Math Feelings SurveysThe survey assessed student feelings about math, but more specifically, in regard to word problems. In general, student feelings about math and problem solving progressed from the pre-survey to the post-survey. I found this result very insightful and quite fascinating to know that even though some students did not perform better on the post-test, their feelings about word problems still improved. Therefore, maybe with additional supports through journaling and math talks, their feelings would continue to improve and so too, would their ability to accurately solve the problems.
Remaining Questions
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This bar graph depicts the data collected from the feelings pre and post survey for the specific 7 out of my 19 students. Though all of my students completed the feelings surveys, I chose to more closely analyze these 7 students due to their higher need of intervention and their lower levels of confidence when starting out. Each category on the feelings survey progressed, and therefore, proved a correlation to their success with their problem solving.
In accordance with the data collected, the most growth occurred within student feelings toward applying accurate strategies. This result indicated that students will be more likely to problem solve with greater accuracy by choosing the correct mathematical operations. Furthermore, the next biggest improvement was indicated as student ability to apply math terms in a discussion, which, therefore, means that my students could better explain their thinking and indicate more meaningful understanding and comprehension in what and how they solved problems. All in all, my goal was to set a purpose and promote greater confidence with each math problem students were faced with. I wanted them to visualize each problem in their head and really picture what was going on in the words before taking numbers, drawings, and operations to pencil and paper. Based on the data collected through the feelings survey, I can see that I have successfully helped my students reach that goal in many different aspects.
To view the feelings survey, please click here.
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Student Conferences and Observations
Because of my observations and analytical notes taken over math talks and journal reflections, I trust that my students were better able to apply, demonstrate, and explain accurate strategies with the use of suitable math terminology.
Triangulation of Data
Quantitative and qualitative data coincided, resulting in an adequate depiction of the impact journals, along with math talks, truly had. Observations, conferences, notes and surveys permitted me to evaluate and keep track of discourse, meaningful reflections, and student feelings, while also adapting future instructional practices. The pre and post tests enabled me to quantify their problem solving abilities. Though the end goal was to help students improve accuracy when solving word problems, it was just as important to help students gain greater confidence when being faced with the challenge of these kinds of questions. Without each data point I collected, reliability and credibility of assessment would not have been plausible. Due to my careful analysis of the quantitative and qualitative data, I concluded that my students were better able to break down word problems in order to solve them accurately, as well as show and share their thinking in a variety of modes.