Embedded Files
Computational Fluency
Computational Fluency
Remaining Questions:
Remaining Questions:
What additional support can I give on-level students to facilitate further growth?
Would continuing number talks increase all students growth in computational fluency?
Would continuing number talks narrow the gap between the scores of on-level and above-level students?
How do timed tests, and potential test anxiety, impact students mathematical performance?
On average, all students' computational fluency scores improved after the implementation of number talks. The practice with various mental math strategies that number talks facilitates helped students grow in their ability to apply these strategies quickly and accurately.
On-level students went from an average of 15 out of 30 points on the pretest, to an average of 19 out of 30 points. Above-level students went from an average of 19 out of 30 points on the pretest, to an average of 25 out of 30 points.
Considering that this assessment was timed and intentionally rigorous, I did not expect all students to score 30 out 30; however, there was a comparatively small amount of average growth by on-level students. I suspect on-level students did not grow as much in this area because they are still developing basic addition and subtraction fact fluency.
Number Sense
Number Sense
On average, all students' number sense scores improved after the implementation of number talks. Number talks helped students think of multiple ways to solve one problem as well as the relationships between numbers and mathematical concepts. These factors increased all students' number sense.
On-level students went from an average of 18 out of 24 points on the pretest, to an average of 22 out of 24 points. Above-level students went from an average of 19 out of 24 points on the pretest, to an average of 23 out of 24 points on the post test.
Remaining Questions:
Remaining Questions:
What additional support can I give on-level students to facilitate further growth?
How can I extend the higher level thinking and discourse that number talks facilitate into all mathematical instruction?
How else can I continue to foster number sense in day to day mathematical instruction?
All students showed more growth in number sense than computational fluency. I suspect this is because there is a lack of explicit number sense instruction in our provided curriculum, as reflected by second grade MAP scores across the district. Number talks provided a supplemental opportunity for students to explicitly name strategies and work with numbers in different ways. The challenge of finding more than one way to solve a problem required students to decompose numbers and find patterns across mathematical strategies. As students became more comfortable with thinking of and working with numbers in different way, their number sense increased.
T-Test Results
T-Test Results
A paired-sample t-test was conducted to determine the impact of number talks on computational fluency and number sense. Below are the results for each mathematical concept.
T-Test for Computational Fluency
T-Test for Computational Fluency
There was a significant difference in the scores prior to implementing number talks (M=17.66, SD= 7.59) and after implementing (M=23.66, SD= 5.15) number talks; t(15)= 6.375, p = 0.000008. The observed standardized effect size is large (1.65). That indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that the use of number talks had a positive effect on students' computational fluency. Specifically, the results suggest that the use of number talks increased students' computational fluency.
T-Test for Number Sense
T-Test for Number Sense
There was a significant difference in the scores prior to implementing number talks (M=19.93, SD= 3.45) and after implementing (M=22.86, SD= 1.14) number talks; t(15)= 3.898, p = 0.0008. The observed standardized effect size is large (1.01). That indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that the use of number talks had a positive effect on students' number sense. Specifically, the results suggest that the use of number talks increased students' number sense.
Math Feelings Surveys
Math Feelings Surveys
The survey also assessed students' feelings about their ability to solve math problems quickly and easily as well as their desire to get better at math.
Overall, students remained stagnant in feeling that they could solve problems quickly and easily. Students who reported feeling confident in this on the pre-survey reported the same on the post-survey, and likewise for students who reported feeling unsure. I found this surprising considering the growth in all other areas, but I am happy that no one developed negative feelings. I did not display this data point because it was not a goal I had students explicitly focus on. I did not want them to get so concerned with solving problems quickly that they did not take risks and have the opportunity to learn from their mistakes.
All students reported wanting to get better at math on pre and post instruction surveys. This suggests a continued desire to improve and learn, and I am proud of my students for maintaining that mindset. I did not display this question because it was not a goal I had students explicit focus on and their was no growth to show. I would be concerned about this data point if all students had not also reported enjoying math.
Post instruction surveys indicate students' feelings about math improved after 6 weeks of number talks.
All 15 students stated they liked math after number talks compared to only 9 students liking math before.
The number of students that feel like math makes sense improved from 11 to 14.
After instruction, 13 students feel they can explain their math thinking while only 8 felt that way before.
While there were additional questions on this survey, I felt these were the most important to display because these were the areas students reflected on after each number talk. Most students met their individual goals of feeling more confident in their mathematical abilities. While I wish all students met all of the goals shown, I think 100% of students liking math is an important foundation on which more mathematical skills and confidence can be built.
Remaining Questions:
Remaining Questions:
How can I help the remaining student feel that math makes sense to them?
How can I help the remaining students feel better about explaining their math thinking?
Do students feel proud of their growth?
Would it be better for students to track progress towards their goals on paper rather than just through reflection and discussion?
Student Interviews and Observations
Student Interviews and Observations
Based on my observations of student discourse as well as my mentor's notes, I believe more students were able to explain their mathematical thinking and name addition and subtraction strategies after the implementation of Number Talks; however, post-interview data was unable to be collected due to COVID-19.
Triangulation of Data
Triangulation of Data
Qualitative and quantitative data worked together to paint a complete picture of the impact of number talks. Observations, notes, interviews, and surveys allowed me to assess and monitor students' feelings and discourse. The pre and post tests allowed me to measure specific mathematical skills like computational fluency and number sense. While I do want students to score well on math tests and assignments, I feel it is just as important for students to enjoy math and feel confident in their abilities. Without all of these data points, I would not have been able to assess progress towards both sides of this complex goal. By analyzing all of these qualitative and quantitative data points, I can conclude that students not only feel confident in their mathematical abilities but are also able to apply efficient, flexible, and accurate mathematical strategies.
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