Data Analysis
Triangulation of Data
Qualitative and quantitative data worked together to give me a full spectrum of the impact of guided math. The pre test and post tests allowed me to measure student number sense and mathematical reasoning, while exit tickets and independent work provided daily formative information that brought even more clarity. Observations and anecdotal notes captured the mathematical behaviors and problem-solving approaches each student took when solving problems independently and in small groups. Without all the different forms of data points, I would not have been able to accurately assess the impact of the guided math model and differentiated math stations on student learning.
On average, students scored 8.77 out of 15 on the pre test. Students 9 and 15 were absent the day the pre test was given, resulting in them not having pre test data. Four students scored 14 out of 15 on the pre test, which led me to creating extension activities for them to work on during station time. I knew those fours students already had an understanding of the mathematical concepts that would be taught. Seven students scored below a 50% on the pre test, which helped me group them together to ensure they would meet with me first and then the paraprofessional during rotations to provide them 30 minutes of small group instruction.
On average, students scored 13.36 out of 15 on the post test. Student 9 was absent the day the post test was given, resulting in the student having no post test data. Nine students scored a 15 out of 15 on the post test and eight students scored a 14 out of 15 which would lead one to believe that use of guided math work stations and differentiated groups and instruction increased students' student number sense and mathematical reasoning.
Remaining Questions:
What additional support can I give struggling students to facilitate further growth?
Would continuing guided math increase all students in number sense?
How else might I foster number sense and mathematical thinking in day to day mathematical instruction?
Pre test and Post test
When looking at the data, 17 out of 22 students demonstrated growth during the research period. Due to the student population, absences throughout my action research were common, producing two students who did not have pre or post test data to analyze. One student was absent for both the pre test and post test. Student 16 scored a 0 out of 15 on the pre test. On the post test, Student 16 scored a 10 out of 15.
Two students (students 7 and 8) demonstrated a decrease in mathematical reasoning, perhaps due to proctoring differences. I completed the test with them independently, but did not count the questions as correct to ensure validity.
One student took the pre test at home during remote learning and returned to in person learning with 4 weeks left of action research. This student did not demonstrate growth. This could have been due to extra support from people at home during the proctoring of her test.
Pre test Average Post test Average
When looking at the pre test and post test average scores, student average scores grew by 4.59 points. I attribute this growth to the differentiated instruction students were receiving throughout this study. I was able to provide students with scaffolds and instruction tailored to their own learning needs. Students had several practice opportunities throughout the day (independent work, technology, exit tickets, and teacher time) to contribute to their success and achievement in the area of math.
T-Test Results
A paired-sample t-test was conducted to determine the effect of the use of guided math work stations and differentiated groups and instruction would increase student number sense and mathematical reasoning in first-grade students. There was a significant difference in the scores prior to implementing guided math stations and differentiated groups (M=9.65, SD=3.80) and after implementing (M=14.14, SD=1.21) the guided math stations and differentiated groups; t(22)= 5.91, p = 0.000004392. The observed effect size d is large (1.29). This indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that the use of guided math work stations and differentiated groups and instruction had a positive effect of students’ number sense and mathematical reasoning. Specifically, the results suggest that the use of guided math work stations to differentiation strategies increased number sense and reasoning.
Exit Tickets and Independent Work
I used exit tickets to demonstrate students' understanding of the concepts learned during teacher time and whole group lessons. As I reviewed exit tickets each night, I was able to observe and analyze a different perspective of student understanding. Since exit tickets were completed independently by each student, I was able to see what knowledge students could apply on their own.
One misconception I saw frequently on exit tickets was that student(s) drew six tallies instead of four with a diagonal line to represent a group of five. When I saw students make this error during teacher time, I had a quick conversation with them and showed them how the fifth stick is a wrapping stick. During small group the next day, I retaught a mini lesson about tally marks to all my students to ensure they were all receiving the information again. I used the same lesson from the day prior, but had students write tallies for different manipulatives I put on the table.
To differentiate instruction, some groups did part of the independent work with me and some did it all themselves. The number of problems varied each day based on the content and rigor of the problems. This helped me scaffold the number of problems and strategies for student readiness. I was able to review how students did either independently or after they worked with me. I used the independent work to help me set the stage for the next day's whole group lesson.
All five students scored a 2 on exit ticket 5. This led me to go back and take a deeper look at all five exit tickets together. Exit ticket 5 was about 10-groups. Two of the questions asked similar content questions and one in which students had to apply the concept. If students knew how many objects were in a 10-group, then they were able to draw a ten group.
Exit ticket 8 (pictured on the right) seemed to be the exit ticket that had the biggest varying difference in scores. Two students scored a 2, two scored a 1, and one student scored a 0. The three questions on the exit ticket involved finding a missing partner and total. The question students often missed was #3, because they had to have background knowledge that the question was written with the total first and was missing an unknown partner, not unknown total.
Individual Student Exit Tickets
Exit tickets were scored on a 0 to 2 scale. Students either received a score of 0, 1 or 2. The students' exit tickets I chose to analyze were from varying skills based groups.
Student A received a score of 2 five times. This showed me that this student was able to perform independent tasks over half the time. Student A was absent for exit ticket 3, which you can see no score for.
Student B's scores fluctuated between exit ticket 1-8. Student B was absent for exit ticket 4 and 6.
Like Student B, Student C's scores varied between scores of 0, 1 and 2 for exit ticket 1-8.
Student D showed mastery of skills until the last exit ticket, in which Student D scored 0.
Student E consistently demonstrated the mastery of learning targets which allowed for extension activities.
Remaining Questions:
Would having students complete exit tickets during teacher time give the teacher a quicker overview of student learning, or would this take away from instructional time?
Does reteaching based on exit tickets always need to be done the next day?
Could students complete exit tickets as a group, as opposed to independently to increase their learning by hearing and working with peers?
Observations and Anecdotal Notes
Along with using anecdotal notes to inform daily instructional decisions, the collection provided insight into the impact of the Guided Math Model on students' number sense and mathematical reasoning. Six weeks of notes were analyzed for themes.
Students' understanding of place value impacted solving naked problems (i.e. 10-7). For example, if students transposed a number "17" and "71," their answers were inaccurate.
Limited problem-solving approaches by certain students (e.g. one student consistently used "slam counting" for every problem, whether it was appropriate or not).
See video for a demonstration of "slam counting". In this video, the student is "grabbing" 5 and counting on 4 more to find the total.
Pictorial Representations of quantities were conceptually difficult (e.g. a "ten stick" which was represented with a line was often misinterpreted as a "1").
When I organized my anecdotal notes and observations into recurring themes, I looked at the number of students who consistently had misconceptions about place value, limited problem-solving approaches and pictorial representations. When I analyzed the number of students who fit into each theme, the following stood out:
Out of 23 students, 5 students consistently struggled with place values. These students often mixed up the numbers in the ten and one spots.
Out of 23 students, 8 students frequently drew incorrect pictures to represent their thinking. For example, students maybe knew the concept but were not able to apply the correct drawing based on math curriculum language and expectations.
Out of 23 students, 3 student exhibited limited problem-solving approaches through the entirety of the action research period. Students would use a problem-solving approach at times that would be inappropriate for the content of the question.
Remaining Questions:
Would continuing to teach multiple problem-solving approaches be beneficial for students who struggled with using the same few every time?
Should all students receive a mini-lesson about place value to help them understand place value?
Are anecdotal notes an assessment strategy that should take place in every math classroom?