Data Analysis
Observational Notes
Themes I noticed throughout my observational notes included counting, running start, writing numerals, and subitizing. These concepts/strategies were being taught and built on during the six week intervention.
Subitizing was present the most compared to the other themes (42.86%). Students were able to look at dot frame cards and say the amount of dots right away without counting. This is called subitizing, the ability to instantly recognize “how many” in a small set. This was a strength overall for the two groups. Students were fluent when reading 0-5 dot frame cards at the beginning and fluent when reading 0-10 dot frame cards by the end of the intervention. They were exposed to these cards over multiple opportunities which helped them to become familiar with the dots and their quantities. Students were able to use what they knew about the tens frames to recognize the number of dots on the cards. They knew the tens frames were composed of two rows of five. Students were encouraged to count on from five. This helped them learn their five plus facts up to ten. For example, students' were able to tell me that they knew it was eight because they saw five on the top row and three on the bottom row and five and three makes eight. I used this strength during group to build on their numeral to number recognition. I would flash them a dot card and they would have to find the number that matched on the number line. This helped them to connect the number name to the writing of the numeral.
Counting was the second largest theme present in my observational notes (28.57%). Most students were successful when counting up from one. They struggled when they had to start from a number other than one or count down. To practice counting from a number other than one we worked on becoming familiar with the count sequence 0-20 first. I would write a number in the middle of the marker boards and ask students "What comes before this number? What comes after this number?". I would have students work together to correctly order numbers 0-20. This let them practice collaboration, conversation, and ordering numbers in the correct sequence with their hands to physically see and touch the numbers. After they put them in order I would have them go to stand on a certain number and walk the number line to 20 while counting aloud (starting from a number other than one). To help them count backwards, we would stand up and touch our heads for five, shoulders for four, hips for three, knees for two and toes for one while counting aloud. Students were able to count back from five successfully by the end of the six weeks. They still need more practice/exposure from ten and twenty.
Running start was a strategy I wrote about often in my observational notes (20%). At the start of the intervention students were not familiar enough with the number sequence to count on from a number other than one or answer questions such as "What comes after eight?" without a running start. A running start is when students have to count from one to answer the question. At the beginning of the intervention I wrote notes about students using running starts to answer questions a lot. By the end of the intervention it came up less because students were more familiar with the number sequence and could answer more questions without using a running start. My notes showed students growth with the standard K.CC: Know number names and the count sequence and K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Writing numerals was the smallest theme present in my observational notes. By the end of the intervention students were successful writing their numbers to ten. I should have taught more lessons with an emphasis on writing the numbers. For example, when I had students match the dot cards with the corresponding numeral cards, I also should have had them write the numeral. Students needed more practice and exposure writing their numerals, especially the teen numbers (11-20).
Pre & Post Test
Student One received three out of ten points on the Pre-Test. This student successfully counted to 13. For the second task, they could count backwards from six. On the third task, they could say what came after five and eight, but could not say what came after 12 and 16 even with a running start. They successfully completed the fourth task. For the last task, they could write their numerals to ten. As a result, I implemted counting while using a number line. I would ask them which came before or after a certain number and use the number line as a visual.
Student One received six out of ten points on the Post-Test. They were able to count to 16. This student counted three numbers higher by the end of the intervention. For the second task, they could successfully count back from ten (four numbers higher than the Pre-Test). On the third task, they could say what came after five, eight, and 12, but said 19 came after 16. They successfully completed the fourth task as they did on the Pre-Test. For the last task, they could write their numbers to 18, but skipped nine. The first time they wrote their numbers to ten but did not skip nine.
Overall, this student showed 40% growth from the Pre-Test to the Post-Test. The graph shows a positive slope representing the students growth. The Pre and Post Test scores support that the intervention was successful in increasing Student One's number sense.
Student Two scored three out of ten points on the Pre-Test. This student successfully counted to 12. For the second task, they could not count backwards at all. On the third task, they knew six came after five but needed a running start. They knew nine came after eight and 17 came after 16 right away. When they were asked what came after 12, they said 14. They successfully completed the fourth task. For the last task, they could write their numerals to ten. As a result, I wanted to focus on counting backwards. I had this student point to certain body parts as they practiced counting backwards.
Student Two scored three out of ten points on the Post-Test. This student was able to count to 13, which is one higher than the Pre-Test. For the second task, they were able to count back from five (five numbers higher than the Pre-Test). On the third task, they could say what came after eight and 16 right away. They used a running start to successfully say which numbers came after five and 12. They successfully completed the fourth task as they did on the Pre-Test. For the last task, they could write their numbers to ten, which was the same as the Pre-Test.
Overall, this student showed 0% or no growth from the Pre-Test to the Post-Test. The graph shows a constant slope representing the students lack of growth. Above, each section of the test was broken down and explained. This student did grow in certain areas even though their Pre and Post test scores showed "no growth". They were able to count higher and backwards from five and knew what came after twelve which they were not able to do at the beginning of the intervention.
Student Three scored three out of ten points on the Pre-Test. This student was able to count to 10, not fluently. For the second task, they could count back from ten to six. On the third task, they knew nine came after eight and 17 came after 16. They needed a running start to say six came after five and 13 came after 12. They successfully completed the fourth task. For the last task, they could write their numerals to ten. As a result, I had this student practice ordering numerals 0-20 to work on familiararity with the counting sequence.
Student Three scored eight out of ten points on the Post-Test. This student was able to count to 49, which is 39 higher than the Pre-Test. For the second task, they were able to count back from ten (six numbers more than the Pre-Test). On the third task, they could say which numbers came after five, eight, 12, and 16 without a running start. They successfully completed the fourth task as they did on the Pre-Test. For the last task, they could write their numbers to 12, which is two numbers higher than the Pre-Test.
Overall, this student showed 50% growth from the Pre-Test to the Post-Test. The graph shows a high steep positive slope representing the students growth. The Pre and Post Test scores support that the intervention was successful in increasing Student Three's number sense.
Student Four scored four out of ten points on the Pre-Test. This student was able to count to 39. For the second task, they could count from ten to nine and then got stuck. On the third task, they knew eight came after nine right away. They knew six came after five, 13 came after 12, and 17 came after 16 with a running start. They successfully completed the fourth task. For the last task, they could write their numerals to ten. As a result, we focused on counting backwards using body parts.
Student Three scored six out of ten points on the Post-Test. This student was able to count to 59, which is 20 more than on the Pre-Test. For the second task, they were able to count back from ten (eight numbers more than the Pre-Test). On the third task, they performed the same as on the Pre-Test. They successfully completed the fourth task as they did on the Pre-Test. For the last task, they could write their numerals to 11, which is two higher than the Pre-Test.
Overall, this student showed 20% growth. The graph shows a low steady positive slope representing the students growth. The Pre and Post Test scores support that the intervention was successful in increasing Student Four's number sense.
Student Five scored six out of ten points on the Pre-Test. This student was able to count to 20. For the second task, they could count down from ten to zero. On the third task, they knew six came after five and nine came after eight right away. They could not tell what came after 12 and 16 even with a running start. They would count high enough, but could not stop and answer the question. They successfully completed the fourth task. For the last task, they could not write any numerals starting from one. The student wrote 10, 8, 9, and 4 on the record sheet in that order. As a result, I had this student practice ordering and writing numerals to 20.
Student Five scored seven out of ten points on the Post-Test. This student was able to count to 20, the same as on the Pre-Test. For the second task, they were not able to count back from ten which they successfully did on the Pre-Test. On the third task, the student knew six came after five and nine came after eight right away, The student was able to successfully say what came after 12 and 16 with a running start, which they were not able to do on the Pre-Test. On the last task, the student was able to write their numerals to 20. This is a huge difference from the first time.
Overall, this student showed 10% growth from the Pre-Test to the Post-Test. The graph shows a low steady positive growth to represent the student's growth. The Pre and Post Test scores support that the intervention was successful in increasing Student Four's number sense.
A paired-samples t-test was conducted to determine the effect targeted small group instruction on student achievement in math regarding number sense.. There was a significant difference in the scores prior to implementing targeted small group instruction (M=3.8, SD=1.17) and after implementing (M=6, SD=1.67) targeted small group instruction; t(5)= 2.56, p =0.0314038 . The observed standardized effect size is large (1.14). That indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that targeted small group instruction had a positive effect on student achievement in math regarding number sense. Specifically, the results suggest that the use of targeted small group instruction increased student achievement in math regarding number sense.
Progress Monitoring Assessment
The progress monitoring assessment was given after module one lessons were completed. Students needed to receive at least 7/10 points to move onto the next module. All of the students got seven or more points. 100% of students were ready to move onto module two lessons. Module one focused on numerals 0-10. Students showed they were ready to focus on numerals 10-20. Module two focused on the "teen numbers" which include 11-20. Student one, three, and five received 10 out of 10 points on the assessment. This showed me they were strong when counting within 10 and were ready to build and work toward 20. They could lead the others in the groups as well. I encouraged students to help one another during group and answer each other's questions. Student four got nine out of ten points. They were able to write their numerals up to seven. This caused them to miss a point on the last task. This showed me that the student was ready to move onto the next module but needed more practice writing their numerals. Student two received seven out of ten points. They could not count backwards from five and received zero points on task two. The student wrote their numbers to ten but could not think of number nine. He lost one point on the last task as well. Student two and four both need to work on writing their numerals. Student two also needs more practice counting backwards. They were able to do it when looking at a number line or their fingers.
Students had to work together to organize numbers 0-20. Students were communicating and moving numbers around that were incorrect to find the correct order and complete the task.
Triangulation
Observational notes
Progress Monitoring Assessment
Pre and Post Tests
Qualitative and Quantitative data work together to paint a picture for teachers that helps guide future instruction. All three of these data collection methods worked together to help me monitor student learning and provide ongoing feedback to improve teaching and student learning. The Pre and Post test scores by themselves were just a number. The Pre and Post Test scores plus my observational notes helped me understand the strategies my students were successful using and the strategies they needed more practice with. I was able to pinpoint students' strengths and weaknesses to drive instruction. The progress monitoring assessment was done after module one lessons to ensure students were learning what I had intended for them to learn. This helped see which concepts students were understanding and which concepts they needed clarification on. The progress monitoring assessment solidified that the intervention lessons were successful thus far and students were ready to move onto module two lessons.