At the beginning of the school year, 24 of my students took the MAP test in the areas of reading and mathematics. One student did not take either MAP test due to the fact that it was not an appropriate assessment for him at the time. Another student started in my classroom in late September and I did not have all of the data for her; however, I had her overall RIT, or Rausch Unit, scores for both reading and math. Based on her data, she was on the lower end when compared to my other students’ data. Both data sets showed me that there was a large range in regard to my students’ achievement; however, I noticed that a fairly large amount of my first graders were considered high or high average on both assessments. In math, 12 students scored in the high range and 4 scored in the high average range. Therefore, 16 students, or nearly 62%, of my class scored as above average. The standard deviation for my class based on overall RIT was 15.3 and the national percentiles in my class ranged from the 3rd percentile to the 99th percentile. A large standard deviation, as noted, meant that there was a large variance from the average, or mean, score. Furthermore, a standard deviation of over 13 signifies that the general curriculum would fail to meet the majority of the students in my classroom. The MAP test also breaks the mathematics assessment into four different strands which include number sense, data, algebra, and geometry.  There were two strands in which I had only one student in the average range and there was a split between above and below average. For both geometry and algebra, I had 7 students, or 29%, of my class that were considered below average. This could have potentially been 8 students when considering the student who joined our class in late September; however, as already mentioned, I did not have her strand data at the time. The data signified that geometry and algebra were two strands that I needed to focus on more than others, especially when it came to differentiating in small groups because there was only 1 average student in each of these. However, when viewing the standard deviation of the different strands, algebra and data had the widest range of scores. When considering both the standard deviations of each strand and the number of students in each percentile range, I wanted to focus on algebra first. Algebra had a standard deviation of 19.7 and only 1 student who was considered average. Therefore, data was a strand that I wanted to consider as well, especially for my lower students.

 

At the time, numeric relationships appeared to be a strength for my class as a whole because no student in my class missed any questions relating to this standard on our Unit 1 math test. For these particular questions, students were to represent a number less than 10 using a five group and additional ones which the data showed me all of my students could do. This baseline data showed that the on-level curricular goals for Unit 1 pertaining to number sense were achieved by my students. Knowing this, my class should have been pushed further and challenged beyond the grade-level expectation into more rigorous material. Whereas number sense was a strength for my students on this test, 8 of my students missed a question about a growing pattern. This is an indicator that some struggled with the concept of algebraic relationships. More specifically, they struggled with connections between counting and addition and subtraction was evident.  Therefore, these concepts should have been reinforced for my students in order to strengthen their understanding of algebraic relationships. Altogether, 7 students in my classroom of the 24 missed no questions on the Unit 1 test and deserved to be challenged because they had shown mastery of many mathematical concepts already. This variety in student achievement levels supported my desire to differentiate instruction during small group math.

 

On our first quick quiz for Unit 3, 19 students answered all 15 addition fluency problems correctly. The most missed out of 15 questions over addition fluency was a student who missed 3 problems. The student who missed 3 was also the student who scored the lowest in number sense on the MAP growth test. This data signified that my students began to master basic addition facts within 10 and were ready for an extension. As a result, number sense was not an area needing intervention but was an area which, when it spiraled through our curriculum, I needed to extend for students.

 

While implementing our math curriculum, I observed students finishing quickly with mastery while others struggled greatly. There was a wide range of independence levels within my mathematics block.  I noticed that concepts such as solving for unknown partners in addition and subtraction could be a hard concept to grasp for many of my first graders. On work pages and during whole group practice on whiteboards, I noticed a common mistake was for students to add the total to the unknown partner rather than leaving a box for the unknown partner. On one of the work pages for Unit 3, 6 of the students who were present that day had trouble with the concept. This mistake was something that I made note of and addressed the following day in order to prevent further confusion. I continued to collect observations of student successes and miscues to be addressed in my small group instruction. This provided that each student only received reteaching and intervention when needed, instead of as a whole group re-teach.

 

The inverse relationship between addition and subtraction was difficult for many of my below average students, as well. For example, on our Unit 2 test, 9 students missed a question pertaining to the inverse relationship between addition and subtraction. Additionally, 6 of those students struggled to recall how to write numbers in vertical form. In regard to the area of geometry and measurement, 7 students missed a question in which they were to count on using a nickel and pennies. The curriculum only spent one lesson on this. Differentiated small group instruction prior to the Unit 2 test could have prevented many students from making a mistake when answering this particular question. The concepts highlighted from the Unit 2 test data were good starting points in differentiated small group instruction for me in order to continue building upon the foundation that my students already had.