Analysis

The graphic representation in figure A1a shows that most students made significant progress toward achieving the learning goals.  The first graph shows the scores students received on the pre and post assessments, which were the same.  The pre-assessment scores are in blue and the post-assessment scores are in red.  I set 80% as my goal for mastery of each learning goal.  Using this criteria, 10 out of 15 or two thirds of the students mastered the entire unit on plane geometry, with 7 scoring at 90% or higher.  Of the five who did not achieve 80%, three achieved at least 70%.  Though I set the expectation at 80%, 70% is an accomplishment for some of these students who rarely perform that well on a test.  The two students who did not achieve 70% both failed the exam.  Both of these students had multiple absences and had to make up the test at a later date. 

Fourteen out of fifteen students raised their score by at least 33%.  The average on the pre-assessment was 22% and the average on the post-assessment was 80%, a change of 58%.  This is a positive change and a good sign is that the average score was the goal that I set for the class.  Some students outperformed my goal and others underperformed, but the average was right on point.  In the pre-assessment there was not a single student that met the criteria for mastery of any single learning goal.  In the post-assessment, several students met the criteria for multiple learning goals.  The performance of most students on this test shows understanding of the material and adequate preparation for the next time they encounter this material in Geometry.

The second graph shows a breakdown of the pre and post assessments by question.  This was later broken down into learning goals with each question being assigned to the most relevant learning goal.  This graph shows that the learning goals aligned with questions 11-19 showed the least mastery in the pre-assessment with no students answering them correctly.  Question 3 also had no correct answers in the pre-assessment, but the surrounding questions were some of the questions answered correctly most often and they are aligned with the same learning goal.  This helped me decide to spend extra time on that question which involved naming planes and refer back to it often throughout the unit so that students would remember it when the test came.  These efforts appear to have worked as question 3 showed one of the largest improvements from pre to post assessment.

Questions 11-19 aligned with three learning goals.  The performance on these questions showed that students had likely not been exposed to these ideas before or they were not intuitive to them.  The post assessment scores on these questions showed adequate if not stellar gains so perhaps more instructional time could have been spent on those topics.  The performance on the post-assessment does show what I expected based on student responses in class and their homework.  The two lowest performing questions were 8 and 17.  Eight required multi-steps and number 17 required some thought and not just a quick answer.

In the next graph, the results are shown broken up into learning goals.  Learning goal 5 showed the least mastery but also showed the most gain in mastery so I feel that the instruction regarding learning goal five was successful despite not meeting my criteria of 80%.

The subgroups I chose to analyze were gender and ELL status.  ELL status was an interesting subgroup to look at because there are some goals that were covered that had a lot of language.  The students took vocabulary notes and practiced notation.  The two most language intensive learning goals were learning goal one and learning goal seven. The first learning goal was that students would be able to identify and name geometric figures.  The seventh was that students would be able to identify and name transformations.  The interesting result from these two learning goals was that the ELL students showed great improvement in the first and one of the least amounts of improvement in the seventh.

Looking at learning goal one, the ELL students increased proficiency by 53% and showed 80% mastery.  Their proficiency in this goal was 16% lower than the average of the non ELL students.  While this is a large gap, the student who speaks the least English got every question right in the learning goal and the other two ELL students performed better on this learning goal than any other.  As I identified this as a point of potential challenge to these students I may have provided more specific help to this learning group.  Though I spent much more time making accommodations for ELL students on learning goal seven and they were much less successful on that goal. 

This data may be slightly skewed because my lowest performing student is also in this learning group.  She is fluent in English but she misses class regularly and rarely completes homework.  If I took any other student in the class and put their data in instead of hers, there would be very little difference between the ELL and non ELL student performance.  When accounting for her score as an outlier as it would be in a statistical analysis, I feel that the ELL students did well in learning goal one and I would be confident in saying that they had mastered the learning goal and that in this particular instance, I was mostly successful in keeping bias out of my classroom.

When I chose this group, we had five ELL students.  One had little to no English skills, two had minimal English skills and two are fluent in English, but speak Spanish at home.  Between the pre and post assessments however, the two students with minimal English skills were removed from the class.  The remaining three students make up 20% of the class so I believed even with the limited sample of three, I could see any patterns regarding this subgroup.

I chose this group because it is a concern to me that all students in the classroom have the chance to learn.  This class is 20% Hispanic and my other classes are about 5% Hispanic.  Many of these students are not proficient in English.  I was interested in their results because my Spanish ability is limited and it is difficult to find the time in class to repeat everything.  I created notes in Spanish for some lessons and provided homework for their ELL teacher if needed.  It is also stressed that these students should use English when possible, so I attempt that in class.  I wanted to identify any bias that might exist in my teaching so that I could work to correct it in future units and lessons.

Looking at the data in the graph representing all student performance based on learning groups, it would appear that the girls and ELL students had a distinct disadvantage from the onset.  Their scores on the pre-assessment were significantly less than their counterparts.  Despite the initial similarities between Girls scores and ELL scores, there is a possible difference in learning by looking at the pre and post assessments.  Both girls and boys raised their scores by an average of 59%, but ELL students raised their scores by only 44% as opposed to 62% by non ELL students.

While the data appears to be clear on this issue, there are many contributing factors to these score differences.  Instruction is the first to look at because it is the most in my control.  By looking at each learning goal outcomes and the instructional and assessment strategies used in each lesson, I may be able to find which strategies worked best for these subgroups.  Knowing the students, I know that two of the big factors that play a role in these students’ success include attendance and parental support.

The two students who failed the test were both girls and one was ELL.  Both of these girls miss school on a regular basis, sometimes parental excused and sometimes unverified.  The ELL student who was among the top performers in the class has a father who checks his student’s homework daily and checks in with his teachers to make sure that he is staying on track.  In addition to checking instructional strategies, more contact with the parents of those students who are not meeting learning goals might help them be more successful in the future.

I chose one student who usually gets high grades on all of his tests and one student who has been a C or D math student in previous quarters in math. 

Student 1 will be referred to as KM.  The initials are not her real initials.  Based on test scores, she is considered low-performance, but she falls in the middle of the pre-algebra class most of the time.  She had one of the lowest performances on the pre-assessment with a score of 8%.  She struggled with some prerequisite skills as is demonstrated on problem 16 on her pre-assessment.  Her coordinate graphing skills are lacking even after a review that took place just before this test.  I chose her partially because she did try problems on the pre-assessment even when she wasn’t sure of them.  Many of the low to mid students did not attempt many problems after the first few. 

Student 2 will be referred to as DC.  These are also not his real initials.  He is a high-achieving student in the class.  He also tests below grade level, but it is because of a lack of confidence and a lack of trying rather than from lack of mathematical ability.  He usually is one of the first to catch on in class and he will try to recall knowledge, though not if it is something he deems too difficult. 

Judging only by their final scores, these two students do not look too different. KM received an 82% on the post-assessment and DC received a 94%.  Both are considered proficient in the end, but they started out in very different places in the pre-assessment.  KM got 8% of questions right, increasing her score by 74%.  DC got 23% of questions right on the pre-assessment and increased his score by 71%.  I think it is important to see how the prior knowledge helped the higher-level student, but also that those with less prior knowledge can also increase their score.  I also think it shows how important it is to reinforce basic skills, making sure that students focus on mastering the foundation skills before moving on to more complex skills.  Both of these students improved their scores dramatically.  A graph of their growth of individual learning goals is below.

Perhaps the most interesting and informative learning goal to look at is learning goal 3.  Both students have 0s across the board on this learning goal.  I believe the main problem with this goal is that there was only one question on the assessment that addressed it directly.  KM’s answer showed a lack of understanding about the difference between complementary and supplementary angles and DC’s answer showed a lack of understanding of the angle measure of either supplementary angles or a line, or perhaps both.  The overall mastery of the class of this learning goal was 87%.  These two students were one of just a few students who missed the problem. 

The other goal that stands out looking at the graph and the data is learning goal 5.  Both students went from 0% on the pre-assessment to 100% on the post-assessment.  This goal involved multi-step equations and either remembering a formula or being able to derive it from knowledge of the angle measures of a triangle. There were three problems of varying difficulty on the assessment, so it accurately assessed the skill.  Both students did an excellent job learning the skill and reaching the learning goal that was set for them.  This goal shows that when the two students come from the same knowledge level on a skill that they can achieve the same mastery.

Overall, the students who came to class, participated and did their homework did very well on this unit.  Many had grades that were well above their previous scores.  It was a great confidence builder and encouraged the students to try to keep their grades as the quarter progressed.  The analysis of their score also allowed me to create better assessments in the future when able and to adjust my teaching to match student learning styles.