Teaching this unit on decimals, ratios, proportions, and percents was a very interesting experience.  The knowledge that I was able to gain, not only about my students, but about my own teaching styles and strengths and weaknesses was very insightful.  Putting together graphic representations that compared students and different subgroups made it very clear where the learning goals were met and where they were left lacking.  Overall exam scores can be very useful in getting a general idea of the success of the students, but breaking the scores down into the individual learning goals and tracking student progress this way truly helps to identify areas of excellence and below-desired level results.  Just for informational purposes, there are 23 students in my class, however, only 21 students are active participants in the class.

Learning Goal #1 states that the student will understand the relationship between decimal numbers and fractions as well as the relationship between decimal numbers and other decimal numbers.  The objectives clarify that the students will be able to perform with 75% accuracy.  According to the pre-test data, three students were able to meet this goal before the unit began.  The post-test data shows that 16 students were able to achieve this goal after the unit was taught.  This indicates that 76% of the active students in my class were able to achieve the desired accuracy level for Learning Goal #1.

Learning Goal #2 states that he student will estimate outcomes of operations as well as perform operations using decimals.  The objectives clarify that the students will be able to perform with 75% accuracy.  According to the pre-test data, five students were able to meet this goal before the instructional unit began.  The post-test data shows that 17 students were able to achieve this goal after the unit was taught.   This shows that 81% of the students in my class were able to achieve the desired accuracy for Learning Goal #2.

Learning Goal #3 states that he students will simplify expressions and solve equations which involve decimal numbers, without the use of a calculator, with 75% accuracy.  According to the pre-test data, nine students were able to meet this goal before the instructional unit began.  This is an impressive number at 43% of the class reaching the goal even before the unit began.  According to the post-test data, 17 students were able to achieve this goal after the unit was taught.  This shows that 81% of the students in my class were able to achieve the desired accuracy for Learning Goal #2.  While this seems like a high percentage, the percentage increase in students achieving the goal from pre- to post- test assessments is not as high as the other learning goals.

Learning Goal #4 states that the students will implement the definitions of ratios, rates, and proportions to solve application problems.  The objectives further clarify that the students will be able to perform with 75% accuracy.  According to the pre-test data, four students were able to achieve this goal before the unit began.  According to post-test data, 14 students were able to achieve this goal after the unit was taught.  This indicates that 67% of the active participants in my class were able to achieve this learning goal.  This is a fairly low percentage and will be addressed in a following essay.

Learning Goal #5 states that he students will use percentages appropriately to solve application and conversion problems.  The objectives clarify that the students will be able to perform with 75% accuracy.  According to the pre-test data, three students were able to achieve this goal before the instructional unit began.   According to the post-test data, 14 students were able to achieve this goal after the instructional unit.  This indicates that 67% of my students were able to achieve the desired level of accuracy for this learning goal.

The overall test scores indicate that the average score on the pre-test was a 49%.  The average score on the post-test was an 83%.  This is a very good post-assessment score for this class.

When dividing the class into subgroups of male and female students, it was interesting to see the differences and similarities in progress towards meeting the Learning Goals.  Dividing the class into male and female subgroups can be very informative for a math teacher especially.  In our culture, it has often been taught in the past that men are better at math than women.  At universities today, there are more men in studying in fields of math and science than women.  Analyzing these two different subgroups can help us to determine if these beliefs (held by some) hold any truth to them.

For example, let’s look at Learning Goal #3.  According to pre-test data, the males achieved and average of 50% accuracy while the females achieved an average of 57% accuracy.  According to the post-test data, the male students achieved an average of 90.29% accuracy while the female students achieved an average of 90.16% accuracy.  The difference between these two post-test averages is insignificant and indicates that, while the male students did do better on the pre-test, the post-test scores showed no difference between the male and female students in achieving this learning goal.  This indicates that male and female students are equally able to achieve learning goals within the field of mathematics.

Another subgroup that I divided the class into was low and high achieving students.  I separated these groups by overall class grade, not just the grade for this particular unit since one unit is not enough to determine whether a student is high or low achieving.  These subgroups can be very important to study and analyze specifically.   While low achieving students will typically score lower on both pre- and post- test scores, the percent increase between the pre- and post- test scores can be very informative.

For example, looking at Learning Goal #3 again, the pre-test data shows that the high achieving students achieved an average of 67% while the low-achieving students achieved an average of 20%.  This is to be expected, given the subgroups.  The post-test data shows that the high achieving students achieved and average of 94% while the low-achieving students achieved an average of 84%.  Again, this difference is to be expected.  However, the percent increase in progress is what I find interesting and informative.  The percent increases of these subgroups indicate that an increase of knowledge and accuracy is being experienced by the class as a whole, not just the high achievers.  This shows that working with the low achievers and assisting their learning is not only beneficial, but well worth the effort.

The two students that I selected as a high-achieving student and a low-achieving student are Student #17 and Student #23, respectively.   These two students are about as different as any students I have ever seen.  Student #17 is on time to class, has near perfect attendance, and takes very careful notes in class, works diligently on homework assignments, takes his time on tests, is well organized, asks questions, and participates in group work and discussion.  Student #23 could not be more different.  Student #23 attends less than 70% of the time, is often late and leaves early, refuses to take notes (insisting he is too tired), performs very low on homework, takes very little time to work on tests, appears to have no organization, never asks pertinent questions and does not participate in group work.  In my mind, it is very clear why one performs better on exams than the other.

It is important to understand these two students, as well as all students, and their differences in order to help them learn and succeed as much as possible.  Understanding their different learning proficiencies can help me as a teacher to assist them in increasing their knowledge of the subject matter and succeed in the class and on exams.

Let’s examine Learning Goal #2.  Student #17 went from a 67% to 100% level of accuracy.  Student #23 went from a 17% to 75% level of accuracy.  In this particular learning goal, both students achieved the desired level of accuracy on the post-test.  However, this is the only learning goal in which Student #23 was able to do this.  Learning Goal # shows that Student #17 went from a 80% to 100% level of accuracy.  Student #23 actually decreased from a 60% to 33% level of accuracy.

The conclusions that we can reach regarding these two learning goals is that attendance, homework, and class participation (including note-taking) seem to make a very big difference in a student’s achievement level.  This conclusion can be transferred to other students and help me as a teacher to encourage these kinds of behaviors in students in whatever ways I can.