As the halfway mark of winter break arrives, interest in my students’ progress this past semester stirs in my mind. Having spent several hours scoring final exams for my three different courses during the break (more on that in a soon-to-follow post), and several more analyzing the scores in multiple spreadsheets (yet another post in the works), I’ve decided to speak to each of them in a series of posts. This first post focuses on the results of my math lab course, which until this morning I believed were less than stellar.

### Algebra Intervention Course aka Math Lab

Twenty-five students initially started the math lab course with twenty-three completing the first semester. Students take the intervention course concurrently with algebra 1; fourteen of these students have me as their algebra 1 teacher. My vision for the course stems from my firm belief that force feeding students mathematics makes no sense when their prerequisite skills hamstring their ability to digest the new material. Hence, over the past four months, we focused exclusively on arithmetic concepts and procedures, spending weeks on end re-learning how to subtract integers as well as how to add, subtract, multiply and divide rational numbers. Through repeated instruction and assessment, students improved their understanding of fundamental properties and rules for arithmetic operations, which is critical for their continued success once we start adding variables to the mix. Even if they struggle later with algebra, their improved understanding of arithmetic should serve them well in life.

My intense desire to help students master key concepts from elementary school helped me overcome periodic bouts of self-doubt as my mentor teacher, the other math lab instructor, plowed forward with more advanced concepts and procedures spanning a typical first semester of algebra 1 topics. Whether my approach to focus on arithmetic so extensively was better or worse than covering the entire first semester curricula will never be known. Fortunately, I now know that the effort paid dividends for most of my students.

### Diagnostic Test

In the first week of school, students took a thirty-question diagnostic test, recently created by my mentor teacher, the math department chair. The test spanned topics learned in grades 4 through 7, depending upon the student, school, and district.

Twenty-one students took the test, scoring a 40% average on the test, with individual scores ranging from 17% to 60%; the median was 37%. These results strongly shaped instruction for the semester.

### Final Exam

Rather than take a new assessment for the final exam, students retook the diagnostic test. With the same set of questions, a direct comparison of their performance was possible. Twenty-two students took the final, scoring a 55% average on the test, with individual scores ranging from 30% to 77%; the median was 55%.

Until earlier today, when I computed the above statistics, I believed the curricular focus for the semester failed to yield worthwhile results. I held this view after I scored students’ exams as they turned them in on exam day. Score after score ended up with fifteen or so incorrect answers out of thirty possible. At the end of that day, I even commented to my mentor that my efforts for the semester failed.

### Performance Growth

As the following graphic shows, overall performance on the assessment improved for most students with a fifteen percentage point average gain on the test, with individual growth scores ranging from -7 percentage points to 43 percentage points; the median growth was 17 percentage points. I do not believe any of the improvement is attributable to students recalling the answers as: 1) we did not review their initial results when it served as a diagnostic test, and 2) the diagnostic test was given four months earlier.

One student, who missed the diagnostic test, improved considerably over the semester, in both this course and my algebra 1 course. Had he taken the diagnostic, I believe he would have scored in the 20% range; hence, his growth approached 45 percentage points plus. I feel similarly for another student.

More analysis of these results are possible, yet the time needed to do so is limited, if not existent. This is one area in our education system where improvement is needed.

### Conclusion

As I mentioned earlier, it is not clear whether the curricular approach I followed this semester for these students was the most effective. Nonetheless, it is abundantly clear that most students benefited. I wish their scores were higher; however, I will chalk this up as a success.

In the coming week, I also plan to check student performance on a question by question basis to plan the preliminary focus for when the class starts back up the following week. My efforts for the first few weeks will still be on arithmetic. After which, we will introduce the infamous letter “x” to our efforts.

This is a rare case where the same test can reasonably be given pre and post instruction. It seems like you had legitimate success; it would be interesting to see which questions ( if any ) were missed by many pre and answered correctly post. Yes, ” x ” continues to be unknown by many.

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You point out exactly where I plan to look next, that is, when I return back to this analysis. Two other courses need my attention until then. Happy New Year!

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Do you think that heading toward a “business math” or “applied math” approach originally would be of more benefit for these syudents? Our Algebra for All stance has never won my support. It seems the main justification is that students need algebra to be college bound. Another issue. But maybe this is too far off topic—–or maybe it’s exactly to the point.

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I believe your point is right on target. I’ve written about m views on algebra for all previously. I believe everyone should have the opportunity to pursue it, heck, maybe even required to take it. Yet, if they are unable to learn it after a reasonable effort is applied, then they should be allowed to opt out of that path and take something more appropriate and likely more relevant to their future. They can always revisit more advanced topics later. I do not see us moving in that direction anytime soon due to the sins of the past.

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There is a text and course called ” Financial algebra “. Taught in some HS in NYC.

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Dave,

I truly appreciate your data. As a remedial math teacher and doctoral candidate, examining student growth is always interesting. Much of the research that I have found on math intervention programs tend to report that test scores almost always improve; the dilemma is that “improvement” and “progress” are not synonymous with “passing” and our struggling students still fail math courses and still dropout of high school. Sadly, the term “passing” has become synonymous with “success” in education. Those of us who teach low performing students believe that results such as yours are, indeed, true measures of success.

Keep up the good work and fighting the good fight!

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Thanks, Chris. My students genuinely worked hard to improve this semester.

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