Chapter/Unit Tests Reveal What’s Important in Math

Math achievement - math proficiency rates are terrible. That’s an important issue because science, engineering and technology are dependent upon success in math.

?Test design reveals what is being stressed in math classrooms across the nation and a major reason why our students continue to struggle. Before instruction begins on a unit, teachers should be clear on what they expect our students to know, recognize, understand, communicate and be able to do. That should be reflected on their tests.

?The following is a very easy problem to solve based on 5th and 6th arithmetic. The math; The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of the altitude is the geometric mean between the lengths of the two segments.

?Related problem: In a right triangle, an altitude is drawn from the right angle to the hypotenuse. The lengths of the segments of the hypotenuse are 9 and 4. What is the length of the altitude?

How is it that the majority of our high school students could possibly get that problem wrong? The answer is simple, the lack of math vocabulary and notation. Students know what’s important because its tested! Vocabulary and notation are not emphasized, to solve that problem, students need to know terms like segment, hypotenuse, altitude and geometric mean.

?The design of a test can set students up for success on unit/chapter tests as well as high stakes tests such as semester exams, SBAC, PARCC, ACT and SATs. Test designs must include three sections. Section 1, about 20-30% of the test, the first page of each chapter test contains no math computation or manipulation, those questions are vocabulary, notation, definitions, identifications, rules, theorems, formulas, procedures, strategies, etc. I call those 3-star questions, that set students up for success on 2-star questions.

?Section 2, about 40-60% of the test, are the types of problems that are usually seen on tests, practice problems, exercises used in instruction and on homework assignments. These are 2-star questions.

?Section 3, about 10-20% of the test, are examples that come directly from the PARCC, SBAC, ACT or SAT tests and are labeled as such. 1-star questions.

?Those questions 3-star questions on the first page of a test take away the excuse that some parents and students believe, that they are missing the math gene and can’t be successful. Since there is no math, only memorization, preferably with understanding with what students need to know to be successful in section 2 of the test.

?That’s actually a tried and true test taking strategy. When we go into high stakes tests, we were often advised that when the proctor started the test period, to turn the test over and write down all the information you need to remember so as anxiety increases and causes some people to draw blanks on questions, you can refer back to that information.

?The only difference on the test design that I recommend is we will give students credit for knowing that information. That will also result in higher grades because of that memorization, but will also help students solve problems in section 2 of the test. For instance, if a question in section 1 was to write the distance formula, then there would be an associated question in section 2 on finding the distance between two points. The fact is, if they memorized the formula in section 1, the probability of getting that problem correct in section 2 increases dramatically.

?Section 3, about 10-20% of the test, increases student familiarity and comfort levels on how questions are asked on high stakes test based upon what is taught in that chapter.

?While that testing strategy sets students up for success on those chapter tests, those 3-star questions on the first page of every test act as a great review in preparation for high stakes tests. A teacher having 4 tests per quarter, will have 8 great reviews with sets of problems to better prepare their students for those high stakes state and national tests.

?Teachers should create and administrators should examine teacher made chapter/unit tests before instruction begins in a unit. That will very quickly inform them if vocabulary and notation is being emphasized, the types of problems being used in instruction and whether students are being prepared for high stakes tests.