It's been a week since I saw the new SBAC math pilot test for high school. Since, then I wake up at night thinking that parabolas and exponential equations are chasing me. I dream of $$$, on how much SBAC is going to charge my district for student's to practice on the computer, buy materials, and pay for the improvement plans. Also, I've applied to get a master's degree in mathematics, so I don't have to go through the embarrassment of being a high school math teacher once the results of this testing comes out.

What I saw was a complete disconnect between the standards and how to properly assess mathematics. The standards are supposed to be deep understanding, not "a mile wide and inch deep", but the pilot questions were exactly "a mile wide and inch deep".

There were two major flaws in the pilot test: (1) The questions themselves and (2) the use of technology. I wrote a blog about the technological problems here: SBAC Follow Up. The question themselves were written for students with a high reading and high math level. This screws students who are good in math but struggle with reading (me). At least on the ACT or SAT, you have a chance at a decent score in math if you do not read at the highest level. So its a double edge sword for math teachers and students, not only do you have to know about mathematics but they also need to be very good readers. I understand that we need to raise the bar, but setting it beyond the capabilities of our young is very troubling.

Other random observations:

- The pilot high school test we took did not include trig, logs, complex numbers, and many geometrical standards.
- No offense to the writers but I found a sick love of completing the square, parabolas, throwing balls, difficult factoring, multiplying many many terms, geometric proofs, and simplifying unnecessary fractions.
- The difficulty level was extremely high, out of 60 to 74 questions, I'd say there were less than 5 questions that were straight forward and did not have multiple parts.
- There is no way any student could legitimately get through the test in two hours.
- The calculator was only allowed on certain problems.
- After 15 questions, it saved the work and students could not go back to those questions.
- Unclear directions: Should students simplify completely? Write the abbreviation for units?
- Questions ran off the screen, which drove students nuts.

Here's an example of type question that may have been on the pilot exam.

Solve:

There's nothing wrong with this problem, except it's way too complex for most students. I believe this is an example of an "easy" problem. Thanks to SBG (Standards Based Grading) see Shawn Cornally's blog for further information about SBG, I know that this is an extremely difficult problem for students.

Here's the breakdown:

for (x + 3)^2 = 16: 77% of students get this correct. N = 92 (sample size)

for 2(x +3)^2 = 32: 51% of students get this correct. 37% get both solutions

for 2(x+3)^2 + 7 = 39: 36% of student get this correct. 22% get both solutions.

The scoring for this would be interesting. Do they get full credit for one of the two solutions? What if they left the answer in radical form or x = –3 +/- 4? What if they write x = 1 AND x = –7 instead of x = 1 OR x = –7, or x = 1, –7? How does the computer score this? I'm sure we'll never know how they scored this problem (unless we pay for it).

I believe if you want to know if students can solve from the vertex form a quadratic the problem (x + 3)^2 = 16 would be a better choice. Perhaps, a better way to assess solving a quadratic function would be a problem like x^2 + 10 = 19, where they could factor it or isolate x.

Another issue was the complexity of the multiple responses. A student should not have to multiply a binomial times a trinomial, five times to demonstrate they understand equivalency. That problem took students 5 to 10 minutes, if they tried it at all.

Solve:

There's nothing wrong with this problem, except it's way too complex for most students. I believe this is an example of an "easy" problem. Thanks to SBG (Standards Based Grading) see Shawn Cornally's blog for further information about SBG, I know that this is an extremely difficult problem for students.

Here's the breakdown:

for (x + 3)^2 = 16: 77% of students get this correct. N = 92 (sample size)

for 2(x +3)^2 = 32: 51% of students get this correct. 37% get both solutions

for 2(x+3)^2 + 7 = 39: 36% of student get this correct. 22% get both solutions.

The scoring for this would be interesting. Do they get full credit for one of the two solutions? What if they left the answer in radical form or x = –3 +/- 4? What if they write x = 1 AND x = –7 instead of x = 1 OR x = –7, or x = 1, –7? How does the computer score this? I'm sure we'll never know how they scored this problem (unless we pay for it).

I believe if you want to know if students can solve from the vertex form a quadratic the problem (x + 3)^2 = 16 would be a better choice. Perhaps, a better way to assess solving a quadratic function would be a problem like x^2 + 10 = 19, where they could factor it or isolate x.

Another issue was the complexity of the multiple responses. A student should not have to multiply a binomial times a trinomial, five times to demonstrate they understand equivalency. That problem took students 5 to 10 minutes, if they tried it at all.

As my students struggled to answer questions, a cloud of frustration hovered over the room, then atmosphere moved to a near riot. My best students worked through problems at a blistering rate of 20 per hour (there were between 60 and 74 questions). So in two hours, they might get 40 to 50 done. At least some of my students were able to swiftly figure out how to move to the next question and "get through" all 74. :)

I know students rushing through the test may improve as students take test after test, year after year, but I have a feeling what I saw will be the norm. Some will try, others will try and finish as fast as possible. I know they do this now on the Michigan Merit Exam, but until I saw them take the test on computer without bubbling, it never really stuck in my brain, that I can't make students do their best on these tests. And this one of my best classes I've had in my career, I'd hate to think what some of the bad ones would do.

What scares me the most is that I've done this type of mathematics (talking about the Common Core and SBAC testing) before, it was called the Core Plus Mathematics Project. For seven years, I taught Core Plus. It took four years just to understand it, then three more to get students to an average level, then my district pulled the plug because students were doing horrible in college math classes and on the ACT. The intent of Core Plus was good, but it ultimately failed because it required to deep of understanding of math and too high of a reading level.

As a teacher I take great pride in learning and honing my skills, through blogs, other math teachers, workshops, and conferences. I stay up-to-date on technology and what skills my students will need to be successful in math. From Dan Meyer to Wayne State University's Dr. Steven Kahn's award winning MathCorps, there are many exciting ways to learn mathematics, unfortunately the SBAC pilot test contradicts everything the math world is doing to improve math education.

Overall, this experience was gut-wrenching, frustrating, and a huge let down. I wish my students did not have to waste their day taking it, nor see that everything they learned about math in the last ten years is obsolete. I think a lot of us would love to have a real crystal ball or see the future like Jedi Knights, for one day I got see the future and I wish not to see it again.

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