If you wake your students in the middle of the night….

If I would wake up my students in the middle of the night, what math would they remember? What math do our students remember to do correctly?

I thought it might be interesting to see how much math these students remember from their past courses by giving them a basic skills math test in the first day of school. (You must be kidding Mr.S! No I am not – it will count for your grade!)

Developed originally by Marianne Johnson and Eric Kuennen (J&K) at the University of Wisconsin (Oshkosh) and extended by M.L. Lunsford and P. Poplin (L&P) at Longwood University, the instrument I chose is a 20 question multiple choices quiz.  These authors looked at predictive factors for success in an introductory college statistics course for business and liberal arts students, with a Precalculus prerequisite in one case  (Johnson and Kuennen) and in another (Lunsford and Poplin) with no math prerequisite.  In both studies, the authors found that “students’ basic mathematical skills… were a significant predictor of student success in the course.”

The graph below shows the percentage of correct answers for each question. MHS stand for My High School. The students at MHS were freshmen and sophomores taking Algebra II.

I will limit my comments largely to My High School (MHS) results.  Only 20% of the students remember the correct formula for a triangle – students forget the ½ and give double the correct answer (Q07). Students have difficulties with proportions – less than 60% of the students gave the correct answer to very simple proportions problems (Q05 and Q06). In addition, proportions – this time percentages – gave dismal results in Q 19 and Q 20.

One third of the students can not do a very simple division of fractions (Q 06).

The worst performance was from the following question:

Q 12.  The square root of 100,000 is about

(a)  30              (b) 100             (c) 300             (d) 1,000          (e) 3,000

Most of the incorrect answers were (b). What is going on here? Following a procedure blindly?

I am kind of puzzled as to what Q10 and Q18 show. They are both very simple word problems that deal with unit conversion.

Considering how simple the test is – the algebraic concepts are truly basic – the fact that we have a quarter of our students (high school and universities) not being able to solve correctly the majority of these problems, shows …what?

(a)   That we are promoting kids that do not know math as well as they ought to?

(b)   That we do not explain concepts clearly and students adopt procedures blindly?  [For example, in class I was shaken by how many of my students went from

–        (x– 3)/4 to

–        (– x + 3)/–4.

They distributed the –1 blindly. Do we have to teach that this –1 is really –1/1?]

What I am going to do is (a) make sure that we do some extra exercises in the weaker areas, (b) communicate these results to my fellow math HS teachers and (c) communicate the results to the middle school teachers.  Hope it helps.

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3 responses to “If you wake your students in the middle of the night….

  1. This is interesting. How much time were they given? I’m assuming it was without a calculator? It would be very interesting to give the test to other students to see how they compare. Curious how well your Pre-Calc students or even your Calc AB students would do.

    • Hi Good to hear from you! Hope your school year is going well. They were given the test for 20 minutes; no calculator. This is the same as the time they were given in the two reference articles. Also, I did it in 6 minutes and my rule of thumb is that it would take the kids 3x my time. I am also planning to give it to my AP Stats kids for the other classes (Precalc or AP Calc) I need to ask the instructors permission. I intend to use the data in my AP Stats classes right now to look at distributions, later for some inference problems.

  2. Hi – Good to hear from you! Hope your school year is going well.
    They were given the test for 20 minutes. This is the same as the time they were given in the two reference articles. Also, I did it in 6 minutes and my rule of thumb is that it would take the kids 3x my time. I am also planning to give it to my AP Stats kids – for the other classes (Precalc or AP Calc I need to ask the instructors’ permission. I intend to use the data in my AP Stats classes – right now to look at distributions, later for some inference problems.

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