Monthly Archives: September 2011

Education Myths Debunked (I)

In the last couple of weeks, a series of unrelated articles seem to debunk some cherished myths in primary and secondary education. These articles ought to lead us to ask – with fresh insights – the essential question: how do we make our students learn?

The first article comes from the New York Times and discusses the fact that introducing technologies in the classroom does not necessarily lead to improved scores (“In Classroom of Future, Stagnant Scores”). The second article, from NPR, argues that the idea of different kinds of learning (visual, auditory, etc.) is not supported by research (“Think You’re An Auditory Or Visual Learner? Scientists Say It’s Unlikely“). Finally, the third article, also in the New York Times (“School Curriculum Falls Short on Bigger Lessons”), discusses the difference between hard work and being “smart”.

The first two articles, although they address two different subjects (perhaps!) –  technology in the classroom and learning styles – both point to a very important conclusion: there are fads in education just like in fashion. The important thing is to use research based evidence and not to give in to these fads.

For example, there are no randomized, controlled studies which demonstrate that introducing such things as Smart Boards, video or Power Point in the classroom will lead to improved student performance. I am aware that we have to be careful in our conclusions: technology indeed may not enhance learning, but it is also possible that we did not yet develop adequate methods of assessing the contribution of technology (per se) in learning. Also, a third possibility is that we have not yet developed the lesson plans, assessments and/or textbooks that use technology in the “right” way – hence we see no progress in student scores.

It may also be that different technologies lend themselves better to different educational areas. Both AP Stats and AP Calc would be much “poorer” courses without graphing calculators. In Stats there is a current to teach the course (at least the inference part) through randomization methods – for this, computer software such as Minitab or Fathom is almost a necessity.

The trick seems to be to stay on the right side of learning and not to stray in the area of entertainment. Faced with “extra” time on a computer, students will easily gravitate towards Solitaire and video games. My hypothesis is that, unlike the majority of teachers, our students have come into visual media via entertainment: video games, movies, etc. Moving images entered our students’ DNA as a form of perpetual motion amusement. In my opinion, it is hard to have these students concentrate on the learning experience and not to be distracted. Furthermore, I think it is hard for these students to extract a learning experience from the visual presentation – in other words, synthesis of learning from visual imagery is difficult for those who have grown up with visual imagery as entertainment.

To extract such a synthesis a lesson would have to be carefully planned, perhaps interspersed with “what if?“ and “what do you conclude?” questions, with the answers written down. From what I have seen around me, most teachers either do not have the talent or (more likely) the time to create a truly learning experience from visual imagery. Most often, it’s “here’s the video” with little student participation and experimentation and, more importantly, little guidance towards a synthesis.

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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.

What math is about

Yesterday, the New York Times published some replies to a previous op-ed page article dealing with teaching mathematics through real-life applications only (see my previous post). I quote two such typical replies.

To the Editor:

Sol Garfunkel and David Mumford argue that high school math curriculums should include more real-life applications so that students will be better prepared for 21st-century careers. I disagree.

Mathematics, like literature, music, science and any other subject worth studying, should be taught and learned for its own sake. Just as we teach students the beauty of poetry, we should teach students the beauty of mathematics — a beauty that does not depend on calculating a gear ratio or estimating a marginal profit.

If we try to make math curriculums “relevant” to daily life, we will end up teaching students a series of disconnected formulas. Another generation will grow up thinking of mathematics as a mess of scary symbols, something with no inherent logic, best learned by memorization.

ANDREW M. H. ALEXANDER
Oakland, Calif., Aug. 25, 2011

To the Editor:

You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things.

JONATHAN DAVID FARLEY
Orono, Me., Aug. 25, 2011

The writer is an associate professor of computer science at the University of Maine

I feel better now – I am not alone seeing that teaching math is not only about standards, not  about recipes for specific types of problems, but it is also about the gestalt of the thing – the universality and beauty of this subject. We ought to find the time in our busy teaching days and take a moment or two and tell the kids that we, the hopefully respected adults,  see a beauty in the subject, that doing math is fun, that there is pleasure in thinking. Who knows? May be the message will stick with a few.