Sunday, March 04, 2012

An update on high school math education

A while ago, I commented on official year 2000 stats that showed 75% of high school kids cannot use math in real life problems. Obviously this is bad. So what happened since then? I found a convenient 2009 data set in the 2010 education statistics digest published by the US government. You can see the table here.

There have been some changes since 2000. In the current table, math students are graded in 6 levels of proficiency, as opposed to 4 in the earlier tables. Here is a description of the levels, and some summarizing I did on my own.

Level 1: Able to answer questions involving familiar contexts where all relevant information is present and the questions are clearly defined.

There doesn't seem to be anything extraordinary here.

Level 2: Able to interpret and recognize situations in contexts that require no more than direct inference; extract relevant information from a single source; employ basic algorithms, formulae, procedures, or conventions; and employ direct reasoning for literal interpretations of results.

There is nothing interesting here either. Actually it reminds me of rote and training as opposed to education.

Level 3: Able to execute clearly described procedures, select and apply simple problem solving strategies, interpret and use representations based on different information sources, and develop short communications reporting one's interpretations, results, and reasoning.

It feels as if we are getting there, but note people at level 3 tend to follow instructions and do, at most, simple decisions. This is not very good.

Level 4: Able to work effectively with explicit models for complex concrete situations that may involve constraints or call for making assumptions, select and integrate different representations, reason with some insight, and construct and communicate explanations and arguments based on one's interpretations and actions.

Finally, students are expected to reason with some insight about constraints and assumptions. This might be enough proficiency to attempt thinking more or less independently.

Level 5: Able to develop and work with models for complex situations, select and evaluate appropriate problem solving strategies, work strategically using broad, well-developed thinking and reasoning skills, and communicate one's interpretations and reasoning.

We have wait until level 5 to see the first call for "well-developed thinking and reasoning skills". So, under level 5, you do not have well-developed thinking and reasoning skills. Ouch.

Level 6: Able to conceptualize, generalize, and utilize information; link different information sources and representations; perform advanced mathematical thinking and reasoning; develop new approaches and strategies for attacking novel situations; and formulate and precisely communicate actions and reflections regarding findings and interpretations.

And level 6, students can think of solutions on their own. A true independent thinker.

So now, with these levels in mind, let's go over the table. First of all, if you go through the digest you will find several tables that assign scores to students. Looking at the scores alone, you'd think the US is doing pretty well because it scores ~265 of 300. But how do you know the tests actually measure something relevant? That is why we look at actual proficiency.

In the US, level 4 and above are still at about 25% of the students. In other words, 75% of students cannot reason with any insight about constraints and assumptions. Things like "can I buy and pay for house X, with the constraint that I have salary Y, and assuming I'm employed along the lines of Z?" are outside the reach of level 3 and below. They need to be told the procedure, they cannot figure it out for themselves. Are we surprised about the results?

But how does the US compare to other countries? First, some countries that are not doing very well. According to the tables, level 4 and above constitute less than 5% in Argentina. Peru for example, has 2.6% for level 4 and above, and 47.6% are below level 1. In Colombia, there's only 38.8% under level 1 so it seems comparatively better, but level 4 and above is only 1.7%. Brazil and Panama are about the same. Uruguay and Trinidad and Tobago are doing a bit better.

Well so much with Latin America. How about Qatar? Aren't they full of oil? Well yes, but it looks like they are having some challenges of their own because 51% are below level 1, and only 6% are at level 4 or above. Dubai is doing better. Other countries look similar to the US, like the UK, the Czech Republic, the Slovak Republic, Italy, Hungary, Portugal and Spain.

Ok, how about some serious competition? Let's see... in Australia, level 4 and above is close to 40%. Canada's level 4 and above is a bit over 40%. Something similar happens with Belgium, Germany, Japan, the Netherlands, New Zealand, Macao-China, etc.

There is a higher tier as well. Finland, for example, has about 50% at level 4 or above. Switzerland is close to 48%. Liechtenstein has about 49%. Chinese Taipei has about 50%. The Republic of Korea weighs in at about 52%. Hong Kong's level 4 or above is over 55%. Singapore has 58%.

The countries that are doing comparatively well (at least ~40% at level 4 or above) are just a roundup of the usual suspects. But who tops the list? According to the table, Shanghai-China has over 70%. In fact, their level 6 population is larger than that of any other level.

So, it could be done right in the US if we wanted to, but effectively we don't. For all we want to "have an intelligent discussion about our problems", exactly what are we going to propose without putting in the time to understand things first? We are the ones who spend an average of 30 hours a week in front of the TV and Angry Birds, so why don't we start putting in the time where it counts?

None of this should be surprising. In fact, it is well deserved.

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