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Understanding Students’ Misunderstandings: Musings on Mathematics Testing and Evaluation March 21, 2011

Posted by Arvin in School.
Tags: , , , , ,

We teachers often rely on students’ written assessments to assess their skills and understanding. But through in-depth probes with students, we unravel valuable information not readily available on written assessments. This information is essential for guiding instructional decisions made by teachers and school administrators, and is sadly under-utilized even at the university level.

Let’s look at one recently-documented case featured in an Educator’s Magazine.

A 5th-grader was presented with a card: 30 students, 4 students in a car. He was asked how many cars are needed to fit in the students. The child answered “7 remainder 2.”

The child was able to compute correctly, but that alone is no indicator of division proficiency. It made sense numerically, but not in the context of the problem. A “remainder 2” does not make absolute sense to the question “how many cars are needed”. Division work on naked numbers – such without connections to context requiring interpretation – may make students fail to see the importance of reasoning to decide on the answers’ meaning.

I have always believed that a student does not stop with acquiring information, but with understanding how that information relates to various contexts and real-life scenarios.

For instance, we do not end with making students remember and know how to manipulate formulas in solving initial velocity or work done. We end by checking their understanding of the interdependence and relationship of each variable, and the relevance of these computations to their everyday lives.

Truthfully, our schools are dearth with teachers who understand and appreciate the relevance of these mathematical operations to their day-to-day routine. Their learning mostly ends up confined in their classrooms and lesson plans. No wonder, our schools are being deliberately plagued by living robots and zombies, inspired by a withering passion for the teaching cause, and slaves to the political machinery of the local bureaucrats.

Too often, we brag that we know and we understand what we teach. But when asked about how it translates to our daily lives, we tend to dismiss it by reasoning “This is not the time for cerebral calisthenics.”

Add up the fact that our current educational system does not afford us ample time to probe and explore students’ comprehension. We are burdened with a thickly-ornamented curriculum

1. that forces us to incorporate all possible combinations of approaches and methods, and

2. does not drill deep into the students’ frail comprehension framework.

We limit ourselves to a pen-and-paper standard, when much of the learning and understanding is masked by a record of outstanding or deficient grades.

Written assessments do not necessarily reveal the real situation of a child’s learning. And inevitably, these patterns of learning carry on from college to workplaces. It is no wonder that despite the brilliant achievements of today’s thinkers and movers of the society, we are still swarming with underdeveloped individuals who trigger societal and economic breakdowns.

Moving forward, we do not want more and more ill-prepared Juans and Marias to fill up the workforce of the coming generations. We must take up arms as teachers and innovate our approaches and strategies to address this harsh cycle of deficient learning and build up a better society that generates life-long solutions for a better and sustainable life.



1. Tony Legarda - April 5, 2011

I’m right there with you! I often think about how what we learn in school may be applied practically.

At the risk of being skewed I would like to express why Shotokan Karate does not do so well in the MMA circuit as compared to Brazilian Jiu-jitsu or even Judo. Shotokan Karate can be very effective. It’s just that most practitioners fail to apply the techniques practically in the ring.

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