Love of Lockhart

I am re-reading Measurement, by Paul Lockhart. His mathematical values precisely match with mine. I want to be him. Read the book read the book read the book.

I wonder what he would say to the idea that the ability to view Math as an imaginary land where you explore and play is a privilege that only some students are able to access? That, due to systemic oppression, we would be doing students a disservice by skipping past mastery of skills straight to open-ended tasks?

Here is me attempting to recreate Lockhart’s ethos in my geometry class, full of curiosity at wandering in the mathematical jungle.

 

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Circles only exist in our minds… But let’s still go and assume that measuring this circle is useful? Ha!
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Other People’s Children

Lent by Ginna.  Some disorganized thoughts:

 

The dichotomy between traditionalist and progressive education is a false one, created by academics for ease of analysis. Good teachers know that both have their strengths, and a balance is the only way forwards.

 

Dry slow-paced practice is terrible. Every task has to be meaningful, taught in context, aimed at a real audience. What does this mean in Math?

 

If you only focus on open-ended rich tasks, thinking about fluency rather than skills, then you widen the achievement gap. Students who come to you with basic skills in place will fly. Students who don’t have this foundation will never be given an opportunity to build them, and will fall further behind.

 

Don’t be shy about exhibiting the fact that I have knowledge-based power. By pretending the power doesn’t exist I am not helping my students. Instead I should be explicit about what the students need to do to gain power themselves. Simultaneously, we should also work to destroy the power imbalances of society.  “Pretending that gatekeeping points don’t exist is to ensure that many students will not pass through them”

 

Students already have a voice. My job is to not help them to find their voice. My job is to help them to hone their voice, and make it work in the dominant discourse of American society.

 

The teacher should act primarily as an ethnographer – actively seeking to  understand the diverse cultures of my students.

 

Teachers are experts in their fields. Students are experts in their lives and communities. Relish and use both.

 

 

Questions:

  • How can I be more active as an ethnographer? Without overstepping the teacher/student professional boundary, and without embarking on poverty porn?
  • I agree that there are many skills in English that are essential to modern life – the ability to write a letter/email or speak in a “sophisticated” way is essential to have a successful professional life. I disagree that this idea transfers well to Math. If my students are unable to write a written argument well, they will be limited when communicating with colleagues. If they are unable to apply the cosine rule, there is no inherent limitation (apart from in the arbitrary world of assessments). Surely the role of Math is to encourage deeper thinking? It’s not that I naively assume that through rich problem-solving my students will magically pick up an understanding of the cosine rule (that thinking would be putting diverse students at a disadvantage and is something that I thought last year), I just don’t care at all about the cosine rule.