Tag: lesson planning

Posted in Mathematics education

Bloom’s Taxonomy and iPad Apps

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The original Bloom’s taxonomy include Knowledge, Comprehension, Analysis, Synthesis, and Evaluation. I was introduced to this when I was in college and I must admit it was not of much help to me in planning my math lessons. I just couldn’t fit it. The pyramid image was not of help at all and I think even created the now much ingrained deductive method of teaching. I think teachers must have unconsciously looked at it as a food pyramid so they give a dose of those of knowledge-acquisition activities first before providing activities  that will engage students in higher-level processes

 

Lorin Anderson, a former student of Bloom, revisited the cognitive domain in the learning taxonomy in the mid-nineties and made some important changes: changing the names in the six categories from noun to verb forms and slightly rearranging them. The new taxonomy reflects a more active form of thinking of Creating, Evaluating, Analyzing, Understanding, and Remembering. I also like the inverted pyramid as long as it is not viewed like there is a strict hierarchy of the categories. In fact in my own experience I just make sure that all these are covered in a lesson as much as possible. The way to do this is to teach mathematics through problem solving or engage students in mathematical investigations. Still, the best framework will still be one tailored to mathematics. For me its my list of Mathematical Habits of Mind.

Revised Bloom's Taxonomy

In searching for Bloom’s taxonomy I came across the image below – Bloom’s taxonomy for iPad. It’s a collection of iPad apps classified according to Bloom’s taxonomy.  I found it cute so I’m including it here. This will come in handy once I have my own iPad and start creating math lesson for this device.

There is also such a thing as Learning Pyramid which compares how we learn things and the retention rate in our brain after 2-3 weeks.

Click here for source of image of Bloom’s Taxonomy for iPads.

Posted in Elementary School Math

Teaching the meaning of equal sign

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Here’s how I sequence my lesson to develop pupil’s understanding of the meaning of the equal sign. Actually the lesson uses the context of the meaning of equal sign to introduce the students to the meaning of variable intuitively. The students enjoyed this lesson and they said they loved the way I made them think. Scaffolding was done through questions that engages pupils in reasoning and making decisions. Note that the emphasis of the lesson is not on computations but on thinking and problem solving. This is also an example of teaching algebraic thinking in the grades.

I first wrote the equal sign on the board then said What does the equal sign mean? You may use an example to explain your answer. One boy said it means you add or do the operation and provided this example 2 + 10 = 12. I asked the class who agrees with him and 25 out of 35 showed hand.

What about in 15 + ____ = 21 + ____? One girl said “It means balance” and explained that 15 plus a number balances with 21 plus another number. When I asked the class who agrees with her 30 out of 35 raised their hand. Everyone’s eyes was on me, waiting for me to say which meaning of equal sign is correct. I just gave them a wink to heighten their curiosity.

Now that I got them all thinking, I asked: Do you think you can put just any two numbers in the blanks? With this question I successfully divided the class into two camps: those who say yes and those who say no and everyone is challenged to prove themselves right or prove the other wrong.

Click here for the slide version of this post.

Posted in Curriculum Reform

(Mis) Understanding by Design

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click image for source

The country’s schools are now implementing ‘Understanding by Design (UbD) curriculum.’ Some private schools are implementing it at all levels while all the public schools are on its first year of implementation starting with first year high school subjects. I’m not a fan of UbD, especially in the way it is being implemented here but that is irrelevant. (If I have my way, I rather spend the money for Lesson Study.) But of course, I want UbD to work because DepEd is spending taxpayers money for it. But from conversations and interviews with teachers and looking at what they call call ‘Ubidized learning plans’, I am starting to doubt whether or not what we are implementing is really UbD. Here’s how UbD is understood and being carried out in some schools:

1. With UbD teachers will no longer make lesson plans. They will be provided with one. Here’s a comment on my post Curriculum Change and Understanding by Design: What are they solving? from a Canadian educator:

UbD may not be your priority–I gather that you see PCK and CK as the core issue. But at least UbD positions teachers as the decision-makers rather than imposing lessons on them…. I am not a UbD proponent, but I think it’s a structure I could work with, a structure I could infuse with my beliefs and goals, because it puts teachers at the center of the decision making, with student understanding as the target.

Indeed, nowhere in the UbD book of McTighe and Wiggins that they propose that teachers should no longer make lesson plans or that it is a good idea that somebody else should make lesson plans for the teachers. What they propose is a different way of designing or planning the lesson – the backward design. Continue reading “(Mis) Understanding by Design” →

Posted in Algebra, High school mathematics

PCK Map for Algebraic Expressions

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When I design instruction or plan a lesson I always start with making a map of everything I know about the subject. The map below is an example of a map I made for algebraic expressions. I won’t call it a conceptual map because it’s only the left part of it (the ones in black text) which deals with the concept of algebraic expressions. Those at the right (in red texts) describe what I know about the requisites of good teaching of algebraic expressions including my knowledge about students’ misconceptions and difficulties in this topic. Maybe, I should just call this kind of map, PCK Map, for pedagogical content knowledge map.

Pedagogical Content Knowledge (PCK) Map for Algebraic Expressions

I find doing the PCK Map a useful exercise because it helps me link concepts, synthesize my teaching knowledge about the topic, not leave out important ideas in the course of the teaching and of course in planning the details of the lesson especially in the selection of activity/tasks and in framing questions for discussions.  I also find it useful in evaluating my teaching of the unit.

There are two ways a PCK Map can be enriched: (1) use Google (alright, go to the library and see what experts think are important to cover in the topic, they’re also outlined in the Standard) and (2), after each lesson or at the end of the unit, write your new knowledge about the topic especially students misconceptions and difficulties and how it can be addressed next time.

Click this link to see a the lesson plan I made based on the PCK Map. The lesson is about teaching combining algebraic expressions via a mathematical investigation activity.