Category Archives: Instruction for Foundational Knowledge

Instruction for recall and understanding, for Lower Blooms, for developing foundational knowledge

Capacity Matrices: Examples & Overview

As Quality Learning Australia points out:

A Capacity Matrix is a tool to describe, document and monitor our learning. It allows us to clearly identify what is it we wish to learn, derived from the curriculum and student interests, and then track learning over time. It can be very effectively used with the Plan, Do, Study, Act (PDSA) cycle and supported with a portfolio that provides evidence of our learning. Capacity Matrices are also used for self-assessment as well as peer assessment.

In Auburn, we are starting to use Capacity Matrices in this way. Our teachers are wondering where they can see examples and where they can learn more. Below are a handful of resources to help address that need.

General Information about and Examples of Capacity Matrices:

We Had It All Backwards: The Two Types of Instruction

When I told my Curriculum Director, Shelly, about my thinking about there being two types of instruction (Instruction for Lower Level Thinking and Instruction for Higher Order Thinking), she seemed to think the idea made a lot of sense to her, especially in the context of our work around Customized Learning.

She agreed that given how curriculum is organized within Customized Learning, we couldn’t continue to emphasize lower level thinking.

And we got talking about how, since all our middle and high school students had laptops, probably the low level learning, the recall and simple application, was something that students could largely do on their own (with guidance, and coaching).

And then Shelly said, you know, we’ve had it all backwards…

She told me about when she was a high school science teacher, she did a cell unit with students. She used to spend about two weeks of direct instruction to insure that students knew all the parts of a cell. Then she would turn students loose to do an analogy project, where they would write about how a cell and it’s parts were like something else (maybe a football team, or a corporation) and its parts. Students largely worked on this project on their own.

And we reflected on the irony that we (teachers) would spend so much time on something students could probably do on their own (looking up background information). And we did so little direct teaching on something that students probably needed more modeling and assistance with, the higher order thinking.

And we reflected on how teachers should really do a unit, like the cell unit, the other way around. Turn kids loose to learn about the parts of a cell, then do a bunch of instruction and scaffolding on how to make a good analogy (or what ever kind of complex reasoning we’re asking students to apply).

Other places do it that way. Carpe Diem is a 6-12 public school in Arizona that allocates its teaching resources directed at the higher order thinking more than the lower level thinking. Students use online curriculum, supervised by educational technicians, to learn the basics within a unit. Then students spend a large block of time each day, working directly with certified teachers, doing projects and other activities that require higher order thinking (nontrivial application, complex reasoning, and creating) with the content and skills from the unit. Watch this video about Carpe Diem’s approach.


What impact would it have on your students, if we turned them loose to use technology to learn the basic information in a unit, and then we spent quality time with them, both instructing students in how to do complex reasoning, and in applying complex reasoning to the content?

Thinking of Instruction as Two Types

When our pilot teachers were visiting a school that is a little further along than we are at implementing Customized Learning, a colleague and I got talking about how we (us and our colleagues) had a lot of work to do on instruction if we were going to be successful with our implementation.

Then it hit us that a lot of teachers would say they already do a pretty good job with instruction and would object to being told that we had a lot of work to do on it.

And then I realized that both perspectives were right. We just weren’t talking about the same kind of instruction in each instance.

There are two kinds of instruction.

There is Instruction for Lower Order Thinking and Instruction for Higher Order Thinking.

So, it doesn’t matter if you use Bloom’s Taxonomy, New Bloom’s, Marzano’s Taxonomy, or Webb’s Depth of Knowledge, Instruction for Lower Level Thinking is focused on recall and simple application, and Instruction for Higher Order Thinking is focused on nontrivial application, complex reasoning, and creating.

Our teachers are really pretty good at Instruction for Lower Order Thinking. But we have a lot of work to do on Instruction for Higher Order Thinking.

The distinction, thinking of instruction as two types, doesn’t just help clarify our thinking.

This distinction would actually help us in a couple different ways.

We now could say, “You guys are really good at Instruction for Lower Level Thinking. But now, to do Customized Learning well, we need to help you get better at Instruction for Higher Level Thinking.” The message about getting better at instruction would have always been about support, but could have been taken as criticism of their abilities. Now, we can differentiate between validating their abilities, and identifying a need, and offering support to address that need.

And it helps us think about when should teachers apply each type of instruction.

And it will help teachers think about how the two kinds of instruction are different and which strategies support which type.

And it helps us think about leveraging what kinds of interventions to support teachers.

What would thinking of instruction as two types mean to you and the work you are doing in your school?

Correct Answers vs. Building Understanding: What Do Learners Need?

My step-son, Sam, is one of those otherwise bright students who struggles with math. Back when he was in high school, his mom asked me to help him. He had gotten a question wrong on a Geometry quiz and didn’t understand the correct answer. My wife hoped that since I was a former high school math teacher that I could help him out.

The question was, “What is the intersection of two planes?”

He told me that he had answered that the intersection was a point, since only lines intersect. Sam went on, “I went in to ask my teacher about the question, but she just kept giving me the right answer. I really don’t understand it at all.”

“So, you’ve only talked about lines intersecting?”

Sam nodded.

“And you haven’t really talked at all about planes and how they intersect?”

Sam shook his head.

“Then I could see why you thought it was a point,” I told him. “But look at this.” His notebook was on the kitchen counter where we were talking and I said, “Let’s say this is one of the planes,” while tapping his notebook. I grabbed a magazine, saying it was the other plane. I held the spine of the magazine at an angle against the face of Sam’s notebook.

“How do these two planes come together? What kind of geometric shape?” I asked.

Sam got one of those “Oh, my gosh! Is it that simple?!” looks on his face and said it was a line.

Now, there was nothing wrong with the teacher asking the plane intersection question without first modeling it for students. It is a great way to have students apply the concept of intersection of geometric shapes and see if they really understand it. And the teacher was a kind and knowledgeable math teacher.

But students who struggle with a subject need more than just someone who is sensitive and kind and knowledgeable. Sam needed more than the correct answer. I think teachers who are intuitive mathematicians (or social scientists, or literacy specialists, or scientists) know their subjects in an intuitive way that makes it hard for them to explain ideas to students who do not understand their subject intuitively.

When students get an incorrect answer, it is too easy for teachers who understands their content intuitively to assume that the student simply made a mistake (perhaps in calculating), or didn’t study hard enough, or is simply a slow student in their subject.

What they don’t understand is that more often than not, a student’s wrong answer is actually a correct answer within the student’s current (but incorrect) schema for the topic – the student’s internal model that tells him how things work.

If the teacher’s goal is to have the student understand the material correctly, then simply offering the correct answer is less productive than trying to understand the student’s misconception and then think of an example or a way to model the material that will create a bridge between the student’s misunderstanding and the correct understanding.

Sam’s schema said only lines intersect and he knew that lines intersect in a point. We could either stop with proving that Sam was wrong by giving him the correct answer, or we could work to understand his thinking so we could lead him in the right direction.

I don’t blame the teacher. She simply did what I did when I was a math teacher. It wasn’t until long after I stopped teaching math and became of student of learning that I grew to understand this principle.

How much more effective would our teaching be if we approached our students’ incorrect answers as misconceptions rather than missing information?


Apple, Textbooks, and Carbon Fibre Buggy Whips…

The other day, Apple held a big education event in New York, focused on textbooks on the iPad. (Info here or watch the event here). Apple released several products and tools, hoping to further impact the education market.

Apple released iBooks 2.0 (supports multimedia in the books, interactive elements, highlighting, note taking, pinch for TOC etc.) and a new category in the store: textbooks. Pearson, DK, and McGraw Hill already have a couple textbooks available. They’re cheaper than a regular text, too: around $15, but I think the goal is to sell one per student, instead of using one with 5-8 students over a period of 5-8 years. (Cool Cat Teacher blogs here about what it was like to work with/test out an interactive text.)

There is a new Mac app (Lion only) called iBooks Author for making your own “textbooks” (think Pages combined with iWeb combined with Keynote). Completed books can be sold in the iBookstore.

Finally, there is a new iTunes U app for iPad which lets teachers harness “courses” based on content from iTunes U, and the addition of tools so you can add your own syllabi, message with your students, make assignments, etc. Looks kind of like if iTunes U, Noteshare, and Newstand combined. Apple also announced that although iTunes U has traditionally been for University use, K-12 can now sign upfor accounts.

I can’t blame Apple for wanting a piece of the textbook market. According to Wired, in 2010, Pearson had over $8 billion in revenues and McGraw-Hill over $2 billion. (Yes. Billion. With a “B”! As in 9 zeros!) And the traditional print publishing industry is struggling. Newspapers, magazines, trade books are are struggling to redefine themselves in a digital world.

What print textbooks share with those other genre’s is that they are not interactive in an age when our students are accustomed to accessing interactive media (as illustrated by Joe’s frustration at his non-notebook computer). At least Apple’s new textbooks and textbook creation tools address this issue and allow publishers to create textbooks with videos, interactive models and other elements. So, if you’re going to use a textbook, I guess I’d rather you use one with interactive elements than a static one…

But in general, I’m not a huge fan of textbooks. I think for me, the problem is that too many places use textbooks AS the curriculum. I’m perfectly happy with good teachers who see textbooks as one educational resource to use as they design (or as students design) learning experiences. But too often it seems the textbook is the only resource. Textbooks are insufficent for the curriclum because they only provide background knowledge. They don’t provide context, or experiences, or allow students to synthesize or apply information. In other words, by themselves, textbooks essentially only provide facts, they don’t help students create meaning.

Textbooks seem out of place in a day when schools are trying to reinvent themselves from a system that was designed to work for only some students. In this economy, we need systems that work for every student. And those systems need to engage students not just in aquiring knowledge, but in creating meaning from it. Textbooks are so “last century”! Given today’s interactive, digital world, educator and blogger Fraser Speirs refers to the new textbooks as “the equivalent of carbon fibre buggy whips.”

In my opinion (and other’s, and other’s, and other’s, and other’s) often the best learning (and teaching) happens when teachers don’t use textbooks. This is especially true, living in a state where every middle school student, and about half the high school students, have a school provided laptop (and all of my district’s kindergarten students have iPads!). You’d think teachers would work with students not only on how to find information, but then also how to leverage their technology to apply, evaluate, and create with that knowledge.

For example, imagine an introductory lesson focused on building a student’s background knowledge on a topic. Instead of having students read a chapter on the causes of the Civil War and then discussing what they read (which, by the way, every single child not only read the exact same description of the causes, but they all have been exposed to only one take on those causes – the textbook’s), have students open their laptops and ask them, “what were the causes of the Civil War?” Students could search and share what they found out. You could ask, “Did anyone find anything different?” You could even compare sources or discuss approaches to surfing and searching. You could have them find perspectives that would reflect substantially different points of view. You could explore and discuss different kinds of sources and the apparent relative value.

Well, maybe not the first time you do this with students, but certainly the more times you do, the more you model for them, and the more they reflect on the process, the more your “introductory” lessons could look like this. And think about the “learning” skills and digital citizenship skills your students would develop!

That all said, these announcements are ripe with possiblities and potential! There is certainly some incremental improvement having texts with interactive elements (still no real model of an interactive text). But I think the understated power of Apple’s announcement last Thursday are iBooks Author and the iTunes U app. I agree with Fraser Speirs’ assessment:

iTunes U is the game changer. Put iBooks Author and iTunes U into the hands of great teachers, put iPads in their students hands, put them all in a room together then step back and see what happens. That’s the ballgame.

Over the next week or so, I’m going to publish a series of posts that explore some of that potential:

  • Product Creation Tools for Students
  • A Platform for Creating On-Demand PD for Teachers
  • Curriculum Creation Tools for Customized Learning

It’s Your Turn:

What was your reaction to Apple’s textbooks announcement? How do you think it will impact schools, education, and educational reform?