WHAT DO LESSONS TELL US ABOUT TEACHERS’ LEARNING

FROM LESSON STUDY?

Interactive Symposium

Presenters: Betsy King, Catherine Lewis, Aki Murata, Rebecca Perry, Mills College Lesson Study Group

Discussant: Brian Lord, EDC

Symposium Overview

In this symposium, we will look at data from two cases of lesson study, with the goal of thinking together about the types of data that should be collected for various purposes during lesson study (and perhaps other forms of practice-based development). Each audience member will be asked to rate the usefulness of various data; results will be posted on the website www.lessonresearch.net.

Background: Contrasting Perspectives on the Evaluation of Professional Development:

Hilda Borko’s 2004 AERA presidential address (subsequently published in ER) suggests one framework for the evaluation of professional development: scale-up and systematic testing in diverse circumstances of “well-specified” PD approaches. Richard Lesh, Roberta Schorr, and others suggest a somewhat different approach: “multi-tier design studies” in which the learning of students, teachers, and researchers (or professional developers) are simultaneously tracked, allowing for revision of the professional development as researchers learn from the student and teacher learning. The latter approach assumes that different learning may occur for different teachers, and that some learning may not be specifiable in advance. These two frameworks expect different types of PD: on the one hand, “well-specified” programs that can be disseminated in a controlled fashion; on the other hand, locally customized programs whose warrant for effectiveness comes from close-up study of use in a particular local setting, rather than from controlled trials conducted in other settings. Thinking about these two very different perspectives helps us frame two different questions we might want to ask about professional development evidence. On the one hand, is there evidence of impact on teachers’ learning? On the other hand, are artifacts produced that enable us to improve the professional learning opportunities, or to create similar professional learning elsewhere? (For example, is the learning creating “actionable artifacts that leverage learning in other sites” (Bannan-Ritland). We look at the two cases with these questions in mind.

CASE 1: THE VOLUME OF RECTANGULAR PRISMS

Case I Context

This case comes from a 5-day cross-site summer lesson study workshop held in the Western U.S. Educators from seven school districts collaboratively studied a series of three research lessons taught to the same fifth grade class on three sequential days. Each day’s lesson built on the prior day’s learning on volume of rectangular prisms. Two primary workshop goals were to: “Deepen our understanding of lesson study, mathematics, and teaching-learning through collaborative, practice-based work;” and to “Study and build classroom mathematical discourse, using lesson study as an inquiry tool.” Three of the 17 group members, all from a single site, collaboratively prepared plans for a series of three lessons on the volume of rectangular prisms, based on Investigations in Number, Data and Space.[i] One member of that team taught the sequence of three lessons to a grade 5 class at a year-round school, serving as a “guest teacher” at this unfamiliar site. Using feedback from the other 14 participants and data collected during each of the lessons, the group modified the lesson plans and used the data to consider the nature of mathematical discourse and how to promote it.

Research Method

The three research lessons and associated debriefs, and all associated planning (approximately 13 hours) were videotaped and transcribed. The first author, a participant-observer in the group, reviewed all videotapes and transcripts, as well as participants’ written reflections, in order to identify “learning threads,” i.e. topics related to mathematics and its teaching-learning that surfaced two or more times in the materials. The natural history of each learning thread was documented, and inferences developed about the catalysts/supports for each learning thread. (These data were then reviewed by other researchers and group participants.) This paper presents several of the learning threads.

Questions: What, if anything, do the materials tell us about whether learning occurred? What materials would be useful in (re)creating this kind of learning in other professional development settings?

Learning Thread /

Natural History

/

Catalysts

Language Use: When to Learn Mathematical (MM) Vocabulary. At outset, so it can be heard and used in discussion, or at the end, after concept has been learned? / Of concern to group that brought in lesson, because students did poorly on content they had been taught, and group conjectured it might be due to vocabulary differences.
Issue raised repeatedly throughout planning meetings (see transcript excerpts) and in individual written reflections / Standardized test performance sparked initial concern about vocabulary on part of initial planning group (IPG).
Disagreement about whether and when to define vocabulary in lesson provoked discussion in large planning group.
Volume is not counted, but measured; moving from counting to multiplicative view of volume may be important to subsequent understanding. / Raised in first large group planning meeting and many times thereafter; shows up in many individual written reflections. / Raised by Japanese colleague in response to IPG’s initial lesson plan
Base times height provides a better basis for generalization to other prisms than does length times width times height / Raised in first large group planning meeting and many times thereafter; shows up in many individual written reflections. / check
Important to establish the purpose of the lesson, not just the activities. / What’s the purpose of this lesson? What mathematics do we want students to learn? Question posed in first large group planning meeting and many times thereafter; shows up in many individual written reflections. / Japanese colleague initially asked “what’s the purpose?” in response to a discussion focused on lesson activities rather than mathematics, and in response to need to choose among activities. In later planning, other group members asked the same question.
The blackboard can provide a record of the lesson, a written history that students can reference. / check / Comments by Japanese colleague.

Lesson Plan

Time / Lesson Plan
Starting Point / Investigations in Number, Data & Space, Grade 5: 3D Geometry: Volume Investigation 1. Recommends use of word “box” initially: “During Investigation 4, students will use the term rectangular prism when they compare different solids, but here, in keeping with the factory scenario, the everyday word box will be used instead.” (p.6)
Pre-workshop / Lesson plan developed by County team; excerpt from end of first part of lesson plan, focused on “prior knowledge.”
Teacher lens: Double circle for rectangular prisms to point out 3 dimensions. Describe rectangular prism. Where do you see rectangular prisms in your life? Note: think about rectangular prisms that are solid, e.g., door, wood 2 X 4
Assessment: Academic vocabulary
*EL: prior experience, vocabulary, realia, graphic organizer
8-15 Planning Before Research Lesson I / With encouragement of larger group, the “double circle” activity that focuses on vocabulary development is omitted from the lesson plan.
9-21
Revised, for Research Lesson in new venue / Ask “what words were used that helped (to build)?”


Transcript Excerpts: Mathematical Vocabulary

The following transcript excerpts highlight the group’s discussions about need to explicitly teach or define mathematical vocabulary.

8.15A,1: JE:We worked for a year very diligently teaching area and perimeter and then the kids didn’t test well. It was like, “Argh! What was going on here?” And so we invited kids –we do a lot of interviewing – so we invited the kids that had been taught area from a previous year and to find out what the issue was. And what we discovered was that because the percentage of EL kids, which is about 70% of the school, is, um, high, that we’d couch the language. So we say, “find the area, measure the space inside.” And the kids can do that very well then. But we don’t ever say, “measure the area.” So we, we needed to attend to our language, um, very carefully. So we learned that the first year.

8.15A,8

Teacher 3: Helping student understand prism, or finding volume? Which is the major goal?

Teacher 6: Vol—finding volume. Um, this part right here is just to get them to understand what is a prism. Um, we, we grappled with the idea of “how necessary was it for them to include vocabulary?” Um, because we originally started off trying to introduce the least amount of vocabulary possible.

3: Well, if, if you expect student to develop the vocabulary on a concept of prism, you need to have a couple of days of lessons. You won’t to be able to help student develop concept of prism in ten minutes or five minutes.

2: Right. And they need to touch things.

3: And if you… If not, you don’t want to go jumping around – volume to prism or something like that. That, I thought that just make student confused. So, therefore, keeping in one core is very important, I think. Therefore…

2: But, but how can you teach volume if they don’t know what a prism is?

3: Why, why do need to prism? Why do you need prism? You can just identify that shape. What is the volume of this shape?

6: We did grapple with that idea. We did originally start with calling everything an object and a shape, and then we started getting into this whole thing. First we did not even define face. We avoided faces and then we were like, well, what do we call them? And then we—we originally were avoiding all kinds of vocabulary and what we found is, should I say prism? And so then we decide, well, we should be… say the word prism since it is a vocabulary word. And then we just—we decide, well, we don’t really want to spend too long defining it, because we don’t want it to be the main goal, but I don’t want to avoid calling it prism. So if I call this a box and then I call it a shape, if I call it a prism, is that… Do I have to clearly define it in such a detailed format at that point, or can I just sort of say it and, if I say it enough times, you kind of get the idea that we’re talking about a prism. So, we included prism here, and when we go to describe it using a graphic organizer, it’s a really brief thing. It’s not the goal of the lesson. And it’s not even that long. The next thing that we’re going to do is the geo-walls. And that’s where we really get into the describing part of it. And the fact that we call it a prism… It’s just like me calling you by your name the whole time. And I don’t need to know where your name came from, I don’t need you to describe to me why you have Akihiko and, you know… It’s more me just sort of saying it, so, yeah…

3: What I’m saying is, if you need to work with a prism, a rectangular prism, and other shapes, you may need to distinguish. But all the shape is going to be rectangular prism.

6: All of them are going to be rectangular prism, right.

3: But in that case, you don’t have to spend much time.

6: That’s a good point.

3: It’s relatively, what is important? That is narrowing down. But since we do not know student, if they already learned prism, they can naturally use this one; that’s totally fine. But if not, maybe in this case, maybe we can reserve that concept later on, but…

??: And keep it out?

6: Well, we could decide that today, if, if we’d like to just avoid using the word prism. The whole day… On Day 1, I can change all the word prisms just to box and shape, and that, that would work out really well. What do you guys…?

4: Is your, is your goal to eventually move them to understanding what the—how to find the volume of a prism, using a formula? Or is your goal just to understand volume?

6: It’s to get to the point where they’re going to say, “to find the volume of a prism, you’re going to need to know three dimensions. They happen to be called length, width, and heighth.”

1: You’re thinking.

6: Mm-hmm.

4: I was, I was thinking, if it were just in volume generally, then it wouldn’t so much matter if you were calling it a prism. But if you’re trying to find the volume of a specific shape, it seems like it should have a name.

8.15A,10

2: I guess [it] never would have occurred to me that I did not, would not need to define prism. I’m like you, I would have thought, well, I gotta kinda get over this hurdle, so that they would be able to proceed with volume. I guess we don’t need to deal with that because, I mean, in fifth grade, we’re not dealing with anything other than a rectangular prism, in terms of volume.

5: One of the other issues, too, is when – especially in, probably with most of our schools, when we’re dealing with a lot of second language students – at least for us, one of the main issues that we’re dealing with is, um, increasing academic language. So when we’re given the opportunity to use some academic language, I think it’s more often than not in our best interest to go ahead and use it. If we were to take this lesson and for three or four days, a week or so, called this, uh, a box or a shape, I think we are missing out on an opportunity to use the academic language and call this a rectangular prism so that they hear that word, are associating it with this particular shape. Um, granted we probably don’t have to go into great detail to define it, but just using that, uh, that vocabulary so that when they’re reporting out, when they’re responding, when they’re dealing with their own discourse, they’re given the opportunity to use, uh, the term rectangular prism. “I found the volume of our rectangular prism.” They’re working in their group, “I found the rec—our rectangular prism has a volume of, of 18 cubic units.” Versus saying, “Our shape has 18 cubic units.” It’s, it’s a fine point, but I think, due to the, um, complexities and the, the, the… um, of our standards, when we’re, when we’re given the opportunity to use the word, it certainly seems to me to be that we probably should be using the academic language, and, and, and exposing that, exposing the students to it as often as we can.