**Two Days of Step One: Inquiry Approaches to Teaching**

The first day, we basically went over the syllabus, filled out scheduling information, and got the tour of the MTeach office, supply closest, and staff. Our first homework assignment was to read a brief paper about characteristics of effective teachers and reflect on a previous teacher that was memorable to us. The message of the paper was fine (care about your students, create a sense of belonging, be fair, be willing to admit mistakes, have high expectations, etc) , but it purported to be research-based and was really just a list of things that pre-service teachers wrote on a survey about what they liked about their most memorable teacher. It’s kind of like determining what makes effective doctors by asking Premeds what they liked about their doctor. All and all I think it was a good first assignment, but in writing it I was reminded how difficult it is to write school assignments, especially when there is neither an authentic audience to read it nor are you in a position to be writing for yourself. Nonetheless, I used the prompt to start a good discussion with my wife, which was meaningful and useful to me. That’s going to me my goal with homework–for it to provoke meaningful discussion, even when I work hard to find a kernel of provocation.

On the second day, we were given our teaching assignments. I’ll be observing the same 5th grade class on two Fridays in September and then teaching three lessons to that same class throughout the semester. Unlike most students who go through program, I won’t have a teaching partner. Over the weekend I’ll be meeting with my mentor teacher, and I’ll find out what lessons I’ll be asked to teach. My understanding is there is a menu of lessons that teachers can pick from. You aren’t expected to do any lesson planning. Rather you are expected to carryout a pre-planned lesson.

On the second day of the class, we also experienced a model lesson and were introduced to the 5E lesson plan structure that is used in the program. The 5E’s stand for Engage, Explore, Explain, Elaborate, and Evaluate. The model lesson involved 2-digit multiplication. I’ll say more about the lesson later.

At the end of the lesson we got a brief introduction to learning objectives and standards. Tennessee, like many states, is in the middle of transitioning from our old state standards to the Common Core Standards. We had a chance to briefly glance at some standards related to the lesson, ultimately finding that it was easy to find Tennessee standards that fit the lessons, but difficult to find any Common Core Standards. Mostly this was because the lesson involved doing multiplication, and little interpreting, problem-solving, explaining, etc. We were also briefly introduced to the ideas about how objectives should use “action” verbs and should be measurable, trying to avoid vague words like “students will understand that..” or “students will know that…” I’d be interested to know more about what students walked away from this tidbit on learning objectives, because I feel like this all happened really fast and students don’t have a lot of context and background knowledge related to this.

**The Model Lesson–Maximize Your Product**

Anyway, so the lesson involved using ideas about place-value to maximize products. There was a brief “engage” at the beginning of the lesson that involved some story about buying candy. The story was basically about if you should choose to go to store that had 42 bags each containing 59 lollipops or 94 bags containing 25 each. Could you figure out which would get more lollipops without formally doing the multiplication? Then our “explore” was the following game. In pairs, you would take turns rolling a die. You had a four boxes on a piece of paper representing a two-digit multiplication problem and you had to decide where you wanted to place the number that was rolled so that at the end of four rolls, your product would be as big as possible. You did this a couple of times. The “explain” part of the lessons involved students coming up to the document camera to explain the decisions they made and to work out the two-digit multiplication, and the teacher emphasizing ideas about place value. We didn’t do the “elaborate”, but it was mentioned that normally students would go back to play game again this time trying to minimize their products. There was also some evaluation questions, which were mostly just worksheet problems that we also didn’t do. The lesson ended with returning to “engage”, where at least one interesting mathematical idea came up, but mostly it just involved having us do the multiplication that was in the candy story.

Some positives I see in this model lesson:

Students were engaged in a task that required *some* mathematical decision making, rather than just procedural steps alone.

Some students were asked to explain their thinking and reasoning in context of the work they did, and other students were expected to listen. It’s nice to emphasize that the explain part of the lesson involves students explaining, not just the teacher.

The teacher did little lecturing. Rather, the teacher help consolidate and synthesize some ideas in the context of students’ just having shared their work.

Things I thought about during and after the lesson

*#1 Engaging Ideas?*

Being in the room, I didn’t have the sense that students’ mathematical ideas were really engaged in the lesson. For context, I’ve seen how our pre-service teachers often seem to have about odd ideas about the “engage” part of the 5E model, almost as if it meant “be entertaining”. In my mind, while an “engage” can certainly be entertaining, the point of the engage is to engage **ideas**, so as to possibly cultivate a sense of curiosity, wonder, puzzlement, surprise, or purpose. With this lesson, I could easily see students walking away from the lesson thinking, “Kids like Candy. This was a good engage because it was about candy. Candy engages kids.” What could have made this engaging of our ideas is if we had the opportunity to think about which one we thought was more candy, to articulate our reasoning and hear others’ reasoning, and then commit to an answer. This would also be an opportunity to model good classroom discourse.

*#2 Learning Goals?*

The discussion of learning goals centered around two-digit multiplication, and there was sort of a message being sent that this lesson was good because it got students practicing two-digit multiplication without it being a worksheet. Almost like it was good because it a fun exercise that tricked students into practicing math. I’m not saying that’s bad, but I was wondering whether the goal of the lesson was more about estimation and place value, and how we can use place value to estimate. One of the reasons I thought this is because everyone proceeded to do all the multiplication using the standard algorithm. [ I used partial products mostly, for example solving 41*41… by saying 41*10 = 410 takes care of 10 of the 41s, then adding 410 four times to get to 40 “41s”, and then adding one more 41 to finish it off. ] The reason I don’t think this lessons was much about two-digit multiplication is because it wasn’t really about ways of thinking about or doing two-digit multiplication, it was just the procedure used to check to see who had maximized their product. The lesson sort of has to assume you already know how to do it. And now maybe it’s getting you more chance to practice it or a chance for the teacher to assess students’ proficiency , but the mathematical thinking would seem to still be mostly about place value and using place value ideas in the context of the meaning of multiplication. Of course, lessons can have layers of learning, and I’m not saying that you couldn’t have multiple goals, or different goals for different learners.

Thinking about the goal in terms of place value and estimation might have made this lesson aligned with common core.

*#3 The Highlight for Me?*

The highlight for me was at the end of the lesson, where we returned to the candy store. I offered the idea that I didn’t know which one would be bigger, but I knew they would be close, because 100*24 and 60*40 are both 2400. Another student offered the idea that if you ignore the “ones” place, then 5*4 = “20” and “9*2” = 18. That’s such a great idea. Not only is it insightful, but it explicitly built off learning that occurred during the lesson. The teacher said that our two ideas were the same, but I said I didn’t think so. I tried to revoice the students’ idea, and asked if that’s what she was saying. I think now I was estimating by rounding and multiplying, and the other student was estimating by attending to place value, but it didn’t occur to me at the time to say it that way. Our ideas are not entirely different for sure, because they both involve doing something to ignore the ones place.

Anyway, I think the lesson could probably be improved by having more of that–students’ sharing ideas, and a teacher facilitating sense making around those ideas. Of course, understanding and capitalizing on those ideas involves a lot of pedagogical content knowledge. But that student’s ideas could have gotten a lot of airtime, because it was like the perfect contribution.

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