Teaching As Learning

Last week for the first time this year right in the middle of a math lesson one of our class's most dedicated students came up to me and said, "I don't get it. I don't know how to do this." Then another capable student approached me and said the same thing. My heart sank. No teacher wants to hear those four fateful words, because it's a code for every teacher's most dreaded thought: I didn't do a very good job teaching this lesson.

It was at the end of the day and I immediately had the children pack up their math books and told them we would go back and try it again the next day. Upon looking closely at the work the students had completed, it was clearer than ever that indeed, they really didn't get it. Even the children working independently had gone off the track.

I went home that night with my head swimming over the day's lesson. What had gone wrong? We had worked for a long time on a thinking out loud problem called a "headline story". I posed an open-ended word problem on the board and the students can fill in the blanks in any number of ways. The students had offered a number of solutions and had been eagerly engaged in the problem. Everyone wanted to offer a solution. In the next activity we worked on making number sentences with our hands, in some cases using three hands to make numbers larger than ten. Everybody was working and learning -- until we returned to our desks to complete the lesson's workbook pages. It was at this point that my student brought me to reality with her lack of "getting it." I hadn't spent enough time making the connection between counting our five fingers and counting by fives.

For the next few days we have been counting by fives, looking at multiples of five using nickels and adding on from five with a vengeance. Having a lesson blow up in your face is one of the quickest ways to examine -- and alter -- your teaching practice. In this case, it made me deeply aware of how important it is to take the time to connect one simple activity (working with five fingers on two hands) with the larger concept (skip counting by fives). Having a student tell me he or she doesn't get it is tantamount to throwing down the glove -- it's an ultimatum I'm not going to ignore. but I also recognize that something else was at work: I'd never taught money using this math book before. I needed the day's slightly painful events to make me aware of how the activities in our new math curriculum fit together. It was one of those "teachable moments" -- only the one being taught was....me!

For the past three years, prompted by parents unhappy with our district's spotty performance on state assessments, a perceived lack of rigor in our town's elementary math curriculum, increased awareness of the national conversation about diametrically opposed styles of math teaching (see "Math Wars") a district-wide Math Performance Review Team met with teachers, parents and administrators over many months. I joined one focus group convened over two years ago (maybe it was three years?). As part of a group of elementary teachers I spent an afternoon discussing our likes and dislikes about the present math curriculum. We listed things we would change if we could. We voiced frustration about gaps in the "core curriculum" that provided a skeletal framework of activities you would teach throughout the year. We noted that if wanted be true to the town learning expectations and the state frameworks, we would have to purchase, beg, borrow and photocopy from as many as ten other books in order to meet these two sometimes differing standards.

For example, in 2005 the town math curriculum contained no unit on money in either the first or the second grade, so teaching money (usually pennies, nickels, dimes and quarters) meant hunting down and deciding which worksheet to use after an activity or game played during class. Over the years my colleagues and I became quite comfortable teaching about money: we refined a number of activities and worksheets that we adapted to various grade levels. We shared materials, workbooks and ideas. The downside of the lack of materials was that our work felt very "random" and of course there was the issue of equity in classrooms throughout the system. It was clear that this lack of district uniformity had become increasingly untenable.

So the good news is, our town made a decision sometime in the past year to purchase a new K-5 math curricula. Pilot teachers were limited to various grade levels -- this year those teachers compose the advanced class. Their one year of working with the new textbooks and curricula provided them with one extra year of teaching with materials that us newbies didn't have. They are the experts in this endeavor right now, although I'm sure they might dispute the label!

Very few teachers will read the directions to a lesson and not change some aspect of the instructions, whether it's changing the unit by adding vocabulary, altering the lesson's pacing, replacing one activity with another, etc. Teachers treasure their independence and value the ability to make spot judgments based on the group of students in front of them. I'm constantly assessing the level of my students' engagement while I'm teaching -- how many students begin to detach from the group and begin rolling around on the floor? While I'm teaching, I'm thinking, "Are they still with me? How many are listening with their eyes and raising their hands eagerly?" I try to gauge their engagement (or lack thereof) in observable terms. If things are going too slowly, even the most engaged learner will start to fidget. If the lesson moves too quickly, or I haven't spent enough time on a critical piece, the lesson will fall flat on its head. I can see it in my students' bodies!

When teaching 1st graders you can also assess whether the students understand what they are doing by how quickly and happily they get to work - on whatever they do. Noise levels are also a major indicator of how well students are absorbing material. If there is a high degree of chatter, it may be because the students are less than excited about what they are doing. They'll talk about anything rather than work on something they don't understand -- not too different from most adults! That's why I knew immediately what the problem was when my student said, "I don't get it!" When I hear those words, I know it's time to go back to the drawing board -- and reteach the lesson. As a teacher of young children, (actually this was true for my 5th and 6th graders as well) you have to be thinking all the time about what successful learning looks like. Any new curriculum worth its salt takes the teacher's need to make independent judgments into account. If it's not working, I'm going to change it!

That need for decision-making independence must be balanced with accountability, and all new curricula published today are keyed to state standards (Massachusetts curriculum frameworks). In our district the curriculum chosen by the town ("ThinkMath!)is more than explicit about what standards are being taught in every lesson. I'm pretty excited about what we're doing in math right now -- we're working on a unit on pennies and nickels -- yes, it IS included in this curricula -- and the students are really enjoying the various activities which range from trading pennies for nickels in games, making change, counting on, skip counting by fives. We'll take up dimes and quarters later in the year, using some of the same methods and games. I like how the curriculum circles back to the same activities at different points in the year, using larger denominations. It gives me and my students a sense of familiarity and confidence.

So back to the original reason for starting this blog -- thinking and reflecting on teaching. Doing something for the first time is always challenging, even for an old-timer like me. Especially for an old-timer like me! Teaching something for the first time feels like the proverbial ground is shifting underneath you. Although I've taught several grades over the course of 20 years, this is my third year of teaching first grade and in many ways, I consider myself a novice teaching young children, since 13 of my 20 years were teaching 5th and 6th graders. There's no doubt about my being a novice teaching this new math curriculum. In sorting out how to approach so much new information and so many ways to present material it really helps to reflect on what makes good teaching, whether teaching the material for the first or the fifteenth (or even more!) time. And most importantly, undertaking a new teaching challenge reminds me of my imperfections, makes me work hard at what I do, and reflect upon what's working well, and what I need to do better every day.