In that amazing experience I met (and hired) several top notch elementary teachers. Today I have a guest blogger - one of the best second grade teachers I've ever seen! I know you'll enjoy her writing!
Glimpse into My Second Grade Math Classroom
I have a confession.
First, I love teaching math. Second, I struggled with math in high school and college. I still cringe when I think about college algebra! Yet, I love math. Teaching math.
My theory as to why I enjoy teaching math so much is this:
I connect with the emotion, frustration and embarrassment of facing a problem that has no obvious starting point to me; I want to help my students succeed and avoid frustration. I have experienced that feeling of accomplishment after unraveling a tricky problem. It’s empowering, and oh, so rewarding when I see a child’s eyes light up with understanding!
Elementary math must seem quite simple to those who teach higher levels of math. It’s simply 2 + 2= 4, right? Count some sets of apples, use your fingers, write a number, and there’s your answer. If it were that easy, every elementary teacher would love teaching math.
Over the course of 22 years of teaching, plus 3 years working with teachers as a trainer, I have witnessed that teaching elementary math is intimidating to some teachers. Some will tell you that they dread or hate teaching math.
Math was certainly intimidating to me when I began teaching! I struggled with determining which students needed remediation, which ones needed more challenging work, and how to manage it all in a 40-50 minute math block. It was intimidating because determining where students were, in terms of their developmental level, was not as simple as administering one assessment (such as the Developmental Reading Assessment for reading).
I learned that it takes observation of how students interact with math tools and how they respond to problems. There are questions to answer:
· Do they have conservation of number?
· Do they count using one-to-one correspondence?
· Do they know how to use math tools?
· Do they have, and can they use, math vocabulary?
If not, then it’s imperative to provide many opportunities to manipulate objects – counters, beans, cubes – any kind of objects that little hands can use to associate spoken numbers with sets. It is imperative to set ground rules for how to use math tools, and use math vocabulary, or the cubes, tiles, beans or other manipulatives will become monsters, towers, or beautiful mosaics. For this reason, I set aside daily play time with manipulatives for the first few weeks of school. I call it free exploration instead of play time. Math is work. Fun, active and engaging work, but work.
During free exploration time, I can kid-watch to answer some of my questions. Can children recognize that ten cubes in a close group is still ten cubes when I stretch out the same cubes in a long line? You might be surprised to learn that in a class of 20 students, four or five of them will count to verify how many are in the long row, even when they have witnessed me take the close group and spread it into a long row.
One tool that is very helpful to me is Kathy Richardson’s Hiding Assessment. I was fortunate enough to attend a one-week training, using Kathy Richardson’s Developing Number Concepts Using Unifix Cubes, when I first began teaching. What a blessing and treasure trove of math learning it was for me!
When I administer Richardson’s Hiding Assessment, I get an initial idea of which of my students are proficient in conservation of number and one-to-one correspondence. This quick assessment has students count out four, five, six, or seven (I start with four) cubes for me. Then, they identify sets of counters, some hidden in my hand, while others are visible. I ask, “How many are hiding (in my hand)?” For example, I might have a student count out five cubes. I’ll hide three in my hand, and show two. The child has to tell me, as quickly as possible, how many are hiding in my hand. Some second graders can identify sets up to seven, and they can do it quickly and confidently. Many second graders can identify sets of four or five. Some visibly count in their head to find the answer. I can see their cute heads nodding as they count. Others toss out answers that are close, and some pull out random numbers that are clearly guesses. In one first grade classroom, I had a student who could not consistently tell me how many were hiding in a set of three!
Based on this quick and easy assessment, I can identify and place students in flexible, small groups for instruction. In my opinion, the results are indicative, to a degree, of the level of previous interaction students have had using manipulatives to solve math problems. Concrete experience with manipulatives is essential for student success!
Students that identify sets of six and seven tend to fall into my grade-level or above-level group. Those working four or five in a set fall into my lower group. As I administer other formative assessments and kid-watch, I refine my groups, but the Hiding Assessment is consistently predictive of student abilities as an initial assessment. It’s quick. The kiddos think it’s a game, and I get good information. It’s a win-win for teacher and student.
One other question that I ask while kid-watching is, “Are my students confident mathematical thinkers and speakers?” My students complete a daily word problem in their math journal. I invite several students to explain their thinking (they write this description in their math journal). Some have an excellent grasp of problem solving; others have no idea how to put their thoughts into words, because they don’t truly understand how they solved the problem. There are always children who write that they “used their brain” to solve the problem. Some of them don’t want to take the time to write out the process, and some don’t know how to break problem solving into steps.
Once we have solved the daily word problem together, and we have agreed that it is correct, even if there are multiple solutions (and when aren’t there?), I ask, “Which answer is right (or best)?” The students that have a solid understanding that math problems have many ways to be solved, will shout, “They all are!”
It’s important to note that to get to this point of a smooth interaction such as this one, it takes four to six weeks of modeling, sharing, correcting, and more modeling. Students use words, pictures and numbers to show their thinking. Four to six weeks is a long time, but it’s time well spent to ensure that students know that they are expected to dig in, dig deep, and discover new math strategies. It is an investment in time that should make future teachers’ math instruction a little easier.
I understand that many of the readers of this blog are middle or high school teachers. To those of you who teach higher math, I salute you! I recognize that what I do contributes to your success. I would guess that you may have a student who still counts on his fingers to add or subtract. They probably sneak and do it under their desk for fear of being embarrassed if someone sees them. I might have been that student at some point in middle or high school. I also recognize that having a strong middle or high school math student means that my second graders need to be challenged, remediated, and enthusiastically exposed to the wonders of math. I once had a precocious second grader tell me that “everyone calls you the math teacher.” She meant that I have a reputation of loving to teach math, and I do love it.
When I started this piece (three different times), I wanted to share a glimpse into my math world. I’ve only scratched the surface. I didn’t mention regrouping, which is one of the biggie skills for second graders to master. I’ll save that for another day. For now, I am enjoying my last few days of summer vacation working on plans for the upcoming school year.
I wish you a successful school year with eager students who love math and don’t have to count on their fingers!