Author Archives: Eric Crantz
Allowing our students to talk to each other about mathematics is very important in today’s educational culture. Gone are the days when students sat in rows quietly working on repetitive worksheets. Instead, we want to hear what students are thinking. How are they processing information? What do they see as important? What solution pathways are they following? Are they able to generalize and take what they learn from one situation, and apply it to a new situation? Students learn from hearing each other’s unique perspectives in solving problems.
Here is the best part… we as teachers learn a lot as well! As we listen in on those same conversations where students are changing one another’s perspectives, we get an insight that we never had before. Our students are learning to verbalize their thinking and we get to take full advantage of that through our professional noticing.
I thought of this as I listened to a 3rd grade student explain her thinking on a subtraction problem she had solved incorrectly. The problem was 70 – 36, which she solved as:
70 – 36 = 46
I have to tell you that when I saw the solution, I assumed that she hadn’t been sure how to subtract the ones place. It can be confusing to regroup with zero in the ones place for students. I thought she had subtracted up: 6 – 0 = 6 in the ones place, and down 7 – 3 in the tens place. But I was wrong! As I listened to her explanation she said,
“I knew seventy take away thirty was forty, but then I thought I needed to add the six to the forty. Now I see that I needed to take away the six from the forty, so the right answer is thirty-four.”
I was blown away by her thought process. This brilliant little girl had broken the number apart in her head and had subtracted (and added) the number in parts! Once she was able to talk it through with her partner, she had even analyzed her own mistake. I couldn’t help but think how little I would have learned if I had just seen the problem and solution on paper. I realize now how much more conversation I want to have with this student, now that I had the opportunity to hear her thinking.
As we attend to our students’ problem solving abilities, it is a gift to get to hear their thinking out loud. It helps us to interpret where they are in their journey through the mathematical curriculum and better enables us to decide where we want to take them next.
Which is bigger 5/6 or 7/8? If the answer isn’t popping into your head in seconds, you are not alone. Fractions are one of the most misunderstood concepts among both young and old in mathematics. They don’t seem to follow the same rules as whole numbers. Many of us purposely never work with fractions at… Continue Reading
Along with a passion for mathematics education, I am also a pretty big sports geek. Some of it is the numbers that go along with every sport. For me, it started as a kid growing up in Oakland with easy access to both the Oakland A’s and the San Francisco Giant’s baseball teams, and trying… Continue Reading
As a constructivist, I believe that young students bring a vast amount of knowledge with them when they first begin school. Whether that time is pre-school, transitional kindergarten, or kindergarten, all students come with experiences that have influenced how they think, what they believe, and what they know. They have constructed knowledge in the area… Continue Reading
Number talks were developed for classroom teachers to engage students in “mental math” by collaboratively grappling with interesting mathematics problems. I was first introduced to the idea of number talks from the book, “Number Talks” by Sherry Parrish. Recently, I had the pleasure of facilitating number talks in 6 third grade classrooms, all at the… Continue Reading
Earlier this fall I was in a classroom where students were using whiteboards to record their answers and then they would hold them up for the teacher to examine. The teacher asked the students to answer several questions in this manner and then the students were dismissed to do an assignment. After the class, as… Continue Reading
Teaching, in my opinion, is one of the most complex occupations in our society. As Miriam Sherin puts it in Mathematics Teacher Noticing, “the blooming, buzzing confusion of sensory data that teachers are faced with” can be overwhelming. Remember back to when you were first learning how to drive. You had to pay attention to… Continue Reading
I have a deep passion for mathematics education. More specifically, elementary math education is where I have spent most of my career. I began my career as an elementary teacher for ten years, and am now a mathematics coach and consultant with the Fresno County Office of Education (FCOE). In addition this year, I am… Continue Reading