Author Archives: Eric Crantz
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 all, preferring to change them into decimals so we don’t have to deal with fractions.
Recently some co-workers and I posed this question to different groups of adults and it caused much controversy. No one was sure what to answer initially and there was some embarrassment about not knowing an answer. Many people were convinced initially that 5/6 was bigger because the “pieces that are sixths are larger than the pieces that are eighths.” After much discussion, several algorithms and drawings, and one number line, the groups finally decided that 7/8 is actually bigger.
This is no insult to these groups of colleagues. For a very long time our understanding of fractions has relied on memorizing procedures, rather than a deep conceptual understanding of fractions. We get mixed up between numerators, denominators, GCF, and LCM.
We want our students today to understand that fractions have a place on a number line just like a whole number. Students in 3rd through 5th grade are having experiences that are allowing them to construct an understanding of fractions, where they can decompose and compose fractions and understand why finding a common denominator to add fractions actually makes sense. Factors, multiples, and simplest form aren’t just terms to memorize for a single test. Instead, we want to start to see the connections between all these terms and connect them to previous understanding. Connections in mathematics are so important, and for the longest time we ignored them in favor of being able to calculate.
This consternation over the teaching of concepts that involve fractions was the impetus for the launch of the Research Division within the AIMS Center. We know that students often miss the critical components in their understanding that allow them to construct meaning around fractions. Perhaps in ten years, when a random group of adults are asked this same question of which is larger, there won’t be so much hesitation – thanks to teachers changing the culture of teaching and allowing students the chance to construct their learning within mathematics and other subjects.
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