Outreach / Misc

Which is Bigger?

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.

AIMS Outreach Role to Increase

Since its inception the outreach side of the AIMS Center has focused upon two major initiatives: The AIMS Colloquium Series and The ZPC Podcast. These have been quite successful with both garnering appropriate attendance and listenership. However, we here seldom like to rest on our laurels. We are planning some significant pushes into both regional… Continue Reading

Change is Hard!

Last September, the California governor signed Assembly Bill 1732 which adds an article to the Health and Safety Code relating to restrooms in a public building. This bill will, commencing March 1, 2017, require all single-user toilet facilities in any business establishment to be identified as all-gender toilet facilities. Our facility at The AIMS Center… Continue Reading

Deliberate Practice

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

Student Adaptive Pedagogy

When our Director of Research attended the Psychology of Mathematics Education – North American conference this year along with a couple of our Senior Researchers, they had the opportunity to meet Dr. Ron Tzur from the University of Colorado in Denver.  Like many others that we have now begun communicating with, Dr. Tzur studied with… Continue Reading

The Shift, Continued

In my last post, I mentioned that I had been seeing a pattern in the presentations at conferences this past fall. Many of the keynote and special guest speakers had incorporated a frame of reference that seemed to me to be a focus on student thinking. “Why is this an important shift?” you might ask.… Continue Reading

What is Changing and What Will Never Change

It is an interesting time in America; there is change all around us.  But, what will never change is the need to educate our children…the need to continue improving the education of our children.  That improvement comes through the hard work of our teachers, improving their skills to improve the experiences of their students. At… Continue Reading

Called on the Carpet: A Reminder of My Own Beliefs

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


When Dr. Thiessen first discussed his ideas about launching the AIMS Center for Math and Science Education with me, he suggested that our motto should be:      “Know the Math; Know the Science; Know the Research.” And, he said, even more importantly, we can never forget that:      “We believe in children’s knowledge!” I have been working… Continue Reading