Fractions: Inside & Out of the #MTBoS
First things first, S/O to Liz Caffrey (@AsymptoticLiz) and her awesome shoes, who’re redefining fashion in sequence.
Lately, I’ve been fascinated by fractions and the conversations that we, (the #MTBoS community-at-large) have about them. When I did a Twitter search for the latest/top tweets (#MTBoS and Fractions), I saw the following words used to describe fractions or the relationship that students have with them: demystifying, challenging, struggle, gatekeeper, break down, and misconceptions. As math educators, we are aware that students’ learning of fractions feels like a make or break point for whether or not students will develop a productive disposition & positive identity in mathematics.So I thought it’d be interesting to look for cases in the #MTBoS and outside the #MTBoS where fractional understanding was of imminent importance.
This week, we got to listen in on a conversation in Marian Dingle’s (@DingleTeach) classroom as her students used the transitive property to make sense of fractions being division. Fractions are Sharing; Sharing is Division; SO FRACTIONS ARE DIVISION!
Berkely Everett (@BerkelyEverett) shared a #samedifferent post to help us think about the way we count denominators.
One of my favorite resources for understanding the conceptual fluency, strategic competence, and adaptive reasoning in fractions is Graham Fletcher’s (@gfletchy) video series on the Progression of Fractions. This was a really helpful video for me, as a high school teacher who sometimes forgets how students develop their thinking in fractions.
Here are a couple of examples I found outside the #MTBoS, where the understanding of fractions played a critical role:
This week, Amber Guyger, a former Dallas police officer who shot and killed her unarmed neighbor was sentenced to ten years in prison after a criminal trial. Several weeks ago, the defense attorney in this high-profile case requested that the case be moved to a different district, to “assure a fair trial”.
In this tweet, S. Lee Merritt, Esq. (@MeritLaw) discusses the importance of having the Botham Jean murder trial heard in Dallas County, where the crime took place, instead of relocating to a different site.
How are fractions being used in this case? How closely does the jury’s racial makeup “reflect the diversity of Dallas County?” To what level of precision (SMP.6) is the prosecutor attending to when defining the diversity of Dallas County? Does the fractional relationship in diversity change depending on this definition?
In another critical example, an impeachment inquiry against the President of the United States of America was filed this week. The President (@realdonaldtrump) tweeted the following in response:
In the thread under this original tweet, the following maps were given as counterexamples to the map provided by the President. Several Twitter users cited the number of popular votes or electoral votes for the different candidates in the 2016 election (“That’s 65,844,954 blue dots for Hillary Clinton and 62,979,636 red dots for Donald Trump.”). Find the Official Election Results here.
Source: (Mark Newman/University of Michigan, 2016 election.)
What is the fractional relationship between blue and red in each map? Why are these fractional relationships so different, even though they span the same area (the United States)? What viable argument might each of the Twitter users be trying to construct (SMP. 3) with the map they chose to post? (Tangent Time: Why aren’t Hawaii & Alaska on all 5 maps?! Talk about erasure!)
It seems that fractions are not only of critical importance for developing a positive mathematical identity for our students, but also in making sense of the world in which our students live.
Written by Lauren Baucom, @LBmathemagician