This moddulel fave me an assurance that I am on the right track. I will continue to start my lessons with visuals and focus on the unit of measure. Wha t is frustrating is what other teachers in the lower years when thy teach a strand procedurally rather than fonfrptually. Pfobably, I will be doing an echoing session tot ir them.The problem lies that many of the elem teache are English major.
Glad to hear that you’re feeling like you’re on the right track!
Your struggle with students arriving with mostly a “procedures first” experience is not uncommon and while frustrating, we are still very far from shifting from a mostly “procedures first” approach to a “conceptual understanding first” experience.
Maybe trying to rally your divisional partners to make a division (or school) wide commitment to work towards that approach might be worth it?
In answer to your question, I am applying ALL of this ALL the time. Even when the focus is not fractions or integers (or multiplying), we can stop in the moment and share strategies.
We are about to have an internal math PD day of our own creation, where we are sharing lessons that focus on numeracy and not algorithms. I am actually overflowing with too many things I want to share with colleagues, but I’m honing in on offering a problem string involving fractions and hoping to work in some ideas about adding, subtracting, and multiplying along the way.
Quotative and Partitive division makes my head hurt a little bit.
Partitive — There are 3 kids sharing 5 pizzas — how much pizza does each kid get? (What is 5 divided into 3 parts?)
Quotative — You have a 12.5-pound bag of dogfood, and your dog eats 3/4 pound per day. How many servings are in the bag of dogfood? (How many 3/4’s are in 12 1/2?)
I haven’t watched this particular lesson yet but wanted to see the comments first. I agree with both of your examples of partitive (I try to think of fair sharing and unit rate) and quotative division (repeated subtraction). I think you are spot on.
Planning will be a key for use of concrete models and visuals with my students as well as being explicit with the units of measure. I will need to think ahead and make some predictions about what they will say and/or think. Some of these topics are very complex but I need to make sure that I do not make them complicated. I do know that when I dig into the conceptual learning some of my students get upset because they are so used to going straight to an algorithm, they have not developed patience while acquiring understanding. I am continuing to search out examples of models/manipulatives to add to my repertoire.
I am curious as to Jon’s or Kyle’s thoughts on using common denominators when dividing fractions after the conceptual foundation had been provided.
I am going to use visuals much more often with my students, even though they are high school students. I believe this will help close the gap of conceptual misunderstanding that they have, and allow them to become much better math students.