Red Dodge Chargers And Conceptual Understanding – Discussion

[Jenny Kinter]

I am wondering how often I should use this method. It sounds like the prep time is necessary and not trivial. I want to use this when I’m ready to introduce proportions to my pre-algebra students. I may try it out on my older students (algebra II and college algebra) just to see what happens.

Each of these videos have been inspiring, but I also feel the need to figure out how to “make the methods my own” so that they flow naturally.

[Kyle Pearce]

Hi @Jenny-Kinter

Just checking in on this. Have you had an opportunity to give this any thought/reflection? How are you progressing here?

[Kelly]

My big take away was looking into my lessons to ensure that there are multiple methods of representation. I also appreciate the breakdown of the paper stacking task. Somehow it seems less intimidating now.

[Kyle Pearce]

@Kelly-Eddy

So glad to hear it. Is there an upcoming lesson you feel like you can apply some of this thinking? If so, please do let us know here how it went and your next steps!

[Kathy Hall]

My big take away is when I”m teaching a lesson I need to think about where the lesson fits in the progression. I will have students that are behind in the progression as well as ahead. When I’m thinking of different representations I need to consider the progression and then show representations that will nudge the students forward in their understanding of the progression.

[Meghan McOmber]

I’m wondering if you can speak to how you structure your class during your lesson. Are students working alone or in groups? How are they showing their thinking?

[Tara Militello]

I like the idea of encouraging students to use friendly numbers instead of the actaul answer here. So many students only care about getting the answer instead of understanding the concept behind the answer.

[Anne Hambrick]

I like hearing everyone else’s thoughts!

In your video, that slide of multiple representations is awesome! It goes way beyond the Big Five I stress in Algebra. I’ve also learned that it’s important to pick and choose what representations to use in one lesson.

Your double number line is something I need to explore more. This isn’t the first time I’ve seen it, but I’ve never used it to teach. Bar models are more my thing, but I see the relationship and want to try the double number line at some point and get comfortable with it.

[Scott Cortez]

One of the biggest take away of the lesson is to use friendly numbers to the lesson is accessible to more students. Friendly numbers, in my opinion, mean more buy-in from the class. It would ease stress levels because of the numbers they can compute with confidence.

What I am still wondering is how do I start from one task and know where to take it. From going to a simple problem to a more complex problem is where I am afraid I will miss an opportunity.

What is something you are still wondering?

Share your thinking below.

• This reply was modified 2 years, 6 months ago by  Scott Cortez.

[Brittany Fraser]

My big take away is that I need to spend more time in the “Anticipation” stage before implementing a task with my students. This will allow me to plan ahead with more intentionality and purpose so that I know which strategies to watch for and which ones I may want to highlight and connect to after students have had a chance to explore the problem. I hope as time goes by, this practice will become more internalized.

[Amy Kopcznski]

I loved seeing the progression from additive to multiplicative and concrete to proportional to function representation for this problem. Scaling the problem back to begin with friendly numbers was also a takeaway/reminder for me.

One question I have is how long do you allow a student to work in the concrete representation before moving them to the double number lines?

[Kyle Pearce]

This is the magic question!
I now realize that we need to be asking students purposeful questions and providing appropriate experiences to help EMERGE the next strategies and models. By directly telling them the next model, I am essentially back to teaching an algorithm and stripping the connections.

[Lisa Hudson]

My big takeaway was being “blown away” by the massive number of multiple representations you showed from the most basic of concrete to a higher level of concrete on to representation followed by abstract. The way that you connected the representations so seamlessly is awe-inspiring. As I was watching the video I was reminded along the way of how some of these “low floor” representations tie into much higher algebraic thinking. As a previous respondent noted, we get sucked into thinking that multiple representations are the big 5 of algebra but they are so much more. This video shows me how much more I need to anticipate and be aware of the various levels where my students are comfortable and think of ways I can guide them to emerge to a higher level of understanding.

[Laura Johns]

I know that my students need multiple representations. Even the students that “just get it” need to have an image in their mind. My two wonders are 1) how do I get the perfect representation for each student and 2) as students build a mental image how do I keep them moving forward (while working with others).

[Kristi Hill]

I love the idea that “multiple reprsentations fuel sense making”. It’s about students showing thier own understanding by representing thier thinking and analyzing and connecting with ideas shown in other ways. If students can understand other ways, then they have made powerful learning connections that provides them avenues to understand things in a variety of ways.

[Ella Platt]

Anticipating student solutions is the most meaningful concept along with the Anticipation framework. I love this! Tell me what to do and give me a tool to do it by myself! I plan to implement this next year.

[Gavin Torem]

My big take away was that you do not need to show every possible representation each lesson. While you need to be aware of as many as possible to anticipate your students’ use of them, introducing more than one new one not done by another student can overwhelm students and reduce retention. Therefore in the future I will rank the representations in order from most important to least important for that day and if multiple are not used by students I will then pick the most important one or most connected one to share with the class.

I am still wondering how to reach students who do not engage. What if my tasks aren’t interesting enough? What if I am not interesting enough? How can I increase student involvement and engagement?

[Kyle Pearce]

Great take aways here and wonders.

It can be tough to get a full group 100% engaged. One thing I know for sure is that if you are able to get a majority, then you’re likely doing something well. For the other student or students who are not engaging, it might require you building your relationship with them. What baggage are they bringing with them? What sort of day are they having? What kind of relationship with math do they have? Can we influence their thoughts / perception of math somehow to encourage some engagement? Sometimes engagement has nothing to do with the lesson itself and more to do with the students situation.