Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 95: Building Number Sense and Fluency – Discussion

Lesson 95: Building Number Sense and Fluency – Discussion
Posted by Kyle Pearce on March 7, 2020 at 12:28 pmCongratulations!
Youâ€™ve now completed the entire The Concept Holding Your Students Back course.
What is your biggest takeaway from this course and what learning do you intend to put into practice immediately?
Share your reflection and final thoughts below.
Luke Albrecht replied 8 months, 3 weeks ago 17 Members · 31 Replies 
31 Replies

Flipping lessons to put problem solving first. Not giving students their reflective scales and term plans up front (keep the anticipation). Creating opportunities for the students to show and articulate their learning

These are huge take aways! So happy you made it to the end and have some great ideas to start implementing in your own classroom!


Thank you so much!
Biggest takeaway….that one question to solve can evolve from the most basic Math concept to one of high level Math thinking!
After I take a couple of weeks off for summer holidays, I will create a year plan where Sparking Curiosity, Fueling Sense Making and Making Math Moments that Matter! I also want to spiral the math course. So… I will be accessing the Academy a great deal in the near future! Thanks, again. Enjoyed the course!

So happy to have learned alongside you! Be sure to keep that learning log active in the community forum area to keep us all posted on your progress đź™‚


This course has reaffirmed for me the importance of K5 math instructional pedagogy founded on problembased learning rather than didactic teaching. And as an advocate of the 8 mathematical practices, “The Concepts Holding Your Students Back, has demonstrated each:
<b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>1. Make sense of problems and persevere in solving them <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>2. Reason abstractly and <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>quantitatively; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>3. Construct viable arguments and critique the reasoning of others; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>4. Model with mathematics; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>5. Use appropriate tools strategically; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>6. Attend to <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>precision; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>7. Look for and make use of structure; <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>8. Look for and express regularity <b style=”fontfamily: inherit; fontsize: inherit; color: inherit;”>in repeated reasoning
Another takeaway is the need for math curriculum specialists in districts all over the U.S. to know about MakeMathMoments and the wealth of resources, units and professional development available at their fingertips.
I’ve learned importance of engaging students in math at varying entry levels through noticing and wondering to spark their curiosity: I’ve relearned the importance of spatial reasoning and the concept of number as it relates to building the concept of units: I’ve confirmed the value of visual representations and models like the double number line: and have been reminded that the person doing the talking is doing the learning which means using math talks: Finally wrapping it all up is the interconnectedness of all the standards that lead to proportional reasoning.
Lastly, I’m pleased to say that in my work in math curriculum and consulting, I’ve had the good fortune to have learned from the best–Cathy Fosnot, Sherry Parrish, Pam Harris, Graham Fletcher, and Jon Orr and Kyle Pearce. Thank you.
 This reply was modified 1 year, 12 months ago by Jeanette Cox.

@jeanetteCox
Wow! What a fantastic reflection and feedback regarding your experience in this course. You have certainly been extremely active with sharing your action items here in the discussion area and it was an honour to read as you were digging into the learning!
We certainly hope to continue sharing the message of building math content knowledge and pedagogical practice… sharing feedback with your colleagues will certainly help!Take care and hopefully we will see you inside some academy courses!

Here are some of my biggest takeaway:
1. Students need more modules to help them build their understanding from concrete to visual to the abstract. Too often our courses and the content we use jumps to the abstract and we lose too many students.
2. Proportional reasoning is more than a chapter in the grade 8 math textbook. More teachers (including myself) need to take the initiative to show others how it relates to so many more concepts and is built upon fundamental knowledge.
3. Using the appropriate language at the right time, will help students learn and understand the concepts. I was brought up with a “plug and play” system (my version of here is the formula and get the answer) which does not lead to conceptual understanding or the ability to deviate from the standard problem. If my teachers used the appropriate language, I don’t think I would’ve struggled as much as I did when I got to university. I’m already seeing results in my classroom but emphasizing language.
Thank you for developing this course.

Wow! These are awesome take aways! I agree with all of them and I appreciate how youâ€™ve suggested that this is a process and will take time – just like how students need that reexposure and opportunity to dive deeper a bit at a time.
So happy to have learned along side you!


It was amazing to see the ladder graphic built out over time and have much better understanding of the concepts underpinning middle school math, all the way from spatial comparison of quantities on up.
I have already fiddled with some lessons during the time I’ve been in the course, and am excited to be able to spiral back to ratio and rate thinking with my 6th graders now having a better understanding of the progression. In one of our first taks this year, I now realize I was pushing them to go all the way to rate thinking when setting a learning goal around using ratio thinking would have been more salient at that point in the year. I see how I can build one on the other through a couple of tasks with the many examples provided throughout the course.
Thank you Kyle!

Great take aways! So happy that youâ€™re feeling good about the progression of the course. That web of concepts can be so daunting early on, so it is great to hear that you feel like youâ€™ve made some sense of that progression!
It is so true that now that there is a clearer understanding of the progression, setting bite sized goals can be so much more beneficial for students. Ideally, if all educators are on the same page, this progression can happen very gradually from kindergarten all the way up to grade 8 and 9… we will get there one day!
Thanks for being awesome and for participating in the discussions!


I think my biggest take away is to keep plugging along! Extending lessons to be lowfloor, highceiling is difficult but necessary to include all students. All of this aligns so closely to inquirybased math, which is what I am focusing on now (teaching at an International Baccalaureate school).
Thank you for this course.

So happy to have learned alongside you! Keep on working on those low floor / high ceiling tasks… it does get easier the more we plan and practice them!
Enjoy the holidays!


I have had many takeaways from this course. Being intentional with the language I use with my students and the language I want them to use when given specific tasks is one big takeaway. Also, and this was a reaffirmation of a big idea I took away from a Robert Kaplinsky course I took a few years ago, problem solving, low floor high ceiling tasks, needs to be a major focus in my mathematics classrooms. The discussions and ideas that evolve from these experiences are so rich and they just foster the development of number sense. Christina Tondevold says that number sense is CAUGHT, not Taught (or something like that) so the more rich experiences students have with various math tasks, the better chance they will have in catching the big concepts and ideas we want them to learn.
Finally, and this was also a big takeaway I learned from Graham Fletcher, but the more we as educators can learn the better we can teach. Learning the progressions of proportional reasoning, counting, fractions, etc, will just help us be more effective teachers. Our learning should NEVER stop after we earn our teaching certification or masters degrees or whatever.

These are huge takeaways and based on some of the other learning youâ€™ve done through Robert, Christina, and Graham it is clear that you certainly havenâ€™t stopped your own learning after coming out of preservice. Great on you to keep on learning and pushing your thinking forward! Itâ€™s been a pleasure learning alongside you!


I have to agree with Tanesha. Throughout this course I realized and mentioned in my responses that I need to incorporate these tasks/problems more as my introlessons into my units. Within these problems I then need to incorporate more methods were students are constantly sharing and working together (at times I still run into issues with the stronger students do most of the talking/work). I have realized that taking on these tasks helps students problem solve. They allow me to see how students are thinking which then provides me an opportunity to help them guide their thinking.
This course also showed me that it is alright to slow down on certain part of the curriculum as students will grasp later on if you spend more time on other areas which are the core parts to the harder material.
Lastly, this course demonstrated to me how much ratio and rate relationships can be used to help understand all the strands in the curriculum. If students are able to grasp these terms and concepts then it will help them process the other concepts as well – basically I need to keep referring to these terms throughout the year. I know I need to rewatch some of the modules throughout the year to remind me of these concepts and how to demonstrate them to the students.
Thank you.

Always fantastic to read such great reflections. So happy to hear that youâ€™ve had so much to take away and so much you can put into practice right away! Thanks for learning alongside us!


Introducing concepts through problems.
Using double number lines to explore the proportional relationship between two amounts.
The abundance of resources available to teach concepts.

Fantastic! We do appreciate your final reflection and are always thrilled when folks have big takeaways that make the effort put into the learning worthwhile! Enjoy the start to 2021!


Oh my goodness… this was a fabulous course. Thank you so much!

Amazing! What is one thing you plan to implement right away and what is something you need more time to think/reflect on before implementing?


My students rush to an algorithm. I want to introduce concepts through problems that are low floorhigh ceiling and make sure that I start with a problem that sparks their curiosity. I want them to want to solve the problem and I want them to feel comfortable trying all different approaches and be able to have a more flexible way of thinking. This course helps me see how to do that.

Fantastic! Such great goals for your students. While it takes time and adjusting along the way, youâ€™ll get there!


My biggest takeaway is how much student curiosity is vital to their engagement and thus their learning. I have already started to use a problemsolving teaching approach (starting there rather than finishing there) and it has not only been revealing, but a lot of fun. Students love being challenged and trying to find different ways to solve the problem. I have been surprised and impressed by how many times the things they notice and wonder lead perfectly into the targeted problem…which is validating for them and exciting for the class.
Another big takeaway for me is how important models are to help students communicate their understanding and link spatial reasoning with more abstract thinking. This has been a very informative class for me.
The only regret I have is that I can’t just use the curiosity tasks as they are presented because I teach in a French Immersion context. I have had to find other sources, make adjustments to eliminate the text in English or just create my own, which is disappointing since yours are so welldone. I know you have thought of this aspect, but it would be great to see more French content, or at least less content with so much English text in the images so it is a little more adaptable to diverse cultures. At the moment I am tempted to upgrade to an academy member but not sure how much I would really be able to access the content…
A great course though and I don’t regret taking it. Thanks.

My biggest takeaway from this course is to keep pushing boundaries in my instruction for math sense making. I started this leg of my math instruction journey in the Fall of 2019 at a professional development introducing me to the concept of math talks. I started using and playing with them in my classroom. Then 2020 and its’ trial came and I hit a hard pause. This summer I read a book Building Thinking Classrooms in Mathematics which challenges my ideas of math instruction. I’ve tried some new things and need to revisit using math talks with these new ideas. Then I found your course and my take away is I can’t go back to to same old ways of instruction.
I’ve been being more intention about using models but I think I am “beating students” with them. This idea of emerging concepts and models is HUGE. I need to transition myself and so do my students. My final thoughts are I need eyes that “wonder and notice,” hands that record and model, and thoughts that reason and consolidate old ideas and new wonderings. This creates new understanding that I can communicate and share with others. If I can proceed in this way, I can work with students to think of math in this way. There is power in curiosity and creation and I need to infuse this into my instruction and ultimately in my students’ learning.

So happy to hear that the learning has been valuable for you and your students! It certainly takes time and adjusting as you go, but it sounds like youâ€™re well on your way!


1) My biggest takeaway is the importance of not rushing to the algorithm or the abstract. Students need to spend more time working with hands on and visual models. Your visuals models have been so powerful. As I have pondered how I taught concepts last year such as equations and slope, I realized that I rushed through the models. I am trying to spend more time at the beginning with problem solving tasks and visual representations in the hope of deepening understanding of concepts.
I have also deepened my understanding of ratios, proportions and rates. I have more precise language that I am able to use and a much clearer understanding of their relationship to each other. I have more tools to use to teach about these concepts. I realize how proportional thinking permeates my curriculum, so I am not worried that I only have one unit in which to teach it because ratios and proportions are everywhere in Math 8.
Thank you for sharing your knowledge!

Your take aways give me chills down the spine. So happy to hear the impact this learning has had and will continue to have in your teaching! Great work my friend.


Sparking curiosity to engage students, using the correct language, and using a variety of models are my biggest takeaways. I plan on revising my lesson plans to include more problem based lessons where we all struggle productively to derive the abstract solutions. They make so much more sense when you start concretely/visually and give all students the opportunity to jump into the learning.
Thanks so much for providing a course like this! It has helped me become more confident in teaching proportional reasoning!

So glad to hear it! Good luck continuing the learning and implementing in your practice!

Always so fantastic to read reflections and big take aways. You made it through a monster of a course and Iâ€™m so happy to hear that it was time well spent!


I have been really thinking about how to build up student understanding. I have really embraced the idea of Spark and I have been trying to figure out ways to go back to concrete ways to model abstract situations.