Make Math Moments Academy › Forums › MiniCourse Reflections › 4 Strategies To Help Students Start Problems & Stick With Them › Strategy #1: Avoid Rushing To The Algorithm – Discussion

Strategy #1: Avoid Rushing To The Algorithm – Discussion
Posted by Kyle Pearce on December 7, 2019 at 6:38 amWhat was your big take away from this particular lesson?
What is something you are still wondering?
Share your thinking below.
Kirk Betz replied 2 months ago 27 Members · 35 Replies 
35 Replies

I loved the quote from Peter Liljedahl. In reflecting back to many of my past lessons, I believe I planned the same: assuming kids couldn’t or wouldn’t think. I tried to “trick” them into learning by showing them math wasn’t that difficult, but now I want to embrace the idea that it’s not me that should be doing the work, it’s them. I need to trust that by emphasizing a class environment of collaboration, exploration of ideas, and embracing mistakes, students will be more active participants in learning math, rather than the passive ones I viewed them as for so long.

I also loved that quote. It really resonated with me and conversations I have had with my peers. I hope to spend more time helping to students grapple with problems using what they know to work through what they don’t.


Its a mistake that I make more often that I want to admit. Sometimes, lack of time pushes me to a situation when an algorithm comes to save the day.

@DanielLaguerre We totally know the feeling.
One of the biggest strategies that has helped me to resist that rush is to reflect on the lack of retention my students have when I do things like rush to the algorithm. If in the end kids don’t remember it anyway, then what is the point of rushing it? That always helps me, anyway.


Sometimes I find myself rushing to the algorithm when it is just a step in a bigger problem that my students are working on. For example, they have no idea how to multiply fractions, but they need to for something or other. We don’t have time for discovery. I’ve found it’s better just to have them grab a calculator for things like that. They can get the calculations done and still solve the problem.

I know I have fallen victim to preteaching and providing stepbystep guidelines to solving problems (I have the Google Doc in my drive), and I wholeheartedly want to change the way my math class runs. My struggle is always in the time that we have and the number of outcomes we are expected to “cover”. I know I just need to take a year and try a different approach and see how it goes, but there is always the fear that the students won’t know what they are suppose to know by the end of the year. I will forge ahead with your awesome courses and keeping trying though. I just haven’t figured it out YET.

I often fall into the trap of the common math class, where we take up homework, do lesson etc. Regardless of the amount of time in a block, to restructure the math class to pique curiosity right from the getgo would be a great strategy in helping to build resilient problem solvers. Also, they may actually enjoy coming to class.

I loved the Peter Liljedahl quote and the area example that you provided for how to turn an average, basic problem into something that allows for exploration and discovery. Any student, regardless of where they are on their learning path, would be able to find success with that area problem because they are given the freedom to approach it as they see it. In reflecting back on my lesson planning process, I think I do a good job at answering the question “What do I need my students to know in order to be successful with this standard?” and then I take a wrong turn. I then think about how I can give that information to my students, thereby forcing them into my way of thinking and reasoning. I think a better lesson planning process is to anticipate where the gaps may arise in a standard and how I can provide learning moments for them to move forward in their ability to think and reason about math.
One question I pondering is this: How do you know if the struggle that is occuring is productive and what level of frustration do you allow before intervening?

Great reflection and awesome question! This is where Making Math Moments is more of an art than a science. While providing productive struggle is the key, how we try to draw out that productive disposition is a difficult task. It can very easily flip to unproductive if students aren’t able to access the task with models and strategies from their own tool belt. This is also hard when we are so used to “telling” vs helping students emerge new strategies.


There are too many times that I rush to the algorithm just because:
because I am running out of time
because I am not getting class participation
because my students have been spoonfed that way for much of their math careers and I could go on. I must allow my students the time they need to develop and build the concepts and also let them know that struggle is OK. It is one of the ways we learn and we appreciate what we learn.

Agree. Same experience. And the rocketspeed pacing of Algebra 1 doesn’t make time for understanding for any but the 5% who “get it” via direct instruction and do the work. Trying anyway.


Like most of the responders, I do this too. And for many of the same reasons. Another reason I do this is because I want to assign some independent work for their study hall(s). This is selfserving I know, and it really isn’t equitable either. The students who “got it” might benefit from consolidating their thoughts, but the “don’t gots” are unable to benefit for practicing a skill they still don’t understand.

EVery time I give word problems, I let my kids notice and wonder, and to analyse each problem. I want to have the patience to solve problems without quitting. The frustration here is that many of my students attend extra math lessons like Kumon or Eye Level. Another thing is that some of them got used to being taught the steps without analysing the problem first. Sometimes I tend to preteach especially when I run out of time . I normally fall behind in my maths lessons in the grade level since those teachers normally tend to preteach the steps or proceed immediately to the algorithm. So, I do not have a choice to rush with my lessons.
 This reply was modified 2 years, 5 months ago by Maria Carmela Sanchez.

That is always a major road bump when students are being taught outside of class to memorize procedures first prior to understanding. It happens for those who get tutored as well as by parents at home. However, that is where the 3 part framework can still help as students often don’t recognize (due to their lack of understanding) that the task they are working with initially is the same concept as the procedure they’ve already memorized. It can still come out in the wash “ok” with no harm done!

The thing that jumped out at me the most is when you said that you would deliver the explicit instruction at the end, to make sure that the ones that were still lost with their thinking would eventually be made right. So the lecture, i.e. direct instruction, comes after students have been struggling with the problem for a while, and are probably more receptive to hearing what the answer is.
I’m still wondering the best way to create a productive struggle. I know 3 act math is great, but I also know that if I now how to structure it, producting struggle could be gained from simply writting a couple equation on the board. I’m also wondering how or if these ideas could be incorporated into blended or flipped instruction.

Great take away! And to be even more clear, we try to elicit the consolidation after the lesson using student work from their approaches. This is a great way to try and highlight all student voices and make connections across the mathematical continuum and across mathematical models!


I love the idea of doing this, I just don’t see how we have enough of time to teach this way. During distance learning I have only had a 35 minute math lesson twice a week. How can you teach this way and still be time efficient?

Hey @nicolette.kranz This is a valid concern and a common question asked. We actually feel we gain time. Listen in to this podcast episode to begin your journey here https://makemathmoments.com/episode12/

Agree with @jon but at the same time, two 35 min lessons a week is simply not enough time – no matter how you lead your lesson.
If you do direct instruction / lecture, the question is “how’s that working?” Probably ok for some students… but they probably aren’t the students you’re hoping to find more ways to reach.
Later in the workshop, you’ll see ways to think from a higher level on “what really matters” for your long range planning.
Stick with it despite the challenges the current model presents.


My big take away was the importance of sparking curosity and the way in whch pretreaching deprives a student of the opportunity to explore.

The children have rarely been taught to think–in any subject… Few teachers allow for questions. I have started my sessions with a thinking challenge–not even directly Maths related, but to get them to start OBSERVING everyday things…and to WONDER about things that are just taken for granted. Then, in working through the lesson, I ask questions about the work or the exercise; I encourage them to explain how they got the answers and why they were correct or incorrect. Checking their answers before submitting work is a new experience for them especially since they were never required to do corrections–at all, never mind in a meaningful way. The children are baffled that I teach this way–but they beg for more! Unfortunately, my time with them is very limited but we do the best we can.

1. Start with a productive struggle.
2. How would this work in a flipped classroom

I like the idea of starting with asking the students what they see…it is very validating and accessible. Making connections to my own thinking was always my favorite thing of mine, so it’s easy for me to imagine it’s true for others too

It just confirms my realizations that our school has to change the way we teach math. We are stuck in the assign a page, do the vocab, do the homework, collect the homework. I need this information and techniques in order to make a positive change in our school.

Hi,
This is so me as well. I look at my students before I teach them and wonder, ‘are they , going to get it?’. In my brain, I am constantly think, ‘how can I engage them more?’, ‘what do I need to do?’
After watching and listening to this video. I thought ‘this is how they truely think!’.
Thanks for the video

I love that I can think of different ways to initiate curiosity and excitement about solving math problems and allow students to come up with ideas. I love that you still give explicit directions after the discovery time. Then, they want it more, and can actually share their discoveries with others, making it their own.

Glad you see value in the approach! Let us know how it goes!


My big takeaway is to stop preteaching. I have always tried not to get to the algorithm or follow my steps and see if the students can come up with them. I really enjoyed the quote about assuming the kids can’t think and won’t think. I feel like I middle school students have been trained to wait and see what the teachers do and then they follow that lead. We as teachers tend to model too much, especially in the elementary world, so thinking for themselves becomes a challenge Putting kids in situations that is unfamiliar I think is super important, and the next steps that follow are probably even more.

Great realization! Takes time and effort to get there – with potential for push back from students – but so worth it in the end.


I love that we need to start to listen and observe what is going on.

Exactly! We can’t just rely on product results to inform us (anymore ).


I would have to agree that we often plan our lessons thinking that our students can’t or won’t think. I think we arrive at that assumption because we have seen so many students refusing to take part in class. However, I do think there are things that we can do to change that, at least for most students. I hope that is what is going to happen in my class this year.

I really like Peter Liljedahl’s comment. Kids won’t think is a prevailing thought in our secondary schools and I have been guilty of thinking that way also. After many PD sessions and much reading (authors discovered through Jon and Kyle’s podcasts), I realize that it is a teacher issue. I need to develop lessons that encourage student curiosity or in my current role to help teachers build lessons to spark the curiosity.

Great realization. I constantly reference that quote because it is a good reminder that humans inherently aren’t motivated to think unless there is a reason to. We can create or craft that reason in our classrooms!


Love the idea of making moments. Read the same book a few years ago and it has changed how I plan events but have not applied it to the classroom. Can’t wait to see more.