Mary Olsen
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I was playing Monopoly with my grandkids over the break and my 7th grade grand daughter had to count the pips on the dice to add them up. I look at the dice and do not even see an addition problem anymore, I just see the sum of the dice as a number. I played a lot of board games growing up and this basic addition became automatic. But not because I sat down and practiced addition over and over. It just happened as I was playing board games. As I noticed this I decided I wanted to play more board games with my grandkids that have 2 number dies in them. So that they will see the addition automatically some day. But it also helped me realize what you are saying about automaticity. I take away two main things. As teachers we need to give opportunities for students to make sense of numbers, addition, multiplication etc.. through planned activities that are designed to help students see the math and experience the numbers. Secondly they need to have multiple opportunities for these experiences. Automaticity does not come from one experience. It comes from seeing the numbers in multiple ways over multiple experiences. Its making sense of the different ways to see them. These opportunities can come as a warmup, a math game near the end of the bell. As an planned activity once a week where students work with manipulatives, draw models, show ways to make sense of what ever math they need to work on. I think every teacher can build these into their weeks. I think if we did we would see deeper understanding of student over time. But it will take time…and we must be committed to the process.

My big take away is using hands on manipulatives. I get frustrated with students that I know are struggling with a concept but decide to “play” with the manipulatives instead of using them to help them understand. I also need to educate students that manipulatives will help them get a deeper understanding…they are not babyish. Students in middle school are very selfconscious. I spend a lot of time in the beginning of a semester talking on growth mindset. Showing the videos from youcubed. Setting up the class as a safe place to try the unknown and explore different things they may not have understood. Many of the students embrace it but I always have a student that has their walls up so high I can’t get around them. I am hoping that the more students explore math using manipulatives the more open they will be to using different tools when they are offered.

I see the truth in this video which is why I am here taking this course. I want to help students with productive struggle. As educators we have trained students to play at school by mimicking the teacher. I have felt guilty when a student did not do well on a test because there were different questions than we practiced in class.
I think really understanding the learning process can help me plan better. Right now I am struggling with the course that I teach. There is no set curriculum. Another teacher at a different school came up with the lessons and everyone is just following. I want to leave it behind this year. I could use lessons that support what is being taught in their classroom but using these open activities to help students learn to apply what they are being taught. My problem is much like that of my students. I struggle with the application. I am good at mimicking and doing things like everyone else. I have always struggled with lesson planning. I used to research for hours looking for different things to do and then in the end would just tweak my notes for this years kids. Find a hands on practice activity or a “good” worksheet. My version of good was one that had students apply their knowledge but because students struggled so much with these over the years I have given these up too. With the pacing guide in a regular class I felt the pressure to get my students to a particular place by a certain day. I hated feeling this way. I tried to keep spiraling the material in warmups so students that were struggling could have the chance to keep learning….but those were the students that just gave up and put no effort into the warmup. I know I am going off task on this reply. But since everyone else finished months ago, I am just trying to reflect on how better to do this teaching thing. I want my students to get the chance to have that productive struggle. I can see that after working hard trying to figure something out how the consolidation step could be more meaningful for them. How when I show them other ways to solve it might be something they would be more inclined to hold onto. So that is the goal I will hold onto for this school year.

I’ve used the estimation 180 in my class but students are so resistant to doing the upper and lower part of the estimation. My answer paper has a place for them to explain their reasoning which they also do not want to do. But they enjoy the actual sharing their estimate with the class part. I tried the would you rather but they did not want to back up their answers with math. I think I will try it again and maybe have students partner up to figure out what they could do to back up and/or tweak their reasoning and answer.
Working with middle schoolers is a fine line. There are things a high school student will do and an elementarty student will do that a middle school student will not just because of the age. But hopefully as we try different things in class and students get used to backing up their answer it will help them. I might start with the which one does not belong as there is not one right answer for the prompt. As long as you have a reason you can be correct. Sounds like a safe place to start with self conscious middle school students. Plus builiding the community of the classroom as a safe place to share your thinking.

Problem: Arturo paid $8 in tax on a purchase of $200. At that rate, what would the tax be on a purchase or $150?
Changed to : Arturo paid $8 in tax on a purchase. WDYN? WDYW?
I thought then students should make estimates on how much the item he purchased cost to have $8 in taxes. Having students partner share and then share with the class.
Eventually I will reveal he spent $200.
Then I can have students find out how much tax he would spend on other purchases if the rate was the same. Or I can give them another tax amount and have them estimate how much was spent before moving onto how much tax it would be for a specific purchase.Problem: Arturo paid $8 in tax on a purchase of $200. At that rate, what would the tax be on a purchase or $150?
Changed to : Arturo paid $8 in tax on a purchase. WDYN? WDYW?
I thought then students should make estimates on how much the item he purchased cost to have $8 in taxes. Having students partner share and then share with the class.
Eventually I will reveal he spent $200.
Then I can have students find out how much tax he would spend on other purchases if the rate was the same. Or I can give them another tax amount and have them estimate how much was spent before moving onto how much tax it would be for a specific purchase.

I like the idea of withholding information to make the task more open. After listening to your blog I tried a few of your tasks and used notice and wonder. The students participated but it did not seem to spark curiosity. I did have a unique class this past year as I taught Algebra Readiness which was a second math class for student that struggle in math. As most do not like math and did not want to be there I worked hard to build a safe culture. One of my takeaways of this lesson is to realize that it is going to take time. Even if the kids are negative or barely participating I can’t give up. I know that these struggling students need this as much or even more to help them better understand math.
I hope I can better learn how to apply these 4 strategies in my classroom on a daily basis. As I get bored with the “normal” I teach you do way of teaching. But getting past students wanting to stay in the normal zone (even though in reality they do not like and and usually don’t get it) takes a lot more energy. I am praying this year I will be more successful than my attempts in the last school year.

Traditional lessons always start with the teacher explaining and demonstrating how to do the math that is being introduced. But this lesson style leaves it a lot more open for students to discover truths found in math. Students can discover the math.
I have tried a few of your lessons. I looked for easier intro type lessons as I am now teaching Algebra Readiness which is for students that are struggling in their regular math class. So my class is a second class in math for them for the semester. Some of the classes really tried to get into solving a given problem, others really resisted diving in. All of the students wanted to be spoon fed….like the traditional math class. They were easily frustrated and after a few tries I gave up. I actually started the semester out with growth mindset videos from youCubed which I showed one daily for the first 78 days of classes. I wanted to break down the negative stereo types and negative self talk and have students understand that everyone can do math. Because all my students struggle in math I have very few students that can be encouragers, and/or leaders.
I truly believe my students can benefit from this type of teaching but the energy to help them overcome their negative attitude and beliefs often drains me. Also even though they have learned some of the tools that could help them solve a problem they don’t know when using them could be helpful.
I don’t know how to reconcile this with traditional teaching. When do students learn how to write equations or how to show proper work for multistep equations etc.. How do they learn this without being taught? I took this course hoping it would help to answer the questions I had when I tried to do this, this past school year. I want to teach this way and help my students to discover their ability to problem solve. I just need more tools and better understanding so that I can figure out how to work through the inevitable bumps in the road as I pursue this way of teaching.

1. There are different ways to solve problems.
2. Math is open and can be fun.
3. Anyone that is willing to try, can learn and do math successfully.

I tried this yesterday with my Algebra Readiness 6th and 7th grade classes. It did not go well. The students just really could not grasp what the question was asking. They kept going back to the 1/3 for the second shoveling and the 2/3 of that portion is left not shoveled. After letting them work for a while and questioning their thinking..trying to get them to understand I had them draw the area rectangle showing the 1/4 that was shoveled first. Then I drew attention to the portion of the driveway that was not shoveled. Students could understand that 3/4 of the driveway was not shoveled. But getting that 1/3 or the 3/4 that was not shoveled did not go anywhere. I know in 6th grade they drew models for fraction multiplication when learning about fraction multiplication but not one of the students went there. Not even my 6th graders that actually have done that recently in their math class.
My question is what do you do when none of the groups is on a real track to solving the problem. One group drew a picture of the fourths and then a second picture of thirds. But they could not see any connection. I thought I was asking good questions to get them to think about strategies. When nothing I was asking was going anywhere I asked what it would look like if they drew the fourths picture and the thirds picture on the same rectangle. What they ended up doing was not even close they just kinda smooshed them together.
My classes are made of struggling students. Some love trying things and have a positive attitude and others are more negative and just want to goof off. I know doing the tasks will be great for them once they start meeting with success.
I wanted to use them to intro the concepts before I reteach them. Since it is the second semester most of the concepts I cover they were taught in their regular math class earlier this year. But maybe I should look at using lower grade tasks that may or may not be what we are learning. Any task that helps them learn how to struggle through is great. But if their struggle is not getting them anywhere near understanding how to solve a task I feel I might be reinforcing their negative ideas on math.
Suggestions greatly appreciated.

I hated having to get students to memorize properties in the abstract. But I love showing them to students to help make work easier. Some students pick up on this right away and use it as a tool to make adding simpler. Other students more rigid in their thinking have trouble with this. I am working on helping students be more flexible in my Algebra Readiness class. Today we were doing an escape room on integer addition and subtraction and I was encouraging students to add the numbers in the order that was easier for them. I have had students break apart numbers and add them differently when we do number talks. I have not talked about that being the associative property. I will definitely have students look at why we can break up numbers and add them in different orders.
I wonder if there are practices I can do in class to help my students that struggle with flexibility in math. I do number talks and I try to encourage my students that are steeped in the algorithm to try a strategy another student showed us or one that I have shown the class. But I would like to find other ways to help students try these different properties even if they do not know the property name.

Honestly as I read other people’s comments I am the outlier. I liked the pictures and found it interesting but I would not want to pursue this with my middle school students. It still seems on the abstract side even with visuals. It may just be my end of the day brain can’t handle this right now.
I guess I wonder where and why I would want to pursue this with my students. I am all about making things more conceptual for my students, but for some reason this did not resonate with me. I will have to come back and hear it again maybe earlier in the day next time. : )

My take away is to ask students their unit of measure if a specific unit of measure was not given.
I need to be sure I am specific about the unit of measure.

I’ve been listening to your podcast and the talk on fractions has really gotten my attention. My big take away today is just seeing that modeling is so important for students to make sense of what fractions are.
My wonder is more about the unit fraction which I heard on one of your earlier podcasts. (I’m only up to 28 right now.) I would like to find more information about teaching fractions this way. I incorporated the little I know in my class this week and it has made a difference in students understanding. When they get confused because they want to jump to the algorithm they learned before, and I have them take a step back and I talk with them about the problem using the unit fraction they have a much better understanding of what the question is asking. Honestly when I get a good grasp of how to teach and model this way I am going to be sharing and sharing with every math teacher in my school and more on what a difference this can make with their students.

The meaning of 11 and 12 is interesting for sure. I wish students in younger grades really had the opportunity to truly understand place value. In my number talks with students when I give them equations like 127 – 279 when explaining their answers I will have students say added the one and the 2 to get 3. and I added the 2 and the 7 to get 9. Often because they are not thinking of the place values the numbers represent they then just add the 9 and the three. I have been emphasizing that even when adding number mentally you need to keep the place values in mind so that you understand the real value of the number. Adding 100 and 200 to get 300 makes it much easier to keep track of the other numbers they are mentally adding. Student have improved keeping the place values as they solve problems with their mental math. But this also makes me wonder it they really understand what those place values mean. I often come into class thinking 7th graders must understand this but this is not always so.

I have not actually thought about magnitude before. The opening number line really opened my eyes on how perspective and understanding on magnitude can make a difference. Someone above mentioned how they like how you can start with smaller numbers and once students have a good understanding you can expand the same thinking to larger numbers. Like my students I sometimes have trouble generalizing what I am learning. But reading the other teachers comments helped me to see how I could bring this into my classroom.

Could you share an example of what you do on google sheets? I too struggle with planning and keeping it all organized.