Last week I had the opportunity to finish up a book study on how the brain learns mathematics. During our last GHO the crew discussed the implications and takeaways from the book. We had instances of affirmation and some of the research had us look at our instruction through a different lens. In my mind this was perfect timing as school is just around the bend or has even started for some. The last chapter in the book discusses the need to connect brain research and how educators teach mathematics. Moving forward there are few different questions I want to consider while planning.
Is the lesson memory compatible?
Basically, are the number of items in a lesson objective too much, too little, or just right? At some point I feel like all students need transitions. Being aware of when to transition comes with teacher experience, but breaking up that time block dedicated to math instruction is important. After the transition students’ working memory has an opportunity to refresh. I couldn’t stand 60 minutes lectures when I was younger and still can’t today. The brain needs time to move items into it’s working memory.
Does the lesson have some type of cognitive opening?
According to Sousa’s research, the degree of retention is highest during the first 10-20 minutes. New material should be taught after students’ are focused on the lesson. The opening of the lesson should provide students with opportunities to see new information and correct examples. I feel like many teachers ask questions about the new topic to get student input and to make curricular connections. This isn’t always the best option because students may reference incorrect information or examples and students will most likely remember that. Instead the lessons should emphasize correct information in some type of mini-lesson format. This was a bit surprising for me because I can’t count the amount of lessons that I’ve started by using some type of KWL activity.
Does the lesson have some type of cognitive closure?
Sousa also concludes the teachers should initiate some type of cognitive closure. This can take on many different forms. During closure students participate in mentally rehearsing and finding meaning of the topic discussed in class. There’s a difference between review and closure. I’ve always put the two words in the same realm. When teachers review they’re doing most of the work. Closure is designed so that students do the majority of the work. Closure doesn’t necessarily have to happen at the end of class. Procedural closure can be used to transition from one activity to another, while terminal closure ties the day’s learning together.
How can I incorporate more writing in math class?
I’ve used math reflection journals before and I think there’s so much potential in having students write about their math experiences. Sousa believes that incorporating writing in math can be an effective way for students to make meaning of what they’re learning. Foldables and Interactive Notebooks have been the rage for the past few years but I’ve always questioned their effectiveness. Students shouldn’t be rewriting the textbook or journal. Students should use their own thoughts and vocabulary in their writing. Students are making sense and connections to the math concepts by writing about them. By writing down their math experiences, students are participating in elaborate rehearsal of newly learned concepts. In addition, the writing can be used to show individual student growth over time.
Moving forward I think all of these questions have me thinking about how lessons are planned. I fell like all of them play a role in how well students retain information. All in all, I think there’s a balance in how teachers plan their individual lessons. Retaining information is important, but students should also be given the opportunity to explore and build a conceptual understanding of topics. Retaining those experiences are pivotal throughout the year as concepts are built upon one another. Being aware of how the brain learns math can help in that planning process. I feel like being more intentional and using a critical eye in how I organize my class benefits how my students understand math. To me this process of planning is more of a journey and not necessarily a solution.
My school finished its ninth day of school yesterday. It’s been a journey as students are understanding class routines better. At this point in the year, students and teachers are starting to become more solid in their processes. Many of my students arrive to class at different times. Some students are at an elective or leave class a bit earlier/later than the rest of their peers. Regardless of the arrival time, when students enter the room they follow a flow chart. Students have their own folder and materials inside that are ready to go. I usually have some type of visual brainteaser for the week and a grade specific Scholastic math magazine. In the past I’ve used different types of math warm-up activities to start class.
This year I adapted my warm-up strategy. I wanted to individualize the type of responses within that warm-up time slot. After researching a few different tools, I decided to try Andrew Stadel’sEstimation180 this year. I think of Estimation180 as an opportunity for students to develop a stronger sense of numbers and practice estimation skills in the process. Initially, I thought that the site would be great for middle or high school students. I then found the below sheet and site that seemed helpful. This is one way in which student can document their thinking. The template also includes lessons that could link to Fawn’sVisual Patterns site.
This template inspired me to adapt the sheet to fit an elementary classroom. I changed the template a bit to work with a third grade math class. A few colleagues and I will be using this sheet early next week.
So now, students enter the classroom, pick up their folder and begin to work on their daily estimation challenge warm-up sheet. The estimation is displayed on the whiteboard. Students pick a high, low and exact estimate. I ask the students to prepare to tell me about the reasoning that they used to come to the concluding estimate. The class then completes the online portion of the site and submits a response. We then look at other responses and reasoning.
After a brief discussion the result is revealed. Students write in the correct numbers and find the + / – . The entire activity takes about 5 – 10 minutes.
I’m planning on using Estimation180 a few days a week and incorporate Visual Patterns for the rest of the days. The template also includes a few different reflection pieces. I feel like these activities provide students opportunities to produce a product and reflect on the results. At some point I’d like to add a journaling component to encourage more reflection and possible goal setting.
I’ve been fortunate to have an opportunity to participate in #MTBoS over the past few weeks. It’s been a worthwhile experience to collaborate with math teachers around the world. I’ve been able to share/use many of the resources found through this community. This post is associated with #MTBoS mission eight.
My upper elementary students are now starting to dabble into a few algebra concepts and will be getting a formal introduction in the next few months. There’s algebraic concepts sprinkled through my district’s curriculum, but solving equations and inequalities isn’t formally introduced till March. That being said, I’m always on the lookout for additional algebra resources that help gradually emphasize the topic throughout the year. Otherwise, the unit kind of brings a sticker shock to the students that haven’t encountered writing or solving equations before.
I’ve used visual patterns and Hands on Equations in the past to prepare students for the algebra unit. Both have been beneficial in wetting the appetite for algebra. While searching for a few other resources I came across the msmathwiki. If you haven’t had a chance yet, check it out and maybe contribute some of your math teaching ideas. I was eventually directed towards @cheesemonkeysf ‘s post about the Words into Math game. I believe the idea was created by Maria and found in her post here. Two pdfs are included for this game, one informally termed beginning and one advanced.
Both of the documents can be used to match equations and inequalities. They’re many ways to use this activity in the classroom. I decided to print one side on orange paper and the other on yellow. Students cut out each rectangle. The easiest way for my students to do this was to overlap the yellow and orange sheets and cut them at once. Both pages line up so it wasn’t that big of an issue. Students turned all the rectangles so the blank side faced them.
Students then took turns and were allowed to turn over one orange and yellow card. All cards that were turned over stayed that way. This is similar to a memory matching game except the cards all stay turned over. Students then took turns to see if they could match any of the visible cards. Each match resulted in one point.
As the games progressed students started to become more comfortable with using equations and inequalities. The game was over after all the game pieces were matched. Students then bagged up the game pieces for future use. I shared the ideas with a colleague at another school but haven’t yet heard how it went.
As the class becomes more familiar with algebra, it’s my hope that students are better able to connect past concepts to algebra topics later in the school year. This was an #eduwin for my class as we continue to explore algebra.
This post relates to #MTBoS assignment four. For this mission I decided to listen to one of the Global Math Department‘s webinars. I came across GMD about a year ago and look back occasionally at the webinars that I miss. While reviewing I found the math games webinar back in January of last year, so that’s the one I picked for this mission. Plus, I’ve always enjoyed using math games (1,2,3) to review and believe that I can always improve in this area of my practice.
Math games have always been a part of my own teaching practice, but I want to learn how to use them more effectively. I’m fortunate to have a curriculum that highlights the use of math games in/out of the classroom. I use math games with my classes approximately once per week and primarily use them during math stations. Most of the math games that I use deal with dice, cards, and/or some type of online component. For me, the reason for using the games goes back to the concept of learning and engagement. I believe engagement can be heightened with the appropriate use of a math game. Math games also allow opportunities to develop skills related to critical thinking and problem solving. Also, guided math has played a role in how I use math games in the classroom. With a push for guided math at the elementary level, students that are not immediately with an instructor need to be able to engaged in mathematical thinking, self-govern themselves, and use their time wisely. Math games at a particular math station provide an opportunity to do just that.
Understanding what makes a good math game is important. Ensuring that the students are engaged is key. Students that drift their attention in and out of the game can cause issues; especially if the teacher isn’t directly at that particular math station. As I watched the webinar, I began to see affirmation and areas where I need to start thinking more critically about how math games are used.
A few takeaways/questions from this webinar include:
Always start with the objective
Does the math actually interrupt the game/fun?
Is the math action the same as the game action?
Time limits can encourage math anxiety
Games can be used to introduce concepts, not just for review
Games can encourage math exploration
Inferencing, prediction, critical thinking and logic reasoning can all be part of the game
Rote mathematics doesn’t have to be the emphasis of game
My fourth grade class is now studying geometry. Geometry at the elementary level allows opportunities for students to get out of their seats and learn while using their compass and protractor. Last week my students dusted off their protractor and compass in preparation for the geometry unit. Throughout the years I’ve added different geometry explorations to this unit. Some of the activities in this post have been modified from the curriculum and others I’ve created or borrowed from some amazing teachers. I’m going to highlight four specific geometry explorations that I find valuable.
Students are given different types of polygons and asked to find interior angle measurements. I tend to group the students and have them work collaboratively to find a solution. Students can use any method to find a solution. I find that some groups use a protractor, while others find the measurement of the triangle and use it to find the interior angles of other regular polygons. Near the end of the session the class creates an anchor chart that shows similarities/differences between the polygon shapes and their sum of measures.
I pass out a notecard/piece of paper to each student. Students are asked to make an arc on each corner of the sheet. The arcs don’t have to be the same size. The arcs are cut out and put together to form a circle. Essentially, students use a rectangle and turn the rectangle into a circle and both have the same interior angle measurements. Students are then asked what conclusions can be made by completing this activity.
I generally use this activity before teaching about adjacent and vertical angles. Students are asked to draw and label two intersecting lines. This should be review, but most students haven’t been using angles in math class for about eight months. Once the angles have been created, students measure each angle. Students are then asked what they notice about the measures of the angles? Do they notice any similarities? This is a great opportunity to fill out an anchor chart indicating what angles are close in measurement.
After all the above activities take place I give students a quick formative assessment. It looks like this:
Students are asked to find and explain the reasoning for the measurement of angle Z.
Overall, these exploration activities allow opportunities for students to engage in math in unique ways. Math manipulative and explorations often open doors that ignite interest in many students.