I feel like the curriculum stars are in alignment. Many of my classes are exploring computation in some capacity. This rarely happens because of the scope and sequence of the curriculum at the elementary level. Computation is an interesting concept to explore in the classroom. I find students come to class with a variety of computation knowledge, although some of the background relates to procedures or tricks used to compute numbers. Other students have a conceptual understanding of the computation, but might be lacking in the procedural department. Either way, I find that students need more practice to become fluent with computing numbers. They also need to be able to distinguish and apply rules to problems e.g. signed numbers, fractions and order of operations.

Developing computational fluency can be found in a variety of forms, but as of late I’m finding games to be the most beneficial. Computation timed tests drive me nuts. I couldn’t stand that as a student and feel a bit embarrassed when they are assigneds. An alternative to this can be found using math games. Games provide low-risk opportunities for students to engage in math conversation and practice computation skills. This past week I was able to use one of these games with students in second and fourth grade.

The game involves using dice and strategy and computation skills. Students were given a game board and recording sheet. I pair the students using Michael‘s grouping spreadsheet and the students grab the sheet, dice and find a cozy place in the room. Students then roll the dice and fill in each line slot and match it with an answer on the game board. The game is over when all the slots have been filled. Click on the pictures to download a file of the game.

I first used the above game with second grade and then decided to use the same format with a fourth grade class.

Both games seem to serve their purpose. Students are practicing their computation skills while using a variety of strategies to compute numbers. Students are also engaging in math conversations around computation and using vocabulary associated with computation. In addition to the game sheet, some students decided to grab a whiteboard and complete their computation there before transferring it to the game sheet. Hopefully these skills will develop into a deeper sense of computational fluency and cement as students progress through school.

In a few weeks my fifth grade students will start their pre-algebra unit. Before delving into the unit students often need a reminder on how to use the order of operations with fractions and decimals. Half of today’s class was dedicated to reinforcing number sense and computation skills. At some point students will need to be able to use these skills along with maneuvering variables on both sides of an equation. I find that some students struggle with pre-algebra if they don’t have sound number sense skills. So today I ended up using an Illuminations operations activity.

I passed out the above sheet to each student then reviewed the directions. Students were paired and asked to find a spot in the room to work. Students were asked to hide their calculators and estimate one path that will lead to the largest number. Each group came up with their own path.

Students were then asked to use a calculator to find the path that ends with the largest number. It was interesting to listen in on the student conversations. Here are a few of the statements that I picked up:

“If you divide the number it will decrease”

“Not really, if you divide less than one the number will increase”

“If you divide by a really small number than our number will skyrocket”

“But we can’t multiply by a number less than one”

“But we can multiply by a large number”

“Let’s just work with the multiplication and division paths, those will make the number jump”

“Let’s work sideways instead of making a path straight down. Gives us more opportunities to increase”

While listening to the students I decided to not intervene. It was insightful to hear how the different strategies were planned and executed. There were some student arguments and stonewalling. Eventually students had to defend their reasoning as groups needed to find a solution. Near the end of class students presented their final paths and the class calculated the total. Students soon started to realize that their answer would differ depending on if they followed the order of operations. This changed many of the answers as some groups completed each operation individually. In the end students all decided on one pathway to find the largest number. Students then informally reflected on this activity through a class conversation.

Before sending the students on to their next class I mentioned to them the Pick-a-Path game website. The interactive component has more options and might be a decent supplemental activity. I’m hoping to see that a few students took the initiative to check out the site tonight. It might even be part of a classroom discussion tomorrow.

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

With some assistance from ISTE13, it seems that the concept of gamification is becoming more associated with education. I was #notatiste this year, but I heard that the keynote by Jane McGonigal was well received. The idea of gaming in education, specifically the use of technology to facilitate gamification continues to build momentum.

The concept of gamification is described by Wikipedia as game-thinking in non-game contexts. The idea is continuing to make an impact as companies and now schools are implementing the underlying concepts of gaming in the workplace/school. I find more and more that gaming is becoming mainstream, from purchasing points to Fitbit badges.

To be honest, when I first heard of the idea of gamification I thought that this idea has a place in the classroom. I then thought of how much time students (and teachers) spend on games and what role motivation plays in those games. Many iPhone/iPad games give multiple, sometimes endless opportunities to successfully pass a level. Think of games like Angry Birds, Doodle Jump, Words with Friends for general examples. If a user fails at a level, they use the electronic feedback (e.g. not hitting the right board in Angry Brids) to make another attempt. I know that that is a generic example but also reinforces the point that feedback is important. Although I feel urged to mention that electronic feedback isn’t always effective … think of Game Genie.

Recognition, competition, and collaboration all have the potential to contribute to learning in the classroom. I think most teachers use forms of gaming in their classroom, but they don’t necessarily refer to it as gamification. Many web-based companies continue to interweave the idea of games and learning. Khan Academy, Scootpad, Class Dojo, and MobyMax are just a few that use points or badges as a partial motivation tool. Many iPad educational games are also adding to the gaming party. SplashMath, a math game used with my second graders uses points that can be used to build an aquarium with exotic fish. Where was this when I was a student?! Teachers often use games to engage students in the classroom. I do believe though that staff should always be aware of what learning outcomes the games address to also validate why they are being played. For some, the idea of playing games is related to entertainment, not learning. Why can’t it be both? Personally, I find that board, card, math contests, and dice games to be effective in helping students retain and apply mathematical practices in the classroom. Not only do they encourage students to collaborate and use social skills, but I find them to be useful during guided math groups. A debrief after the game also allows time to reflect on strategies and reinforce mathematical processes.

The focus now seems to be placed on technological uses of gamification in the classroom. One of my goals this next year is to incorporate additional gaming opportunities in the math classroom. I’m still in the process of researching and finding additional resources related to math gamification. If you’re in a similar boat, Trever Reeh’s page on math gamification is a good place to start gathering a few ideas. I believe gamification in the math classroom has its place, but finding a balance between different teaching strategies is important. How do you use games or similar activities in the math classroom?

I noticed a theme while observing an educational math chat on Twitter. Many of the participants spoke of how math and reading don’t necessarily have the same “emotional knee-jerk reaction” in education or at home. One tweet I remember reading stated that there isn’t a math equivalent to reading a bedtime story, emphasis on reading. As far as I know, there is no such thing as a math before bedtime. Reading often takes precedence over math, especially at the elementary level. Reading / Language Arts often requires or is mandated to take 1 1/2 – 2 times as much time as math. Don’t misinterpret what I’m writing here – reading is essential and absolutely needed. I’m advocating for the math crowd – the people who despise hearing the words “I hate math” coming from anyone. Math has received a stigma over time and there are even adults (you may be one of them) who can’t stand thinking about math. An interesting perspective comes from Michael Schultz in his recent blog post. As you can imagine people dislike math for a variety of reasons. Unfortunately, many adults remember math as one of the least favorite subjects in school. Their math teachers were less than stellar and used (and only used) the text book for all math instruction. How do educators and administrators decrease the negative stigma associated with math? I believe removing the stigma starts before and during elementary school. Educators need to make math relevant and engaging. How does that happen at the elementary level?

Use Manipulatives

Educators understand the often use manipulatives to increase student engagement, especially when introducing a topic. Looking back at my own experience, the times I enjoyed or expressed interest in math were when my teacher used manipulatives in the classroom. Using manipulatives creates student engagement, which often leads to increased learning. I still remember using the base-ten blocks and geometric solids to learn math back in the day. A couple specific examples:

Base ten-blocks

Balances – Mathfour video

Use Technology

Students use technology everyday. But teachers need to appropriately (that’s key) utilize technology to increase student learning. Most curriculum publishers have a technology component (like math games or instruction slides to show students) already part of their program. There is a wealth of knowledge and information available online for teachers to use. Personally, I’ve used Youtube, Power Point, Audacity, Google Docs, Movie Maker, and Flip Cam regularly. There are many more tools available to use – I just wrote down what what was used last year. I’ve placed a few links below if you’re looking additional content. Using Google Docs

Students are much more motivated to complete problems that are relevant and applicable to their lives. A student wants to know why they are learning specific math concepts. If students aren’t sure about where or how to apply what they are learning, what motivation is there to stay engaged? Finding practical math problems is important and gives students an opportunity to apply their learning. Even having students create and solve their own problems is a good start. Students need to understand that what they are learning in math class is relevant. I tend to show my students the following video from IBM. Also, during the first week of school I generally show the students a macro picture of what they will be learning throughout the year and what skills that they will need to proceed through each unit.

IBM Math Commerical

I also ask the students the following questions:

Can I think of a story problem where I could apply this concept?

How will learning this help me in the future?

Play Games

Play games? Are you kidding? I think at times, educators and administrators downplay the importance of playing mathematical games. Games give students an opportunity to use learned skills, such as, but not limited to: numeracy, collaborative teamwork, and critical thinking skills. There are online math games and boardgames that are relevant to what is being taught in the classrooms. For example, games like Battleship can help teach algebra quadrants and axis. An example: Board Games

Disclaimer (unfortunate but necessary) : The thoughts and opinions expressed in these pages are my own, and not necessarily the opinions of my employers.