February 16, 2014 by Beyond Traditional Math

The Fishbowl: A Peer Modeling Strategy

Whenever I notice problems in the classroom, I pull out one of my favorite instructional strategies, the fishbowl.

The fishbowl strategy is an awesome way to showcase model behaviors in ANY subject. I particularly like to use it when I notice students are skipping steps or struggling with a certain activity. I have used it to model word work strategies, reading behaviors, problem solving, computation and even science class behaviors.

Here is an example of how I used a fishbowl last week to help model effective problem solving and group work behavior.

We are working on some collaborative problem solving, which requires an intense amount of group work. The problems are differentiated so they are just right for the groups, but that means they require some really tough thinking. Often, I’ve noticed that the behaviors of group work can get in the way when they are pushed like this. In an effort to prevent this, I set up the fishbowl before even beginning to problem solve collaboratively.

1. First I put up a t-chart that had 2 columns. We filled in the left column as a whole group activity. I recorded their answers on the board as they shared them with the group, and they recorded them on their paper. I purposefully left the right column covered until the next part of the activity.

2. I asked my strongest problem solvers (I know they are strong problem solvers, the other students do not) to go into the middle of the circle, while the rest of us surrounded them. I told them that they were going to be solving a very difficult level four problem, and that the rest of us were going to take notes on their behaviors. The students taking notes had their t-charts in front of them, ready to go.

3. As the students in the middle began to problem solve, the observers on the outside of the fishbowl started writing down everything they did. They wrote what they did with their bodies, how they sat, what they said, the voice levels they used, etc.

4. Then, after a few minutes, we debriefed and shared what we noticed up on the t-chart.

5. The rest of the students were now dismissed to work on their problem, with the expectations all laid out for them. I explained that if a group encountered problems working together, they could call a “timeout” and recheck the board to see how they were doing.

As they began working, it started out great. Students were problem solving, everyone was engaged. Then, like usual, I noticed in a few groups a couple of students starting to drift off and let the others do the work. In other groups the voice level was rising. That is when I called a timeout and asked them to look at the board. They quickly adjusted their voice levels, how they were sitting and re-engaged themselves in the activity. They very badly wanted to be just like those students they watched in the fishbowl. Peer accountability is huge!

I love this technique, and the best part is that it becomes an anchor chart for the wall whenever we do any collaborative problem solving!

February 1, 2014 by Beyond Traditional Math

It’s About the Process: Not the Answer

When I first started teaching, I was always looking for the correct answer on a math problem. I would mark it wrong or right, there was no gray area. I began to change my thinking a bit when I noticed my students weren’t really growing. I knew that I needed to do something differently, so I began to start looking at the process of their thinking so that I could give direct feedback to help them get better.

If you think about it, we do the same thing in reading. We don’t expect students to become perfect readers overnight, so we give them reading strategies to become better. We look at their fluency, comprehension, how they monitor and self correct…we intervene and give feedback to help them.

With problem solving it can be the same way. We can take a look at the work a student writes down and see what feedback (direct and on the spot) can be provided to help them get better.

Here is what that looks like. This is a student’s response to a problem (I’m looking at the top one) I gave yesterday as a tiered pretest:

It is clear that he got started with the problem, figured out how many games could be played with one dollar, but didn’t finish his calculations. This tells me that it isn’t likely that he went back and checked his thinking. This is an easy strategy that can take 30 seconds to do! It is also something that we can see quickly, and give feedback about quickly. This is something that I write in my notes, confer with him about and look back again later to see if he is still making the same error.

I can’t check every problem of every student every day, that would make me totally crazy! But I certainly can take careful notes on several students each day so that I know I am getting around to everyone. Those notes also help me see patterns of which students are constantly struggling, which means I can pull a small group!

How do you find ways to give students some problem solving feedback?

January 30, 2014 by Beyond Traditional Math

Push Past the Tears: Peers Teach Perseverance

Today was the final stage of our Elementary Architects Project. Students were about to turn in their design plans for approval (and classroom money), and were feeling the pressure as the clock was winding down. With 5 minutes to go, one student (“Corey”- I certainly don’t want to cyber embarrass anyone with their real name) came to me, tears welling up and blurted, “I don’t want to turn this in, I don’t want to be paid, and I just want to throw it in the garbage!”

I was a little taken aback, because Corey’s blueprint of his dream bedroom was beautiful! It had all the right things, and was designed with all kinds of creativity. Miraculously it was to scale (many third graders struggle with this a bit!) and it was a totally perfect birds eye view.

So I sat him down at my table where four other students were sitting. Corey was fighting back tears as we went through the specifications sheet. As we named each specification the other four students at the table gave him encouragement, pointing to each item on his blueprint as I read it off. When we got to the part where it said to calculate the area of the space, that was when he really broke down in tears.

Now I know I should never underestimate the power of anchor charts, because at that moment, one of the other boys at the table looked at him and said, “Look up on the Smartboard!” We had worked through calculating area in three ways just a few days prior, so I’ve kept this slide up every time we worked on the project.

Then, he proceeded to help Corey figure out which way would be the best way to calculate the area of the space. The student who was helping used a calm voice, and his method was methodical. Once Corey had the help, the tears went away and he handed me his final page with a very proud smile.

I learned today that a kind classroom community will support all learners. Students can stay calm in the face of obstacles if those around them are calm and supportive! I think sometimes I feel like I have to be the one to help them, but their peers can be just as helpful if not more so. As I reflected on my day today, I want to think more about how to foster that type of community so that everyone can learn to persevere together.

January 14, 2014 by Beyond Traditional Math

Intentionally Make Mistakes as a Learning Tool

Last year when I was teaching area and perimeter, we wrote all over the floor with a dry erase marker to block off shapes. When I “tested” it on my own, I was able to wipe the marker away with my finger because the ink was still wet. However, after all the students had written all over the floor, I learned that once the ink was dry, YOU CANNOT WIPE IT AWAY with your finger. Oops. I learned from that mistake! We all learn from our mistakes daily!

We learn from our mistakes in math as well. Sometimes I think the best mathematicians are the people who are the very best at analyzing their mistakes. I’ve noticed for students who struggle, it is very difficult to find their own mistakes.

So I’ve been incorporating a short game called “What’s My Mistake?” each morning during our morning meeting. Here is a photo of the one I had up today:

I let them take a long look at it, and then I pick popsicle sticks. Students always have the option to pass if they aren’t sure, but most times they spot my error!

The most important part though, is to be sure that you’ve shared plenty of examples of the right way (sometimes I make a mistake that is actually correct on an anchor chart that is hanging on the wall). If they haven’t seen many examples of the right way to do it, they won’t be able to spot the mistake.

My students sure to LOVE to prove me wrong!

January 13, 2014January 13, 2014 by Beyond Traditional Math

Top 10 Tips for Teachers of Elementary Math

I saw this awesome pin today on pinterest, and haven’t been able to get this post out of my head, so I thought I’d author it and link back to the original author, Love, Laughter and Learning in prep (click below to see her page!):

So here are my top 10 tips (basically the top 10 things I wish I had known as a first year teacher) for teachers of elementary math:

1. Stop being scared of math! I spent a good two years being terrified of math because I was terrible at math my entire life. If you can embrace the fear right now, you can also do tips #2-10.

2. Make a lot of mistakes. In fact, make a TON of mistakes in front of your students. They will love you for it, and it helps them see things they wouldn’t see if you always did math perfectly.

3. Allow your students to make many mistakes. Don’t grade everything they work on, give them time to practice. If they make mistakes it should be without worry of a grade so that they can analyze them.

4. Make your students analyze their OWN work. If you correct their work, hand it back with a note that has all the right answers, they are done learning. You are the only one that did any of the learning unless they can analyze what they did wrong.

5. Get in their space. Walk around a lot and get down next to students, work with them and talk to them about their thinking. Keep them accountable with group shares and math talk.

6. Let them share. You aren’t the only one with great tricks and strategies, let the students share their thinking so that they can inspire their peers.

7. Give immediate feedback on their performance. Allow them to take home work occasionally, but encourage most of it in class where you can correct misconceptions right away.

8. Practice doesn’t have to mean a worksheet. I use worksheets from time to time, but that isn’t the only way to practice skills. Pull out the manipulatives, dry erase boards or other tools. Let them draw their thinking all over the easel paper and chalkboards. Let math be messy, and let it take on the beauty that it really is.

9. No matter what, ALWAYS connect math concepts to their world. Math does not have meaning unless they care about it, and can use it in a setting that is motivating to them.

10. Use data to drive your instruction. Using exit slips for every lesson is a very powerful way to form groups, and to figure out who needs what immediately.

Good luck to all of those who are beginning a new semester or a new school year. I wish you lots of math love!

January 9, 2014 by Beyond Traditional Math

Drop Everything and Try it! Multi-Digit Multiplication Interactive Tool

I was told about this *amazing* online tool today. It can be used in SO many ways. Here is one:

There is a core groups of students who have been absolutely flying ahead of the others with multiplication. They are ready to go deeper and play around with double digit by double digit numbers. The last thing I want to do is try to teach them the traditional algorithm I was taught in school at this point in their learning. I’d like them to understand what is happening conceptually first.

So I brought up the dreambox learning teacher tool page today during our computer lab time. I pulled that group of 7 students over to take a look at the Fourth Grade Multiplication and Division section. You are looking specifically for the tool titled Multiplication: Open Arrays – Students compose arrays, use partial products, and develop understanding of the distributive property to mentally multiply up to 3-digit by 3-digit numbers.

THIS IS AN AWESOME TOOL. My group of third graders went crazy over it. After I showed them a few examples (like below). They were so excited to be multiplying such huge numbers. Not to mention the fact that it helps solidify the concept of arrays and area.

This is a screenshot of the game. It totally walks them through the entire process. Since they just recently learned how to multiply by multiples of 10, they were eating it up.

The best part? It’s FREE!

P.S. Just as an FYI, we had a lot of problems with googling it, we had to actually type in http://www.dreambox.com/teachertools.

January 5, 2014January 13, 2014 by Beyond Traditional Math

Bump and Wild to Three in a Row: A Math Play Activity

I have to say that social media has really opened me up to be a better parent and teacher. The amount of things I see on a daily basis make me a better thinker and person. I’ve been on a mission to do 20 minutes of math play with my daughter, and was inspired by these posts by Pre-K Pages and Scott’s Brick by Brick.

The ziploc quilt is extremely easy to make and the building of this game was an entire 20 minutes of math problem solving for one day alone! We made our quilt out of stuff that we already had around the house:

colorful duct tape
ziploc bags
paper
masking tape
giant duplo blocks

All we had to do was make a simple array. While we were making it we talked about skip counting by three. I made mine with 12 ziplock bags and made a “quilt” by laying them onto the sticky side of the duct tape. Then we covered the sticky underside with masking tape so it wouldn’t stick to the floor.

The object of the game? Simply get three of your game pieces in a row horizontally, vertically or diagonally.

For our first game I made a deck of cards for the draw pile of three types to be played in the following way:

Numbers 1-12 in standard form: Find a matching representation of that number on the board. (If your number is already taken due to a bump or wild card, you lose your turn.)
Bump card: bump someone’s piece off and replace it with your own.
Wild card: place your game piece on any open space.

Then I made 12 cards to slip into the ziplock bags for the game board. I mixed the representations up and made tally marks, word form and dots to make the standard form cards. I wanted to make five and ten frames but I wasn’t sure I could draw them evenly enough (and our printer is out of ink!). I’ll probably try that next time.

Playing with three players made each game both quick and fun. We were totally addicted. I think the three of us played for an hour straight. The game wasn’t purely about matching, but included thinking about where to put a wild piece, as well as which piece would be the best to bump. My five year old began picking up strategies and we were amazed at her thinking!

The possibilities are endless for what can go in the quilt!

I think I am going to see if we can make these in my third grade classroom for the kindergarten mentors we work with! Making them will mean that they’ll need to use their multiplication skills to make the quilt.

This is a great after school play activity!

January 4, 2014January 4, 2014 by Beyond Traditional Math

Inquiry Learning: YES!

A little while back I wrote about letting students discover math patterns and connections on their own. Inquiry learning truly does help students do the majority of the learning.

Well, check out this blogger from The Research Based Classroom. I love her post this morning citing Piaget:

“Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely.” Piaget

Right on Brandi!

How do you all help your students discover concepts on their own?

January 2, 2014January 4, 2014 by Beyond Traditional Math

Transform Problem Solving: Push Them to Explain Their Thinking in One Simple Step

A few weeks ago it was time for our daily problem solving block in math class, and I looked over a few shoulders to find the most aggravating thing. The answers written (sometimes incorrectly) with nothing else.

So here was the problem (from Practice Problems for Multiplication and Division):

Jessie bakes cupcakes for her local business. Six orders were called in on the phone. Each order included a half dozen cupcakes. How many cupcakes should she make?

Young learners are notorious for answering math problems like this:

That’s it. Granted it is the correct answer, but no explanation of their thinking or their strategy. SO aggravating for a teacher who is constantly pushing for students to explain their reasoning. SO not in line with the math practice standards and what they are pushing students to do.

So I implemented a little game to help transform problem solving, specifically targeting how they are explaining their thinking. This poster is up hanging on my chalkboard:

Here is how the “game” works:

1. A student rolls the dice.

2. Whatever we land on is the preferred method of communication for the day. The students must try to explain their strategy on their papers using:

words to describe the steps taken to solve the problem, including how you arrived at the answer.
a picture or a model of the problem.
a number sentence to show how the problem was solved.
tools (manipulatives) to act out the problem. We typically gather around a desk (each student has their own bag of tools) to see how they solved it.
FREE choice means just that, they can use their favorite way to solve the problem (maybe some other creative strategy beyond any of these four).
Teacher’s choice. This is kind of awesome because I can ask them to use number lines, graphs, skip counting or some other type of strategy that is appropriate to the problem type.

3. The same student reads the problem out loud to the class (twice).

4. The students solve the problem on their paper as many ways as they can (choosing their best way first), but when they explain it they should try to use the method of communication that was rolled.

5. Two students are asked to come up to the board to show how they solved the problem, and explain their thinking. At least one of the students must have used the method of communication that was rolled.

Since I’ve started to use this, students have gotten better at showing their work, which in turn has made them better at explaining their thinking verbally. It also leads to awesome questions asked of the students who come up to explain their strategy.

Here is what that same problem looked like after we rolled the dice and asked that same student to use the strategy of a model/picture:

Additionally, the other student who came up used a number sentence.

Both great strategies! I love that it encourages the use of different ways to explain, especially when some students get in a rut by only one strategy or one way to explain. It has also been a big help to students who have trouble putting their picture into number sentences.

The best part? The kids think it’s like they are playing the lottery every day.

January 1, 2014January 1, 2014 by Beyond Traditional Math

Math In Real Life: I Am The Worst Party Planner

So I am the worst, and I mean the WORST at estimating party needs. In the past I have ordered pizza for my classroom and ended up with 6 extra pizzas. Part of the problem is that I’m not very good at estimation (including how much less pizza an average third grader will eat compared to myself), but also I rarely practice this skill.

This year for our holiday party, it COMPLETELY slipped my mind to ask parents to volunteer to bring snacks, napkins, drinks, etc…somehow the day of the party was only 2 days away and I was in a bind. As we all know, no one has tons of cash to throw around for holiday parties anyway.

So I was determined to NOT screw this one up. I was going to go in to the grocery store with a calculator, the number of students in my class, and a tight budget. I felt good about this trip, I knew that it would be easier because I was calculating 1 candy cane per student, a handful of pretzels per student and 1 capri sun per student. I even found some napkins…on sale!

So get this! After the party I ended up with 2 leftover candy canes, 4 extra capri suns and a stack of napkins.

Why I have been historically terrible at this is sort of a mystery to me. It’s not like it is complex math, rather it involves using simple math in a complex way. This was not how I was taught math growing up, so I have to actually practice this to get better at it! It is why I created the Party Planning Awesomeness Project for my students. It is the reason that I create all of the things I do, because I feel that students really do need to be able to practice these skills.

Check it out! We actually did this prior to our last math test, with a class goal. If we got 94% as a whole class average, we’d earn the party that the students voted for. And…they did it! I now have another party to shop for, but this time the student did all the math!

Thanks to these ladies: 4mulaFun, Fourth Grade Studio, Teaching to Inspire in 5th, AND MissMathDork for the opportunity to link up! Apparently this is a monthly thing that they do, being new to blogging for only a few months, I had no clue how awesome this is.

Beyond Traditional Math

Fostering conceptual understanding with real world connections.

Tag / problem solving