Tag / education

by Beyond Traditional Math

Data Doesn’t Have To Be Overwhelming!

The idea of collecting data has really been getting a bad rap lately. Have you heard these comments (or comments like these) in your building?

  • “We are drowning in data!”
  • “All we do is test our kids.”
  • “I feel like our kids are just numbers, like we are ignoring that they are PEOPLE.”
  • “We collect all this data, then we have no time to analyze it and use it.”
  • “I don’t have time to enter in all this data.”

I think we’ve probably all heard some version of this at some time or another. Some of these comments might actually be true in some districts. I’ve heard horror stories about schools that are doing so much test prep, that they really aren’t finding time to intervene and help their students when they struggle. I feel lucky to work in a district that believes firmly that our data should drive instruction, and if it doesn’t, we shouldn’t collect it.

I had an amazing moment about 5 minutes ago. (Yes, I was working on a Saturday night, not totally uncommon around here!) I was looking at some problem solving we did for report card purposes/parent teacher conferences (THAT explains why I’m working on a Saturday night), and I noticed something amazing.

I use multiplication and division word problems in my classroom about 3 days out of the week. I am a firm believer that students need simple problems to try out before diving into difficult and complex ones. I use Practice Problems for Multiplication and Division because according to the Common Core these students must have multiplication and division mastered by the end of grade 3.  There are also 9 word problem types that are broken down in the common core for students to master in grade 3 so why not teach these things together?

Instead of just diving in and giving everyone all the problems in the entire booklet, I first assess each student on each problem type by giving them the first one. Then, I set up a spreadsheet to look at my results.  I noticed that my class was really struggling with the Type 2 problem, only 8 students got this problem correct. (I score this according to a standards based grading scale, it could also be scored pass/fail.)

My chart:

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So we practiced this problem type. We tried this type of problem five times, each time giving students a chance to come up to the chalkboard to explain their thinking.  Awesome strategies were shared, and students asked many questions to see how they solved it.

The student on the left has pretty good knowledge of multiplication, while the student on the right is just beginning. Both strategies are successful.

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Now we fast forward to tonight.  For parent teacher conferences, I decided I wanted a sample problem solving exemplar to show to parents (it also made sense to have the latest info for report cards!). Naturally I choose this same problem type, since we’ve worked so hard on it. I just finished scoring them, and noticed that 21 out of 25 students got it right this time! I started yelling to my husband (who probably thought I was crazy) that I was so proud and excited for my students.

It really DOES work.  Using data to target instruction is a much more focused way of going about planning instruction.  I haven’t wasted any time on problems that students already knew, and now I know exactly who needs a little intervention work with me! The best part is, this entire process was so simple.  (Instructions are included in the Practice Problems for Multiplication and Division resource. You could also set this up with your own problem types!)

I can’t wait to share this awesome news with my class. I am hoping celebrating our success will motivate them to continue to work hard.

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by Beyond Traditional Math

When Differentiation Feels Impossible

I know that differentiation is SO important.  I know it is the right thing to do. But sometimes it is SO difficult to make sure I am meeting the needs of all learners.

Right now we’re plugging away with the concept of regrouping when adding 3 digit numbers.

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There is a group of 6 students in my class who’ve gone BEYOND mastering that concept. I know that I can’t spend an extra day with their bored faces staring up at me.  I just can’t take it, and I know in my heart it isn’t right to continue whole group teaching when they need the support of a higher level thinking challenge.

So…meet Open Ended Problems! I’ve used them before when students have mastered content, these problems get them thinking and are REALLY challenging and complex. Great, right?

Well today something went wrong. In a perfect world, I’m instructing the students who are struggling with adding/regrouping as a whole group, while the other students are working on the open ended challenge at their desk. That didn’t happen today. The students who were struggling with adding/regrouping were frustrated…and the students working with the open ended challenges were frustrated. Everyone in the room at some point had red cheeks, tears in their eyes at times, scrunched up faces, and a general lack of unease.

Why the frustration?  What was happening?! I realized that while I was working with my group, we were being interrupted by the students who were working on the open ended challenges.  They weren’t coming up all at once, rather, they were coming up one at a time, every minute or so, interrupting the thought process of the group. They weren’t interrupting to be rude, they simply ran into a problem while they were working, and came to ask me what to do.

That was when it hit me that we are sorely lacking in the Math Practice Standard 1: I can make sense of problems and persevere in solving them.

Instead of making sense of the problem, those 6 student’s first course of action were to come straight to the teacher. Not used to feeling challenged, they were “stuck” because they are used to answers coming quickly.  They weren’t used to having to read the problem more than once, and didn’t even realize that their questions that they asked were answered RIGHT in the problem they hand in their hands.

After about 5 minutes of these interruptions, I explained to the group of students working on the challenges that they would be meeting with me in 15 minutes.  Once they knew this was coming, the tension in the room released. ALL of the students began to breathe and feel more comfortable.  That simple gesture of letting them know that they’d get their time with me was the solution.  The students in front of me relaxed, the students at their desks relaxed and we were able to go on with our work. By the time I got to that group of 6 students, most of them had figured out the answers to the questions they had!

Sometimes, differentiation feels impossible. It is difficult, but it is RIGHT.  Everyone in the room had a challenging task, and that is how it should be.  Now, I’ve just got to reteach and work on my expectations and routines for small group work.

Differentiation looks different in all subject areas, but I find it to be the MOST challenging during math.  How do you differentiate and hold students accountable? Do you do centers, or a math workshop style? I would love to hear suggestions, comments, questions and more!  The more we share the more we learn.

by Beyond Traditional Math

Problem Solvers Aren’t Born, They Are MADE

My first year of teaching, I was the queen of teaching problem solving. I would stand up in front of my students each day, and show them my beautiful strategies for solving the problems. Over and over, they would see my drawings, my number sentences and my solutions. I would ask them to copy them down if they couldn’t figure it out, so that they would have an idea for the next time. As I’d look at my data, I would notice that I had a top group of problem solvers who could always solve it, a big group of solvers that would typically get the problem correct, and a group at the bottom that would NEVER get the problem right.

I was foolish enough to believe that this was okay. I thought that some kids just weren’t very good at problem solving. I was SO wrong, and I am SO embarrassed to admit this now.

My second year of teaching, I heard this quote: “The person doing the talking is the person doing the learning.” I honestly felt sick to my stomach, because I realized that I was doing WAY too much of the solving, working and showing. I needed my students to take ownership, stand up, share their thinking in kid speak and start to GROW. I learned a lot that year, that students aren’t born to problem solve. It is something that requires an immense amount of practice.

I’ve come a long way since then, and would like to describe what I have done to be SURE that all of my students are getting this problem solving thing down before they leave my classroom. First of all, we take TWENTY minutes per day, every day to practice problem solving. This is something that is a priority during my math block. Then, I follow the steps below (UGH, I realize this looks like a TpT commercial, and I don’t mean it to be! You can do all of these things with your own resources.):

1.  I assess what problem types the students can solve. Did you know that there are 9 problem types for multiplication and division in the common core?  I use a series of multiplication and division problems, administering the first in the set to see how they do on each of the 9 problem types.  I compile the results in a data table to see which ones the class struggles with as a whole.  Then, we attack those problems one by one throughout the school year. I assess them again at the end with the last problem in the set to measure growth.

2.  I introduce the Standards for Mathematical Practice. These standards are SO important for students to develop as math habits.  They cannot be stressed enough. It takes us about a week and a half to get through them all, but it is worth the time. I post our work daily on the wall. The vocabulary from these standards becomes a part of our every day language.

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3.  I start small, with practice problems that are simple that they can relate to. Then, we go BIG.  I have three types of problems that I use juggle through and use.

Simple Problems:  There are so many problems out there about trains arriving and leaving on time, or other topics that students cannot connect to.  I finally broke down and created problems over the years that would allow for practice of multiplication and division concepts. The problems are about things that students can understand. These are done on most days, with other problem types sprinkled in from my current math series.  These simple problems are NOT done every day.  That is not enough for students to become strong problem solvers.

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Open Ended Problems: These problems require more reading, more steps and are much more complex. There are times that these problems require two 20 minute class periods to complete. These are the types of problems we will find on the Smarter Balanced Assessment next year.

Here is an example of an open ended problem:

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Project Problems: These are always my student’s favorite type of problem.  They spend several days on these problems and are a bit more out of the box. I always begin with the Book Order Proposal and go from there.

Book Order Proposal (Free to try out!)
Housing Market Analysis
Mini Golf Course Geometry
Party Planning Awesomeness
The Wind Powered Car
Elementary Architects

4.  I make manipulatives available to them from the start, and I encourage their use.  The idea that hands on problem solving is for young students only, or for struggling problem solvers is incorrect.  Manipulatives are wonderful for any level of problem solver, it promotes deep thinking of the math concept you are working on.

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5.  I allow students to model their thinking in front of the class.  More about how I do this you can find in this post. They solve it, explain it to the class and accept questions and compliments from the rest of the students.  This is where the students do the talking, the questioning, the complimenting. They are seeing multiple strategies each day, they can “steal” ideas from each other and are held accountable for their work.  I keep a tally chart right on the chalkboard so that students can see how many times everyone has been up. We try to make it equal, even though problem solving comes more naturally to some than others. This helps everyone know that they are ALL welcome up to the board, even if their solution is wrong.

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6.  I intentionally plan out which problems to do and when.  I carefully monitor my students to be sure we are using our time effectively. I watch to see how we do as a class as we solve the problems.  When the majority of the class is getting the problem type, I’ll switch to a similar problem type that requires a tiny adjustment in their thinking. I always incorporate a problem from the book that has to do with the concept we are studying from time to time as well. A two week plan might look like this (and it is always flexible):

  • Day 1: Equal Groups (Unknown Product)
  • Day 2: Problem from math series covering current concept.
  • Day 3: Equal Groups (Unknown Product)
  • Day 4: Equal Groups (Number of Groups Unknown)
  • Day 5: Problem from math series covering current concept.
  • Day 6: Equal Groups (Number of Groups Unknown)
  • Day 7: Equal Groups (Number of Groups Unknown)
  • Day 8: Equal Groups (Unknown Product)
  • Day 9: Open Ended Problem – Day 1 of 2 (complex, many steps)
  • Day 10: Open Ended Problem – Day 2 of 2 (complex, many steps)

7.  I keep accurate records for myself. I have a class list so that I can see when students are getting the problem correct.  I keep the problem as our daily focus until 90-95% of the class has mastered it.  I have an answer key that allows me to check off when we’ve done the practice problems so that I don’t accidentally repeat the same problem.

8.  I intervene with students when the problem type is a struggle.  I pull small groups during our math work time, in the morning when students come in, during recess, during our intervention block time, whenever I can to get those students up to speed.  Many times they just need more one on one support to be successful.  I don’t wait any more for them to figure it out on their own. I intervene as soon as I notice the struggles.

It sounds like a lot, but once we get in the groove, and routines are in place things get ROCKING!  I didn’t realize how much students love this process until we had a substitute teacher in for a day.  The teacher worked the problem out on the board much to the anger of my students! The next day, they were SO fired up and upset that she didn’t give them time to work it out on their own.  That is when I knew that the students in my classroom were finally owning their own learning.

by Beyond Traditional Math

Just Make it Real World

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I am not sure if you’ve ever had that “moment”.  The moment where you are at a frustration level with why things aren’t working. I used to look for extra worksheets to give more time for tricky math concepts to “stick” with students. I looked online for further practice activities, I asked colleagues for their extra resources for more practice, I looked for games. I felt like I’d tried everything.  That’s when I read some research that making math real world, connecting it to student’s lives was REALLY good practice.  So a few years ago I started to create real world problem solving projects to help this problem.

That was how the Book Order Proposal project started (for my gifted and talented students I’ve used The Housing Market Analysis). I knew that I needed to continually reinforce the concept of rounding/estimation, comparing numbers, and mental math addition strategies. I gave my students the chance to do just that by offering to buy books for our classroom library. I decided to coincide this project with my parent Scholastic Book Club order.  Here is how it worked:

  • I made it my problem of the day for 4 consecutive days, giving 20 minutes each day for the project.  The first three were days for them to work (with a mini lesson or two if needed), and the fourth day was the peer review day.
  • All students were given a budget of $50 (bonus points offset this cost-I was able to get all of our books free this last round) to look through three Scholastic flyers.
  • The students had to put together a proposal, thinking about their classmate’s reading interests, as well as thinking of what we currently have in our classroom library.

What happened was kind of interesting. The majority of the students got within $2 of the $50 budget.  A few of the students tried to hand in proposals that were $1, $30 or $25.  When we talked as a class on the second day, I asked my students if it was okay if someone didn’t get close to $50.  The resounding answer was “NO!”.  When asked why, they explained that it would be a waste of money if they didn’t spend it all, especially since they would become THEIR books for their classroom.  I handed back those few papers and asked them to start again. (Now that is what we call peer accountability!)

At the end of the project we laid the papers out and did a gallery walk. Students voted on their top 3 favorite proposals. The proposal with the most votes actually got ordered!  It was such a fantastic way to end the project.

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My favorite part though, the very best part of the entire project, was the gallery walk and natural reflection. Students could see how others choose to put the proposals together. Some were neat and organized, others were missing information, some of them had a hard time with their handwriting, and other student’s numbers didn’t quite add up.  It led to great discussion, and the students wrote goals on their proposals for the next time we have to present information to our peers.

It has been clear to me that making math real world, and connecting it to their own lives is a powerful thing!

by Beyond Traditional Math

Manipulatives Aren’t Just for Kindergarteners

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In our classroom we’ve been working through the math practice standards. We just finished number 5 today: Use appropriate tools strategically. Last year I researched the math practice standards, re-wrote them to be kid friendly, and turned them into learning targets.

I can use the right tool for math, and explain why I chose it. 

We talked about the kinds of tools that mathematicians use, and they came up with a healthy list. After that, I read the problem, made sure to show them where to find the manipulatives, and turned them loose to work. I thought this math practice standard would be a breeze!

Some of the tools I put out:

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In the past I’ve always offered the appropriate math tool for them, taught them how to use it and that was that.  This is the first time I’ve ever asked THEM to choose a math tool from a bunch of options.

I learned today that math tools are much more complex than I expected. The result of today’s lesson was a total surprise.  (I LOVE that even after 8 years of teaching I can still be surprised.)  Every student in the room was comfortable with using the manipulatives, but only about 5 out of 25 were using them effectively.  Rather than thinking about what tool might help them solve the problem, many of them chose tools based on their shapes.  For example, the problem was about cookies, so they picked the fake money manipulatives because they were round and they could trace “cookies” on their paper.  They were using a math tool (clearly not the right one), they could explain why they were using it, but their use of it was not exactly accurate for the problem type.

I took this moment to reflect and think about how I can incorporate math tool use more intentionally. I think that there are many tools appropriate for third grade. I used to think that math manipulatives were just for kindergartners or the early primary grades, but I have realized quickly today that their complexity is vast and allows for deep thinking.  I am excited for the challenge of exploring each tool’s unique properties!

by Beyond Traditional Math

3 Step Process to Strengthen Problem Solving in the Elementary Classroom

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Problem solving seems to be an issue time and time again every year in my classroom.  When the math practice standards came out, I thought that they paired nicely with problem solving. These standards are deep thinking math habits that students can try to develop for all areas of math, but I noticed specifically how they were helping my students problem solve. I developed a way to introduce these standards in the beginning of the year as a way to start up my math workshop. There are 3 components to how I do this.  It takes 20-25 minutes per day of my math workshop for this process for my third graders. That means I can introduce all of the math practice standards in about a week and a half.

1.  Students solve a problem and model their strategy for the other students:

The photo above is a screenshot of my SMARTBoard today from the Guide to Introducing Math Practice Standards.  We’ve been introducing the math practice standards each day during math by working out a problem that is related to the standard.  I am a firm believer that students can become better problem solvers by seeing each other’s strategies and by describing their thinking. Every day when we work out a problem I choose two people to go up to my chalkboard, and one person to go up to the SMARTBoard. They write their strategy out for others to show how they solved it.  While students show their strategy, and explain their thinking to their classmates…I start to see the lightbulb go on for those students that day who did not understand the problem.

2.  Allow the students in the “audience” to interact with the students who are modeling:

I allow the students who did not get to go up to the board to ask questions and give compliments using the math practice standards in their language.

Today was an awesome example of that happening! After they explained their thinking the students complimented the people at the board for not giving up, noticed how the young man underlined the question to the problem, asked how they knew to multiply instead of divide…it was just beautiful. The math dialogue flying around the room was amazing.  It gives confidence to the students in the spotlight, and clarifies the problem for the people at their desks.

3. Close the lesson by asking the students to rate themselves on their problem solving for the day:

As an example, I closed the lesson today by asking the students to rate themselves using Marzano’s Levels of Understanding. We hung up the math practice standard poster with a student’s sample paper.  We talked about how we can continue to use that standard every day, and as if on cue one student shouted “especially the part about not giving up!”  If anyone had a less than 3 rating, we talked about what we could try next time.

Seeing how far the students come from the first week of school to the end of the year is very motivating for us all!

by Beyond Traditional Math

You Hate Math? Let’s Fix That

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It never ceases to amaze me on open house night, when a third grader comes in and tells me that they hate math.  It is heartbreaking, really.  How can someone so young, come to hate math already?!  

I start to wonder…

  • Maybe their parents talk about how they were always “bad at math”.
  • Does math make sense to them, or is it still very abstract?
  • Have they been worksheet/workbook-ed to death?
  • Does learning math happen a little slower than other subjects for this student? (Which is totally OK by the way!)

It hurts me a little when kids feel this obsessive need to compare and rank subjects. To be fair adults constantly ask students what their favorite subject is. I think it’s great to find out what our students enjoy the most, but can they really dislike a subject SO much (use the word “hate” even) by the age of 9? 

I welcome students like this to my classroom. I try to discover all of my student’s attitudes about math right from the start. Then we dig in.  We’re going to make math fun, engaging and REAL.  We are going to get messy with math, we’ll feel frustrated at times, and even if it kills me we’re going to leave this school year feeling a bit better about math.

 

by Beyond Traditional Math

Don’t Be Scared of Those Math Practice Standards!

Don't Be Scared of Those Math Practice Standards!

I will never forget my first reaction when I read through the Standards for Mathematical Practice.

Huh?

I think it took me another 5 reads to even scratch the surface of what they meant. The rest of the common core seemed like a piece of cake in comparison!

I really tried hard to understand them, but truth be told, I wasn’t sure how they fit in to my classroom. How were elementary students supposed to understand this stuff when I barely could?

As we began to implement the common core, I noticed my students struggling with the deeper problem solving concepts. I was so frustrated. I tried everything…I looked for strategies online to see if there was some kind of magic answer, I asked colleagues what they had tried and began to pull my hair out.

That was when it dawned on me…why don’t I try to incorporate the Standards for Mathematical Practice?  So I dug deep and did some research. One of my favorite things I found is from our friend Marilyn Burns (if you don’t know who this is, get to know her!). Her site is amazing, and the video series is really great.

All of the research allowed me to create a guide to introducing the standards for my students. I started with putting them into kid friendly I can statements. I added some sample problems and allowed the students to see each other’s work habits.

Voila! It was like a revolution was born. One of my students had the idea that we should post the standards on the wall, and get a point every time we had a question or gave a compliment with the language of the standard in our comment. Done! We had points like you wouldn’t believe by the end of the school year. (Incidentally the points counted toward absolutely nothing, they were just points for the sake of getting points!)

Intentionally putting the language of these math practices in our every day commentary did the trick. Students gained confidence, it was fun and best of all problem solving was no longer a stress in our classroom.

by Beyond Traditional Math

Winner! Winner! Winner!

Congratulations to 4th grade teacher Jen Jones on winning my Back to School contest. She chose the following products from my store for FREE!

Mini Golf Course Geometry
Housing Market Analysis
Open Ended Word Problems 

Thanks to all for the follows.  If you have a blog that you’d like me to feature or publicize, please contact me so we can all learn together!

by Beyond Traditional Math

Anchor Charts = Google for Kids

Anchor Charts = Google for Kids

If I were to count how many times I use my Smart Phone to look something up every day, it would be at least a dozen…maybe more! I use it to find out random facts, convert numbers, convert languages, remind myself of an interesting article I read 3 months ago…I could go on and on.

Anchor charts are truly “Google” for our students. I’ve seen it time and time again. The students are sitting at their desk, drawing out something for their latest project. When they can’t remember what an equilateral triangle is they simply look on the wall where the lesson they just learned about (but haven’t memorized yet) is hanging nicely there. Whenever I have massive amounts of students coming up to me to ask me what something is, it never fails, I’ve forgotten to hang the anchor chart.

So hang those anchor charts! Give them the tools they need so that they can use and remember these important concepts.