Changing Our Thinking: Access to Math Manipulatives

Changing Our Thinking: Access to Math Manipulatives

There are many practices from long ago that we need to rethink as teachers. This series looks to bring up those practices and offer alternate ideas that are more relevant in today’s classroom. Today we’re discussing where and how we store our math manipulatives. 

WHat We've Always Done

When I was in elementary school math manipulatives magically appeared when we needed them. Oh, today we’re measuring things? Well, look at that! The rulers have made their way to the front table. Oh, we need a calculator for today? Look what has appeared out of nowhere! Teachers controlled the manipulatives. They pulled manipulatives out of the cabinet and then put it back. I assume this is because of storage space. Let’s face it. We don’t all have a lot of room in our classroom. The idea that I have to have room for an entire classroom library plus my math manipulatives is a lot of space. We don’t always have a lot of space… or the organizational storage we need. 

What's the Problem?

If students don’t have access to math manipulatives then they don’t have any choice. Natasha! Do kids really need choice about math manipulatives? YES! The answer is alway yes! In a teacher centered classroom it makes sense that the teacher is the only one who can access the math tools. She gives the kids the rulers when they need a ruler. They get to use base ten blocks when it is time to learn about place value. The tools are controlled by the teacher and are handed out when the teacher deems them necessary to use. Students don’t get to explore them and they don’t have very many options. Each tool has just one use that is predetermined by the teacher. We limit student’s use of manipulatives and we limit their creativity with them. 

What to do Instead

First and foremost in most elementary classrooms there is a space for a classroom library. There should also be a space for math manipulatives. Take a minute or two to look around and analyze how you’re using your space. What do you have that could make your math manipulatives more accessible to students? Maybe you don’t have ideal storage right now, that’s ok! Even making them the slightest more available to students is a start. Once you establish a space and a storage system for math manipulatives teach your students about your space. Tell them they can use any math tool during math time. Teach them how to use all of the different tools you have available. Let them explore and give them choice. 

Instruction today should focus on independence. What skills can children complete independent from an adult? This is how you truly know what your students know. If you are constantly giving students math manipulatives you take away their choice and their independence. Once students are familiar with all of the manipulatives available to them they are able to choose which tool will work best for them. Some of my kids use rekenreks while some use 10-frames. I ensure that my students know how to use all tools but they have the freedom to choose which ones they use. 

Here is the cool thing about giving kids the power to choose math manipulatives themselves, kids use tools in unconventional ways that you might not have considered. Last year during recess one of my diamonds made up her own math game with a 100 bead string and two dice. She would roll the dice, add them up and then move the beads along the string. If you played with a partner the first person to 100 won! Later in the year a different student used a 10-frame as a measuring tool. They measured how many 10-frames long our carpet was. If I had told them we were only measuring (grade 1 uses non-standard measurement) using measurement tools this student would have missed out. It is always cool to see how students use their tools. 

Share Your Thoughts

Do you allow students access to the math manipulatives in your classroom?

How do you have your tools organized? 

Any other comments or suggestions? Let me know down in the comments below! 

Weekly Wisdom

Weekly Wisdom


The culture of math classrooms is rapidly changing to become more inclusive. The days of math classrooms revolving around the students who understand while letting the students who don’t understand get left behind are fading into the past. THANK GOODNESS! When I was a kid usually Kevin was the only student called on in math class. Kevin was a kid who got answers in math very quickly and always correctly. Kevin was working to complete 90 math problems on a time test in 60 seconds while I couldn’t even solve them all in 3 minutes. The days of only teaching Kevin while the rest of the class strung along are dwindling!

When kids see answer getting as the way math is done they not only miss out on the connections and the value of knowing how answers are formed but they also start to count themselves out of the game. Kids who can’t get answers quickly begin to not identify as a “math person.” On this topic, enough with this I’m not a math person mentality. Once I knew a teacher who referred to herself as a not mathy math teacher. What sort of message is this sending to students? Anyways… I’ve seen kids as young as kindergarten begin to count themselves out of the math game. That is not ok. Math is so much more than arriving at answers quickly. Please listen to Phil Daro’s Answer Getting in Math for further information against an answer-getting mindset.

How are you working to shift the culture of mathematics within your classroom? Let me know in the comments below!

Changing Our Thinking: Alligators in Math Class

Changing Our Thinking: Alligators in Math Class

There are many practices from long ago that we need to rethink as teachers. This series looks to bring up those practices and offer alternate ideas that are more relevant in today’s classroom. Today we’re discussing using alligators eating bigger numbers to teach comparison.

 

The time has come in my class to begin comparing numbers using > and < but guess what? We’re not using alligators or crocodiles and there are no numbers are being eaten. Instead, the symbols are being taught in a way that students can understand. We’re using language to teach the symbols and trust me, it really isn’t too hard!

Why Alligators and Crocodiles?

As teachers we love doing things that are cute. Trust me, I love using cute things with my kids. Its fun, it makes the learning fun and it engages the kids. Cute teaching resources can come in handy. When comparing numbers it can be hard for kids to understand. Especially when we are using symbols that kids haven’t seen and symbols that look very similar.  So we did what we do best as teachers and we made up a cute story for kids to remember. The alligator eats the bigger number. It seems simple enough. The kids can get the answer and they can solve problems comparing numbers. But what if our cute teaching resources are undermining students’ understanding? Maybe not even at our grade level but at grade levels higher than us. 

What's The Problem?

When we tell kids to draw the symbol with the alligator eating the bigger number, we are only focusing on which one is larger. Every time the child draws the symbol in their head their thinking, “12 is bigger so the alligator eats the twelve” while writing 9 < 12. You’ll notice that the symbol drawn was less than but in the child’s mind they were focused on which one was greatest. Many of my students who learned the “alligator trick” will read this as 12 is greater than 9. While not incorrect, 12 is greater than 9, this should read 9 is less than 12. This is very confusing. Yes the answers are correct because they know how to draw the symbol but there is virtually no understanding of the symbol. Most kids don’t even realize that there are two different symbols!

Build Understanding

This year we began saying the words “is the same as” when we saw an equal symbol. Why not just use the word equal? Too often students understand the equal sign to mean the answer is coming next. That isn’t what the symbol means. 

The = symbol means that what is on the left is the same as what is on the right. 

Just shifting our language within the math classroom helped students gain a better understanding of the equal sign. According to the Common Core State Standards students in grade 1 should under the meaning of the equal sign. (1.OA.D.7) How many upper level students don’t realize that the symbol means that the expression on either side is equal, or the same?

We also switched up our equations so that sometimes there were answers that didn’t come after the equal sign. The equations we showed the students had the equal symbol all over from the very beginning of grade 1. Blanks were in different spots and answers were in different spots and the equal sign moved all around. This helps the kids see that equal really means the side on the left is the same as the side on the left.

This work ties in with the mathematical practice standard 6- attend to precision. Attending to precision doesn’t only mean paying attention to the problem and solving it accurately. It also is  using precise language when we talk about math. I highly recommend reading this Think Math! article about this standard. 

Use Language First

When it came time to compare two numbers this year we created three sentence strips.  We have already been using the phrase, “is the same as,” so it was not new to students. Once they had these three sentence strips, I had them build two numbers and choose which strip went in the middle. I reminded them that just like readers, mathematicians read left to right. 

To my surprise and joy they were able to start comparing numbers accurately from the very start. Some of my most struggling mathematicians found success in using the sentence strips. I was very excited to see where this was going to go. They were not only able to compare two numbers but they were also able to use the correct language while doing so! This is just what we want our kids to do! 

As we finished math class on this day, one of my students asked if he could guess what was coming next. Of course! He whispered, “I know there are symbols that go with these words. Is that what the blank space at the start of our sentence strips is for? Are we going to get to use the symbols?” 

Isn’t it a magical moment when kids predict where their learning is going and they are excited about it? Guess what, we were going to learn about the symbols next!

Then Teach Symbols... Relying on the language

After using the sentence strips to build our understanding of the language we use to compare two numbers we introduced the symbols to the class. You’ll notice that I put the symbols on post-it notes. This was done as a scaffold in case students need the symbols removed in order to practice longer without them. 

Before putting the symbols were in place, we had an understanding that in math we use symbols to represent certain words. They already knew the symbol = went with the words “is the same as” so adding two new symbols wasn’t to tricky. 

To introduce the symbols I wrote them on post its and placed them on my sentences strips. Then the class did the same. As they were drawing the symbols on to their post it notes I could hear a small buzz of observations. Many kids noticed that the symbol opens to the side that is greater and is closed on the side that is less. This isn’t a bad realization to have but it wasn’t their only knowledge of the symbols and how they work. 

As we compared numbers that day I noticed most students relying on the language and then matching the symbol with the language. They would look at a problem like 82 __ 45 and say “eighty two is greater than 45. Then they would get their sentences strips and match the strip to the problem. Finally writing the symbol on the line. 

 

What I've Learned

This is my first year as a grade 1 teacher. In the past I have taught second and third grade and my students have already come to me with the alligator story. Once you learn a trick it is hard to ever go back to reasoning. I wasn’t sure how this approach was going to go when I introduced it to my students. In fact, I waited a long time to even complete this post to see if this method of teaching symbols really even worked. Let me tell you, it did! Right now almost all of my students can compare two numbers using the symbols on their own. They now know which one means greater than and which one means less than. We still have our sentence strips to use in case we need them but the kids have eased themselves off of that scaffolding. 

 

One Last Word About Tricks

As a former Math Curriculum Leader I have a lot to say about tricks in math. So often we teach kids tricks because we think that the math is difficult and we want to make it easier. Or we learned with a trick and we really aren’t sure about the real math behind it. Math is built on reasoning. If you are able to connect knowledge and reason through a problem you can more than likely solve it. When we teach kids tricks oftentimes it eliminates reasoning. When we take away this reasoning we are limiting our students’ math potential. Mathematicians rely on reasoning more than anything else.

Next time you go to teach a math trick in your classroom can you ask yourself these questions?

-What mathematical properties does this trick rely on? If the trick doesn’t rely on any math but more of magic then it isn’t really teaching math at all.

-Is the mathematical reasoning eliminated through this trick? Math is built around reasoning and we don’t want to take this away from students. They don’t really have the right answer if they can’t reason through a justification.

-Is this trick just getting the right answer? Math is so much more than answer getting. Please check out Phil Daro on Answer Getting

 

Changing Our Thinking: Stop Waiting For All The Kids

Changing Our Thinking: Stop Waiting For All The Kids


There are many practices from long ago that we need to rethink as teachers. This series looks to bring up those practices and offer alternate ideas that are more relevant in today’s classroom. Today we’re discussing waiting for all kids to be finished.

Why we wait

As teachers, we spend a lot of time waiting. We wait for our whole class to line up before taking them to specials. We wait for the whole class to sit on the carpet before beginning a lesson. We wait for all kids to finish eating snack before we move on. We wait patiently for all partners to finish before we bring the class back together. We wait for so many things and we wait for many reasons. One reason is so that all students feel like they had enough time to finish what they were doing or saying. We also wait so that we don’t have to repeat directions over and over again. We wait so that all kids are ready. But when we wait it starts to cause issues even if we don’t notice them right away.

What happens when we wait

When we always wait for kids we create a culture of waiting in the classroom. Kids know that we are going to wait for all kids to get to the carpet so they take their time. When they know that we are going to wait there is less of a sense of urgency. Kids losing their sense of urgency is one the worst things that can happen in your classroom. It happened in mine last year and I thought I was going to lose my mind.

Another teacher would take my students to specials every day. Every day I would leave my classroom at this time to avoid being in the classroom for the chaos that was created by waiting. Natasha, why didn’t you stay and help? I will admit that I tried but this teacher was so convinced that we needed to wait for all students to be ready before leaving that I could do nothing. Within a few days, I found kids slowly dragging themselves to the carpet. They came slow as can be to reading groups. They moved at a snail’s pace because their time was never respected. Their on-time behavior was never rewarded. They saw no reason to do things quickly and on time because they would always have to wait for someone else.

This teacher once waited for 16 minutes before leaving. SIXTEEN! Kids can’t lose 16 minutes of instruction time! Ain’t nobody got time for that! Repeating yourself over and over doesn’t help the kids. You might think the longer you wait the more kids will be ready. WRONG! I can tell you from experience, the longer you wait the fewer kids are ready! Threatening with empty threats also does nothing. Do you know what does do something? What motivates those friends to get a move on? Leaving them behind and making them catch up. Creating a sense of urgency deep inside their little hearts.

Urgency in the Classroom

Teachers would all pretty much agree that there aren’t enough hours in the school day to accomplish the job we have been tasked to do. Every moment my students are with me is a precious moment for teaching. We don’t have any minutes to lose! If you visit my classroom you’ll find that I frequently send kids off using the phrase “Hurry! We have no time to lose!” Soon kids start using this phrase to others and our class has a sense of urgency. My kids know (because I tell them over and over) that we don’t waste time on things that aren’t important. If we are doing something it is one of the most important things in the world. Kids know that they will be left behind if they don’t hop in line for library. Kids know that when I say turn and talk they have to start talking immediately or they won’t get their chance. They know that snack is over we go to specials and we leave kids behind.

Waiting is your frienemy

Waiting might seem tempting. It might seem like you want to wait for the class to be ready. Guess what? Waiting is your frenemy. It isn’t your friend. It doesn’t have your best interests at heart. It is going to suck you in and tear you down. In the past, we’ve rationalized waiting with things like:
Kids will feel left out if we leave them behind.
Kids need to finish what they’re saying in a turn and talk.
We don’t want them to feel rushed.

While each of these statements does carry some truth, kids don’t feel these things when we teach with a sense of urgency. Maybe kids feel left out the first time they get left behind as the class walks to PE. The next time the class leaves that child will be right in line with everyone. Kids who have too much time for a turn and talk lose focus and get bored. If they know they only have a small moment they have to share quickly and there is no time for being off task. We don’t want to create anxiety in kids by teaching with urgency but instead show them that we have no precious moments of learning to waste. None.

Students in my class understand that their time won’t be wasted. Due to this, we are able to follow directions immediately. We have a collective understanding that every moment we are together is a good moment for learning. What we’re doing in the classroom matters and we won’t waste time for kids who aren’t with us.

Changing Our Thinking

I hope this small shift in thinking is helpful in your classroom tomorrow. Try it out. Don’t wait for all of your kids. Of course, you will be met with some complaints but soon your kids will be following your directions right away instead of in a few minutes.

Leave a comment below about your shift in thinking, any questions you might have, and how this is working for you within the classroom.

Changing Our Thinking: Prompting Kids with “You Know This!”

Changing Our Thinking: Prompting Kids with “You Know This!”


There are many practices from long ago that we need to rethink as teachers. This series looks to bring up those practices and offer alternate ideas that are more relevant in today’s classroom. Today we’re discussing using the prompt, “you know this” when a child gets stuck.

Why Do We Prompt?

We give kids several prompts in a day. I would say most of the prompts I give students throughout the day are not academic prompts. Most of my prompts are for shoelaces that are untied, pencils that are on the floor, or behaviors that need to be changed. When we prompt students we want them to recall a very specific set of information and change something. When I say, “step out of line and tie your shoe” to a child he or she knows what to do. It helps him to recall a system of steps to go through in situations like the one he is in. Eventually, I would want to see him look down and step out of line to tie his shoe all by himself. We prompt kids to help them remember and help them create an internal dialogue for situations they might encounter in future. The goal is always independence. 

Teach, Prompt, Reinforce

Many times teachers begin prompts with the phrase “remember…” This assumes that students have already been taught the prompt. Before I can expect a student to step out of line and tie his shoe I have to show him what I mean. It might seem simple but we must explicitly teach what we mean by a prompt before it can be used by a student. During the first week of school when a child’s shoes are untied, I prompt them and show them what to do. After they catch on I can simply prompt. After a while, my words become the voice in their head. Now, when they notice a shoe is untied they simply step out of line and tie it. First I teach the prompt, then I can prompt, then I reinforce if needed. I do, we do, you do.

Using “You Know This”

If we prompt a child by saying, “come on, you know this” or “we just did this yesterday” or even “think back and remember” when they don’t know we aren’t helping them recall any information. All we are telling them is that they should know. Guess what, if they knew they would do it. If they remembered from yesterday you wouldn’t need to give the prompt today. They would just do it. This prompt doesn’t help them it only frustrates them and it frustrates you. When we prompt with our classroom we want it to guide students to the right choice and help create an internal dialogue for them.

Do This Instead

Instead of prompting with you know this, go through the steps: teach, prompt, reinforce. If a student gets stuck on a word, saying “we read that word yesterday” isn’t helpful. Instead, try this:

Teach:

The first few times teach the child the prompt. I have just selected a simple prompt and a simple situation to see what it might look like.

When I see a word I don’t know I look at the first letter and get my mouth ready to say the sound. I notice this word starts with a d. I know a d makes the sound d. Here I told the child the situation they might find themselves in- I see a word I don’t know. I next told them what to do- I look at the first letter and get my mouth ready to say the sound. Then I showed them what I meant and said the d sound. Prompts need to be short and they need to be direct. First name the situation then tell what to do.

Prompt:

Once you have gone through the teach a few times, prompt the child to have them go through the steps on their own. “When you see a word you don’t know, look at the first letter and get your mouth ready to say the sound.” This reminds the child of what they can do at an unknown word and sets them up for success. This prompts should also have the child recall all the times that you showed him how to do this as a reader. Again the prompt is short it names the situation and it tells what to do. Soon this prompt will become the voice inside their head when they approach an unknown word.

Reinforce:

After a while, the student won’t need this prompt anymore. Your prompting voice will now be the internal voice inside guiding them in this situation. They should now be able to notice what situation they are in and recall what to do. Every once in a while you will need to go back and reinforce their knowledge but they should be able to do it on their own the majority of the time. Independence is always the goal.

Changing Our Thinking

I hope this small shift in thinking is helpful in your classroom tomorrow. Try it out. Just select a certain situation it doesn’t even have to be academic and try out the teach, prompt, reinforce method.

Leave a comment below about your shift in thinking, any questions you might have, and how this is working for you within the classroom.