## Changing Our Thinking: Allowing Productive Struggle

## What is Productive Struggle?

I’m going to tell the simplified story of how I learned to ride a bike. First I had a tricycle when I was young. I learned how to pedal and move it with the handles. I started to grow out of that tricycle and my younger brother could have used it so my parents got me a two-wheel bike with training wheels. Once I got the hang of riding it around with training wheels they made the training wheels uneven so I would tip a little back and forth as I rode. This helped me start to learn balance. One summer both of my cousins who were my age were not using training wheels and I decided that I no longer needed them. My dad took them off and I put on my helmet, determined to master riding a two-wheeler. My dad gave me directions and started running while holding on to the seat of the bike. I begged him not to let go but he did anyway. I moved forward a little and then fell to the ground. My dad came over and calmed me down and told me I needed to do something. I needed to steer or pedal it wouldn’t work if I didn’t do anything. So we tried again. My dad ran and let go of the bike and a steered a little and then fell to the ground. My dad again came over and helped me up. This time he wanted me to pedal. I wasn’t so sure about pedaling. That meant I would keep going and I might even go faster than I wanted to go. We tried again. This time I pedaled and steered and managed to go farther than before when I hit a rut in the ground and fell over. Again and again, my dad patiently helped me up and we tried again. Soon he wasn’t running over to me every time I fell. He was having me bring my bike back to him. Slowly I started to gain more and more independence. Finally, I could steer and pedal and not fall over for long periods of time. I was riding a two-wheeler. My dad allowed me to struggle forward. At no point did he take my bike away from me and do it for me. That wouldn’t have worked out and seems silly to actually think about.

Productive struggle is allowing students time to fail forward just like I had on my bike. Productive struggle is so important and too often as teachers we swoop and save instead of letting students fail forward.

## Why Is Swooping A Problem?

Imagine a classroom where kids are learning about place value. A student builds the number 23 with five tens instead of two tens and five ones. The teacher looks at the child and says, “no remember twenty-three two tens and three ones.” The child then fixes their number and now they understand place value… uh… no. Now they got this one problem right but because they were basically told the answer.

A child is reading a book and they get stuck on the word like. The teacher says remember this is a silent e so the i says its name. L-i-k, like. The child mumbles along with the teacher and the teacher says, “good you got it!”

A writer is writing a story with no punctuation and the teacher comes over and adds punctuation with a pen to the child’s’ writing.

The examples can go on and on. So often when children make mistakes teachers fix the mistakes. The problem with doing that is that we are robbing children of learning moments. When I swoop in to solve all the problems a student could encounter how do they become stronger? What did they learn this time that will help them solve the next problem?

## What to do Instead

For a long time, the role of the teacher was to help students fix mistakes. I’m not saying this isn’t the role anymore but the role is more of a facilitator of learning. If all of my students don’t understand a certain skill or strategy it isn’t my job to correct them so they no longer have mistakes. It is my job to help them recognize their mistakes and continue to fail forward unit they understand.

Let’s go back to the base-10 example. This happens quite frequently in the grade 1 classroom. This child doesn’t yet see 10s and ones. If they start counting by ones then they continue to count by ones. If they start counting by tens they continue to start counting by tens. They don’t yet see the longs and cubes as worth different values. What if, instead of correcting him I asked him a question that would push his thinking forward. What if I asked, “how much is this worth” holding up a long. He could count the individual squares and determine that it is 10. Then I could ask, “so how many do you have here?” He could count by ones or tens and determine that he had 50. After that I could ask, “now what can you do so that you have only 23?” I could then let him go back and try again. Maybe this time he grabs 5 cubes. Maybe he goes back and gets three tens and two ones. Even if he just groups his tens into a group of three and a group of three he has begun to fail forward or productively struggle. If he continues to productively struggle I allow it. Productive struggle is good and it is so important.

When a struggle becomes frustrating I would come in with some intentional teaching and modeling for the student. Then we could work together to solve a few problems then the student could try on their own. As long as a struggle is productive and the child is getting bit by bit more correct each time they’re wrong I should allow it. I’m allowing students to build understandings and develop a conceptual understanding on their own.

## What I've Learned

It is really easy to swoop and save or to remove all obstacles from a child’s path but it just isn’t helpful to them. I work hard to allow productive struggle in all of my students. I still haven’t mastered it yet but I too continue to productively struggle forward as a teacher.

Let me know your thoughts and questions regarding productive struggle in the comments below! I would love to hear from you!

## Weekly Wisdom

## Changing Our Thinking: Assessing, Not Assuming

## How We Discuss Students

Kevin is good at math. DaQuain is good at science. Kara is good at reading. Amaria is good at writing. Teachers used to define students by what they were good at and what they aren’t good at. Recently I heard a colleague say, “And she is really good in math… you know, even though she is a girl.” This came out not even moments after I was praised for including STEAM (Science, Technology, Engineering, Art, Math) in my class this year. “It is so good for the boys. They really need that time. The girls like it too…” There is a real danger in categorizing kids and then holding kids to the label that has been applied. This becomes sort of a self-fulfilling prophecy. Teachers end up pushing kids harder in the subjects they are good at and creating excuses for them in the areas they aren’t so good at. I’m sure that as a child I was labeled good at reading and not good at math. I knew it. Teachers had lower expectations of me in math and I had lower expectations of myself.

We need to believe that all students can learn every subject. All students can do challenging things. All students can learn. Our learners might have different learning styles and they might become proficient at different times but all learners can learn.

## What's the Problem?

Recently I completed an addition fact inventory of my students. We sat down one on one and I asked them different facts. What is one plus four? What is six plus zero? I took note of what they did. Could they answer the question? Could they answer the question within five seconds? This is *part* of our schools definition of fluent. Could they explain how they solved the fact? What strategy did they use? This information was so helpful to me as a teacher. My role in the assessment process was simply to document- yes they did, no they did not, what did they do. I was as objective as I could be. Later I was asked by a peer why I assessed everyone. Why didn’t I just assess the kids who were bad at math?

The assumption that some of my students are bad at math and some are not is inherently problematic BUT the fact that we would assess students only based on our assumptions is extremely problematic. Listen, there is a saying about assuming things. Do you know it? If you assume you make an ass out of you and me. Just look at the spelling… Ok, inappropriate jokes aside, assuming is so harmful to student learning.

While completing this fact inventory one of the students who might be considered the highest struggled the most. Had I assumed this student knew because he almost always has an answer first would have meant I missed gaping holes in his understanding of numeracy. One of my students who takes the longest to answer math problems and might be considered low actually had the best strategies for solving. This student consistently structured to five or ten and could always explain how they arrived at an answer.

In reading, the same applies. I have a student who is quite a high decoder but while reading has very limited comprehension. This child would be considered a good reader and might not be assessed because she can decode. When kids miss comprehension questions while doing B.A.S. I can’t say, “Oh they know. They just made a mistake.” If kids actually know, they’ll do it. Sure, everyone has off days but, is this mistake due to an off day or a lack of understanding somewhere. I always try act as though it is a lack of understanding. Giving the benefit of the doubt during assessments doesn’t help student learning.

The problem with making assumptions about our students is that we’ll usually get it wrong. When we make incorrect assumptions we are missing out on opportunities to teach.

## What to do Instead

**Remain Objective**

The most important thing I know about assessing students is go in with an empty mind. Try to be as objective as possible. Notice what students can and cannot do. Act as though this student belongs to another teacher. What do you notice? What can this child do independently? What understandings does this child have? What partial understandings does this child have? Are there any misunderstandings? These are the questions that will assist us as teachers.

**Assess Everyone**

Don’t skip over kids because you’re sure they know. Assess all of your students. If you think they have an understanding and then see that they do have understanding- great! If you think they have an understanding but see that there are some misunderstandings- great! Now you can use this information to guide your instruction. Just the other day I noticed a student drawing tallies to solve a math problem but then counting by ones. This is information I can use to teach. I now know we need to work on structuring to fives. What do you know, this student doesn’t know how to count by fives past 20. Ok, now we’re talking. Now this is information that I can use. Imagine if I saw tallies and then just assumed this student knew how to use them.

**Don’t Give Kids the Benefit of the Doubt**

Just, please. Recently during reading assessments I had a student who retold every story backwards. The student always started with the ending and then retold back to the beginning. This is something I hadn’t noticed before. I immediately thought, he must know. Why is he doing this today? If had just made an assumption and given him the points on the assessment he didn’t earn I would have missed this opportunity. Later while speaking with him he said he likes to start with what he remembers first. We later read a story about how a caterpillar turns into a butterfly. Being able to retell a story in the order it happened is an important skill. We can work on this skill now. Giving him the benefit of the doubt would have meant a missed opportunity for learning.

**Understand That a Single Assessment is a Snapshot**

I know this is totally cliché. I know but I am still going to say it. One assessment is just a single picture of learning in one particular moment and setting. You need to take each assessment as fact but don’t forget to put it back into the larger context of learning.

Maybe today one of my students didn’t know four divided by two when I asked on the fact inventory but can always do it in class. I watch for the next few days and notice that this student consistently demonstrates proficiency. After observing I notice that the student does know how to divide by two. I can ask him the problem again and see or maybe I just decide he knows based on what I have observed and move on. Just make sure that this decision is based on something concrete and not an assumption. It is never bad to give additional practice just to check.

## What I've Learned

Assessing students can be a tricky thing. I know that it is best to try to remove all bias when assessing. Look into their misunderstandings and try to understand where they are coming from. It’s tricky but I know that with practice it gets easier.

## Changing Our Thinking: Access to 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!

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