January 31

Problem of the day…with a twist!

I am a former math teacher. Don’t run away (yet)…this won’t be a math lesson (or maybe it will…math is EVERYWHERE!). There was a time in my career where I started the class with an “opener,” which was typically the “Problem of the Day.” The problem may have had a connection to the lesson for that day, or it may have been some sort of spiral review. Regardless, a big part of this problem was to provide my learners with a time to start thinking about math.

I tend to reflect, a lot, about how I can continue to improve upon my teaching. One day I had a realization. My learners asked me A LOT of questions, not necessarily related to the “problem of the day” that I had projected. It was more like, “Mrs. Q, why do parents have to go in to the parking lot this way to drop the kids off if teachers have to get in, too?” Another example, “Mrs. Q, do you think I can raise my grade before the end of the quarter?” Or my favorite, “Why do they serve this for lunch if it’s supposed to be “healthy”?” I began to realize that I was spending a good portion of the beginning of class answering these questions. Could my middle school kids have been derailing me to keep the focus off the problem of the day, quite possibly. But they were also genuinely curious about these questions. And these were middle schoolers – I could only imagine how many questions an elementary school teacher must get asked a day with those big imaginations in their classrooms!

I started to move away from giving kids the answers to their questions. I mean, I never simply give an answer to a math problem; they need to persevere and problem solve and analyze their work when it is incorrect in order to understand. So…why would I answer their questions? It’s not meant to be rude at all, but how am I teaching them anything if I keep providing the answers to them?

Out of this reflection, I brought a box into my classroom with a cut out at the top and labeled it, “Problems of our Life.” I started asking kids to write their questions down, the ones they would ask me verbally on a daily basis, and place them in the box. I had paper that was color coded based on when the answer was needed (red – needed ASAP; yellow – needed within a week; purple – needed within the month; blue – doesn’t matter but would like to know). Those “Problems of our Life,” pending they were appropriate, became the starters of our class period. My kids were thinking critically, problem solving, and collaborating. They were learning about real life issues, and were discussing solutions together. They were realizing that in some situations, there were multiple ways to solve these problems. We were even talking about problems that we thought we solved but did not go as planned, and shared our whys. In some cases, we were able to use their problems towards an entire math lesson/unit which allowed them to make immediate connections to their learning. The best part is these problems were coming straight from my students, which made them even more engaged with learning from the start.

Other than learning math, my kids were learning how to handle situations and challenges that happen in life. Some questions that they collaborated on were about how to get to McDonald’s from school to meet their friends, how to finish homework and study when they had to go to play practice, how to make a necklace out of sea shells for a gift, etc. These were all questions that my students generated because they were curious and needed to know; and they wanted to work with others to find solutions.

Don’t be afraid to navigate away from your “content focus.” Your kids are still learning something that they will be able to take and apply somewhere else. =)

 

January 31

Encourage the learning – don’t force it.

I’m back! It’s been a while, I know…times have been busy and I apologize (if you’re truly a loyal follower…anyone, anyone??!!). I have been learning, reflecting, engaging, collaborating, and encouraging each and every day. I am happy to be back sharing another little blog with you in hopes to bring inspiration.

Back in November, my daughter approached me and said, “Mom, I want to make pillows for everyone in the family for a Christmas gift.” I thought..wow, that is super generous, but also a very big task! To no surprise, she had already generated a list of individuals that she wanted to make pillows for, which she had shared with me so I knew how many pillows she needed to make. She told me that she saw someone making them at school, and wanted to use her sewing machine that she was gifted last Christmas to try it out. I asked her what was needed, and this is what she said:

“Well I need fabric for everyone, but I want to get everyone fabric that they will like, maybe what they’re interested in. I need the stuffing to put into the pillows, and I need thread.”

She went on to tell me that she didn’t want the pillows to be too big, maybe just slightly bigger than a piece of paper. She went and grabbed this paper and started tracing outside to show me what she was thinking in terms of the size of the pillows. At that point, we had a conversation about how much fabric she would need. “Can’t you just buy it and if we need more we can go back and get some?” She asked. I explained that we want to buy the fabric that we need, and not too much so that there is a lot extra; but we also don’t live particularly close to the fabric store where I can jump in the car and run out if we needed more. So then my 8 year old says, “Well we can measure it!” Next thing I knew, she was going over to the junk drawer (don’t lie – you have one, too ;)!!) to grab this ruler that I know for sure I have not yet taught her to use. She started measuring the paper and figured out how much fabric we would need for each pillow. We also talked about how much stuffing would be needed for these pillows (we already had the thread).

After a trip to the store, she got home and went straight to work to make these pillows…and she did so with minimal help. She began to measure the perimeter of the pillow out, sewed around the outside edges while the fabric was inside out, turned the fabric around, stuffed the pillow, and finished by manually sewing the pillow closed. I was amazed at her creativity, patience, and drive throughout this entire process.

Now, why do I share this story with you today in a blog that is entitled, “Encourage the learning – don’t force it.” My daughter saw someone at school doing this and was encouraged by her observations. Throughout this entire process, I heard and observed my daughter thinking critically, problem solving, and collaborating with me on the steps she would take to achieve her goal. She used the tools that she needed to make this dream become a reality. And those are the “non-academic” skills that she used. I also watched my daughter use her knowledge of math, reading, science, etc. to create these pillows. I also witnessed her creativity and imagination. She learned so much without even knowing exactly what she was learning and the best part – she had fun doing it and it was something she wanted to do.

I want you to reflect on what the kids in your class are doing when learning. Are they watching you teach them, or are they being guided by you as they problem solve and think critically to navigate through their learning? Are they sitting down and filling out worksheets, or are they allowed to demonstrate their understanding in a way that not only makes sense to them, but is how they choose to demonstrate their learning? Yes, we are bound by standards that need to be covered in order to prepare our kids to move on to the next grade; however, are we being creative in the way we are doing this? You may be and if so, I would encourage you to reach out to some of your colleagues who may be having difficulty doing so and partner with them to generate even more ideas! If you’re not, I challenge you to think of how to bring more of these engaging experiences in to the classroom. Let’s put the fun back in learning!

 

July 19

Aim to understand, not to memorize.

Let’s do a thinking activity. Without Googling or asking for help, can you tell me what the names of Christopher Columbus’ three ships were? Most of you likely passed that first question and were able to say the Nina, Pinta, and Santa Maria.

Now, without Googling or asking for help, can you explain to me why there were three ships and the purpose for each one?

This is likely where we lost a few of you who were able to answer that first part of the question. There have been a lot of questions about Common Core state standards and why students aren’t learning like their parents did back in the day. The reason for that is because most of us learned in a way where it was more important to memorize flashcards and facts rather than understanding the information. Not to mention, we were then responsible for regurgitating information back on classroom or state tests. Were we really learning, or were we just really good at memorization? I know there are things today that I cannot remember and I know I received A’s and B’s on my assessments when I was younger. All these grades told me was that I was really good at memorizing most of the time. This is to no fault of the teachers, either; it is just the traditional way that schools have always operated – which is why it is time for a much needed change.

You may see posts like this on social media sites:

Why can’t we answer a basic math question? Most of us learned PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) – which is also why we sometimes get confused when someone says order of operations ;). Unfortunately, this exact order is incorrect; but we were taught Please Excuse My Dear Aunt Sally to help us remember an order (that was not even correct), rather than understanding what and why we were doing what we were doing to solve these problems.

Traditional ways of teaching and learning do not work for our students, not to mention they are not always the most fun way of learning. With the amount of resources at our fingertips, we have an amazing opportunity to allow our students to learn much more than what we have ever been able to do before.

When I was moving into teaching how to find volume of 3D objects, I found a way to help my students make a connection immediately. I noticed that many expressed their interest in the TV Show, Tanked. I decided to use a small clip of this show to introduce the idea of what volume was, and the importance of understanding how to find volume. The end goal of our learning was for students to demonstrate their understanding of learning volume by drawing/building their own fish tank, and it needed to include specific amounts of water and shapes. Throughout this unit, I never just gave them the formula; instead, we explored different characteristics of shapes and what was happening when we poured water into a fish tank in order to understand where those calculations were coming from. Why did I do this? I knew that if I had just given them a formula to memorize, they might memorize it for the assessment; however, would they know what to do when they came across a volume question again in life? This is why it is so crucial to aim for understanding, and not for memorization. I know how difficult it is to not just give the information that is needed; but we need to provide time for our students to work through the challenges. Not only does this make them better learners, but it builds their confidence and allows them to see that they can learn, and that learning is endless! As the teacher, I was there to guide my students along the way and provide support when it was needed and necessary. That is our role as educators: help them to start and provide them the resources, then guide them as they take off on an incredible journey of learning.

August 28

The F Word…

Let’s talk about a scary, yet very important word in the educational world: feedback. Yes, I referred to feedback as scary – want to know why? As educators, we wonder how to provide feedback to our students often. What is the right approach in terms of delivering the feedback? What is too much feedback? How specific should we get? The questions are endless, but the topic is one that is incredibly crucial and necessary towards helping students to grow. But, why? Why is it necessary to continuously provide feedback to our students?

When I go to the gym, there is an individual there coaching us along the way. One day, as I was working on a particular workout, the coach came over and said, “I like the heaviness of the weight you chose. Now, let’s focus on not jumping too much. Try this…” She proceeded to show me how to execute the workout again, then stayed around for another 30 seconds to ensure I picked up on it correctly. Why was this so important? First, she applauded me for something, which made me feel good and reminded me the next time we performed that workout to stick with the weight [even though it was really challenging]. After that, she corrected my form. This was especially crucial in order to prevent injury. Finally, she stayed around while I performed the workout again in order to ensure I applied her feedback correctly to avoid getting hurt. Not one time did I feel embarrassed while she was providing me the feedback during class. This didn’t only help me do better for the rest of that specific class, but it helped me to improve in following classes.

Feedback to our students is important in aiding to their academic improvements. Whether it is written, oral, or recorded – it is a necessary part of education. How will our students know when they are making a mistake, and what will help them to improve? But, as with many things, there are barriers to the feedback that is provided to our students (especially as they get older). Take this for example: you spend hours correcting those essays and writing feedback throughout each one to help your students understand where they did great and where they struggled. You are proud of that feedback, and know that it will help them to grow. You add the grade at the top, or on the rubric. You hand those essays back to the students and the majority immediately look at one thing – the grade. They focus on the grade (this topic is for another day…), but don’t spend much time paying attention to the feedback. Often times once this happens, we move on to the next topic.

Feedback must be purposeful and meaningful. I’ll say it again – FEEDBACK MUST BE PURPOSEFUL AND MEANINGFUL. It must inform our instruction. If nothing is being done with the feedback, then you, as an educator, just wasted a whole bunch of extremely valuable time writing meaningless words on a piece of paper. So what do we do? How do we overcome this? I don’t have all of the answers, but I do have a few ideas!

Give them a day!

When I taught in a setting where I was giving quizzes and tests, I would always build in time (sometimes a full class period…) allowing students to work on corrections. We did this together because I knew that my middle school students needed guidance and support with how to do this in a way that was beneficial. As a matter of fact, the first few times we did this I modeled how to do it using a made-up assessment. I walked

my students through the process. I told them to never forget about the ones they got correct, that those show us our strengths. We discussed the importance of looking at problems that we got correct, but remember feeling nervous about while taking the assessment. Then, we focused on the mistakes we made. We discussed the importance of reading the feedback. I would copy a problem from the test for students to see and we had in-depth conversations about what the feedback meant for that problem, and how we would use the feedback to correct our understanding. Once the students got the hang of this, we would spend half or a full class day working on corrections. Not only did this help improve their grade, but it also helped to improve their overall understanding, preparing them to move on to the next topic.

Use the same homework for many days in a row

As a math teacher, I thought that it was important for my students to complete a lot of problems for homework because practice makes perfect. After many self-reflections, I realized the importance of quality over quantity. What does assigning a ton of homework (or homework, at all – yes, I said it) do for many of our students? Well, some won’t do it at all because it’s just too much and overwhelming. Some will cheat because they didn’t have the time to finish and they don’t want to see a zero on their progress report. Some will take the time to work on it. These are just a few scenarios out of many. But, even if they do take time to work on the assignment, what good will it do if all we do the next day is quickly go over the answers (like I used to do)? You know what I am talking about:

“Okay, so we just finished going over the twelve questions from homework. Does anyone have any questions or need me to repeat any answers?” [Crickets. Not one word] “Great, then let’s move on to the next topic.”

You know there are definitely students out there who are still struggling after that assignment, but just may be too embarrassed to say anything. Now let’s reflect – how did this assignment help us to improve? Did we provide specific feedback to any students, or did we just check for completion and move on? Feedback on homework is just as important as feedback on assessments. If you are going to have your students complete an assignment, just to show you that it is done and listen to you recite the answers, then that homework is not meaningful. If you are going to assign homework, provide students with an opportunity to grow with that assignment. If I were still assigning homework, I would have started with assigning my students a few – maybe two or three – problems on one night. The next day I would give my students the answers (yes, I said it – I would just give them the answers). I wouldn’t spend time reviewing at that point. The homework for tonight would be to take those problems and redo any incorrect questions. Got them all correct? Great! You’ve mastered that topic. Here are a few optional and/or challenging questions if you’re wanting to do more with this. They come back the second day and some still got wrong answers. What do we do from here? We create a small group, provide feedback on the questionsand help the students to understand better. Does this require a bit of time management? Yes. However, I would rather try to find a way to make this work than go over homework everyday when I know my students aren’t going to ask questions because they don’t want to hear me talking about it anymore (you know I’m right!).

Provide VERBAL feedback – digitally!

Since the pandemic and beginning remote learning, many of us have been assigning activities/assessments on a digital platform. There are many tools out there that can allow you to provide verbal feedback to students digitally. Grading something on Google Docs? Open up a Screencastify and talk your feedback as you are grading the assignment. Did you just finish grading a project that was turned in? Open up FlipGrid and allow your student to watch you point to their project as you are speaking and providing feedback. Not only will this be done quicker than hand-writing all of the feedback, but it will also allow your students to build more of a connection with you as they are watching and/or hearing you provide feedback and explain.

These are only a few suggestions on how to provide meaningful and purposeful feedback to students. Remember, feedback is meant to help them grow and improve; but only if we are providing them a way to do something with the feedback. Taking it one step further and using what we provided to inform our instruction is what will really aid in their overall understanding. Please feel free to share in the comments with ways you allow students to grow from the feedback you provide them with!

April 25

Math Toss Across – An ABSOLUTE MUST for the Classroom!

I enjoy taking worksheets and finding unique way to have students practice from them without filling out the worksheet itself. Additionally, games are something that always keep my students engaged and motivated to learn. Changing things up allows students to do something different on a daily or weekly basis.

While searching for some new ideas to practice skills in the classroom, I came across another blog that took the idea of bozo buckets and turned it into a math review game. I thought this was an incredible idea; but I wanted something a bit more challenging. I took the buckets and decided to use cups, while using a ping-pong ball for students to toss into the cups. Students toss the ball into a cup, which contains a problem. They solve the problem with their group in order to earn the cup. The team with the most cups at the end wins the game!

Let me break it down a bit more for you:

The Set Up

  • Get some cups and ping pong balls. The number of cups depends on how many problems you want to include in the game, as well as how long you want the game to last. The number of ping pong balls depends on how many teams will be in the game.
  • For each problem you have in the game (this also depends on how many cups are in the game), write or type it on a slip of paper. Put each slip in a cup (so each cup should have one slip of paper with one problem).
  • Figure out where you want to place the cups in your classroom. I pushed a table up against the wall (so that students had a backboard) and organized them in rows and columns. Then, place a piece of tape on the ground where you want the students to stand when tossing the ping pong ball.
  • Place your students into groups (I had groups of 3 or 4, based on how many students were in the class). Each person needs paper and something to write on.

Playing the Game

Students will be tossing a ping pong ball into the cups to try and get a question. I told the students that every person needed to toss (so that it was fair for all teams). You may want to have the students figure out an order ahead of time so that it is not confusing while the game is in play.

  • The first group of students go up to the line. They all begin tossing the ping pong balls (yes, at the same time; I had numbered them with permanent marker so students were able to tell which ball was theirs). Once they got one into a cup, they took the cup back to their table where the group was sitting. Students continue throwing the ping pong ball until they get a cup. If a student has been up there for a while, they may swap turns with another partner in their group.
  • At their table, students work together to answer the question that was in the cup. Once they have agreed on an answer, they bring their work and solution up to me. I check their work and solution. If they are wrong, they bring it back to their group and continue working until they get a correct solution. If they were correct, the next student goes up to toss a ping pong ball. The game continues like this until all cups are gone (or until class ends).
  • The team that has the most cups by the end of the game wins!

The students not only enjoyed the challenge of the game itself, but also had fun collaborating and working together to find a solution. Some teams decided to work together to find one way to answer the question, while others decided to work on the problem independently to compare what they had in groups. They also learned a great deal about how rushing to get a problem done typically presents a lot of errors! This one game taught the students a lot, and they had a very enjoyable time playing.

April 2

‘Tricking’ Students into Mathematical Dialogue

We all know the importance of mathematical discourse in the classroom; however, it is always a struggle to get strong active participation out of most students. The reasoning behind it varies – students are not confident enough, embarrassed to share their answers, or just don’t know how to talk math. In an earlier newsletter, number talks were shared as a way to encourage more math dialogue in the classroom. What else can be done in order to inspire students to share their mathematical thinking? Here’s an idea: switch roles.

Okay, I know, I left it at that – ‘switch roles.’ What does that mean? Switch roles with who or what? Think for a moment about this profession. As teachers, how do we teach our students a new skill? We explain, create steps, use manipulatives or drawings, and even think of questions to ask students. What if we put students into teacher shoes and have them do the same? Here’s an example:

I’m teaching a lesson on finding the area of shapes. The students were presented a lesson on the topic, and now need to practice finding the area. Rather than give them a worksheet to complete, I will provide each student with his or her own shape and dimensions. Students will be given the class time to not only solve the problem, but thoroughly explain what they did in order to obtain the solution. They will be encouraged to draw pictures, create charts, or whatever else they find useful with solving. Yes, I require them to take the entire class period (or maybe half of the period) to complete this work for one problem.

The next day, students will be partnered up in order to work on the problem. This will be done in a very different way, however. The partner will have a blank piece of paper in front of him/her. The individual with the problem will begin explaining his or her response to the problem, without having shown the original problem. On paper, the partner will try to generate the original question based on the explanation being presented. Once finished, they will compare work. If the original work was close to the response the partner came up with, then that student had a strong explanation to his/her response. A strong explanation also goes along with a good understanding of the problem.

As mentioned before, number talk was one strategy to use in order to encourage mathematical discourse. This is another useful strategy that will hopefully challenge students into their own thinking, while creating a collaborative environment.

January 3

C.E.O. – Checking for Errors Often!

For today’s instructional strategy, I decided to bring a few of our past strategies together to focus on an important thing – errors. None of us are perfect, and we are all bound to make errors in math. This is an important message to relay to our students so that they feel comfortable solving problems. One thing that I have heard often from students is that they are “afraid of making a mistake.” As teachers, it is important that we share the benefits of mistakes; that they help us expand our learning. Error analysis leads us to rich discussions and deep thinking.

In two previous shared instructional strategies, the practice of allowing students to analyze their mistakes on quizzes and homework was mentioned. We want students to have that time to review their errors and any error patterns so that they could avoid making future mistakes, as well as improve in understanding. Something that is often overlooked, however, is whether or not our students know how to do an error analysis. Do they know what to look for? Do they understand how to fix it? These are important pieces in aiding understanding.

In order to teach students how to analyze errors, we need to help them understand what to look for when checking a problem. Students need to walk through each step confirming that there are no conceptual, computational, procedural, or even careless errors. If and once an error is discovered, have a conversation around how to fix that one error and redo the problem so that the students can compare one to the other. Spend time re-teaching or providing remediation to students who need more help. In addition, ensure that students are using a resource when fixing the problem. They should never assume they know how to do it right the second or third time; even if they do! Encourage students to take out notes, look back in a textbook, or even sit with a partner and complete a peer review.

Finally, provide students with time to look for any error patterns. Discovering error patterns will help students and teachers to identify any gaps in learning that may be hindering them from solving problems successfully. As I always say, embrace errors now so that they aren’t made when it’s really important!!

December 5

The Power of Quiz Corrections

One word: feedback. Oh, you thought we were going to talk quiz corrections? Well, we are – we’ll get there. But to start the topic off right, we need to mention feedback. We all know that feedback has been found to improve student outcomes. We know that it is important to ensure the feedback we provide is specific and meaningful. In addition, I am certain that most, if not all, of you provide written feedback on assessments. The question, however, is what our students do with that feedback once they receive the assessment back.

I don’t know about you, but I have witnessed many students look at their grade, quickly browse through the quiz or test to see the questions they got right or wrong, and then put the assessment away. When asked if they read what was written, 9 out of 10 times the answer was ‘no.’ So why continue to provide the feedback if they won’t do anything with it? Well, what if we give them an opportunity to do something with the feedback? Insert . Quiz . Corrections.

As a teacher, I always allowed my students to complete quiz corrections for a few “extra points.” Sure, it was another thing to add to my list of things to grade; however, it was a good thing. Without providing my students this opportunity, how will they master this topic or skill on the final test? How will they retain this information if they truly never understood it the first time? We can most certainly practice it more in the classroom, but think of how much more beneficial it would be for a student to use their original work, your feedback, and their resources to persevere through solving and understanding the problem.

It is important for students to solve the problem again with a goal to get it right the second time. It is equally as important for students to evaluate and analyze their work, providing a written explanation on where they went wrong the first time. In addition, affording students an opportunity to reflect on their study habits is crucial for helping them improve their study skills. Perhaps the student failed his or her quiz but spent hours studying [raise your hand if you’ve ever heard that – I bet you are!].

In summary, quiz corrections are powerful. They help our students to not only improve in their mathematical ability, but also increase their mathematical understanding. In addition, they teach our students to go back and look at notes to find sample problems and model questions, as well as how to persevere. Finally, quiz corrections help our students to reflect on their study strategies. No, we are not giving them an avenue out from studying the first time around. Instead, we are saying, “Just because you are struggling, doesn’t mean you’re failing.”

December 5

DON’T spend time going over homework EVERYDAY (yes, I said it!)!

Our school district has had a lot of conversation around homework – and we know that our homework is purposeful. It provides additional practice for students, and practice DOES in fact make perfect! But, have you ever thought about changing what you do with homework up a bit? Let me explain…

As a classroom teacher, I assigned homework daily. When students entered our room, the first thing they took out was their homework. The first thing I checked was their homework. The first thing we went over, you guessed it – their homework. Homework took a solid 10 – 15 minutes out of my daily instruction. Now, don’t get me wrong; I believe going over homework is crucial. We all know it’s important for our students to check over their mistakes and fix their errors to build understanding. But how many of them are actually doing this? Or how many are doing it the right way?

How often do you assign homework on the same skill? For me, I assigned it at least twice a week – but more along three times a week. That’s three days of reviewing the same thing. If I were still in a position where I was assigning homework, I think I would change this up a bit. Here’s what I’m thinking…

Assign the homework on a skill on day 1 of the lesson – and I’m talking everything. Concepts, word problems, things you may not teach them on day 1 (yes, I said it – stick with me here!). Provide the answers only on day 2.  Don’t go over it, any of it (unless they are really lost and have questions on the skill itself). Then, for homework that night, students need to redo problems that were incorrect from day one. The start of day 3, show them the answers again, and for homework that night, they have to redo any more problems that they may still be getting incorrect. Finally, on day 4, go over questions that they may not have been able to figure out themselves.  Providing students with the chance to keep redoing homework assignments not only helps them to build understanding, but it also teaches them to persevere through problem solving. That last day is crucial. I wouldn’t just spend time going over problems that were difficult through the process; but I would also have a final discussion with the class in what questions they found to be the most challenging and why. I would also ask for students to chime in and discuss how they overcame the challenges that they faced through the homework process. Using this process can also help you to target students who are truly struggling with the skill that you are working on in class. I understand this is a change, and change can be scary. But think about it. Are homework grades more important than building student understanding through homework?

December 5

Allow Students to LEAD their LEARNING!

Let’s get real here and talk about a sensitive subject: Common Core. The CCSS bring us the eight mathematical practices (which I know you have memorized them by now, so let’s cut to the chase!). I would like to focus on one of those standards:

Make sense of problems and persevere in solving them.

So, what does this mean? Well, it means that students should be understanding problems and continue to work at it until they have not only solved the problem, but really gained a deep understanding of it. Yes, that means everything you do in your classroom revolves around this one standard! Often times we may get frustrated because we feel as if we are spending so much time on a specific skill, but yet students are still struggling with understanding. I want you to think about what you do in your math class. Let’s say you’re starting a brand-new topic in class. How do you begin? Do you lecture? Do you have them watch videos? Do you ask students to read the textbook ahead of time? How do you introduce this skill to them?

These “new” standards have provided teachers with the chance to help students to see that problems can be solved using multiple strategies. So, I ask – how are you allowing your students to discover these different ways of solving one problem?

What if we began introducing our topic by not directly teaching them anything about it at all? Whoa now – I’m not saying to not do your job! But what I am saying is what if we left it up to the students to control their learning (while we guide them through)? Let’s take integer operations, for example. I am starting a new section on adding integers. My students walk in. On the board, I have the problem written:

-3 + 8

I ask the students to look at the problem. Then, they are provided with 5 minutes to jot a few notes down that answer the questions:

– What do you notice?

– What do you wonder?

Those two questions right there – they are pretty powerful in a math class. Not to mention they open the door for some rich discussion. These discussions can lead to multiple views of how this problem can not only be solved, but also understood. If we gave our students a chance to look at every new problem like this one, do you think that they would make sense of the problem a little more? Do you believe they would want to persevere in solving the problem? I challenge you to not only think about those questions, but to also give this a try; and if you do, let us know what happens!