What Makes a Good Math Program

What techniques and strategies should teachers use in their math programs if they want to teach math effectively? In this episode, we share a few techniques that you can use to spiral the curriculum, differentiate throughout the year, assess more efficiently, and engage your math students.
In this episode we explore: 

• Why teachers should have high expectations
• How to build students who are willing to take risks in their learning.
• How to use assessment to inform your instruction
• The importance of differentiated instruction in the math classroom. 
• Strategies to help students become better problem solvers. 

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Transcript

Patti Firth 0:00

you can have a rigorous math program that engages your students and is effective, that fits in all of the things that we're supposed to do from beginning to end and actually helps your students learn math. So let's take right in. The first question we're gonna tackle is what actually makes a strong math program? So there's probably a lot being thrown at you in terms of how do I do, how do I teach, how do I spiral? How do I do all of the things? So we have to really narrow down and focus what are going to be the strategies that are going to give us the most bang for our buck in our classroom. So what exactly makes a strong math program? Well, a strong math classroom has instruction. So the stuff we do in our instruction is gonna be focused on teaching students a conceptual understanding. So not just teaching math robots, but that they actually understand what is happening. They have a much deeper understanding than just, I can memorize the steps, follow them, but really have no idea what's. We also need to remember that part of math is still having procedural fluency so that they do have a conceptual understanding, but they also understand that basic math skills, that we want them to develop those skills. We want them to know their multiplication facts. We want them to understand how to add quickly and efficiently. We want them not only to be able to do, but also to be able to communicate what it is that students are doing and what they're thinking is happening. So we want them to have that metacognitive piece as well that helps them to really understand what they're actually doing instead of just functionally doing kind of what we've shown them to do, but not really getting. And finally, we want them to understand how to solve problems. Math is full of problems and sometimes math isn't in the real world. Always this cookie cutter, textbook type math where it's all clean lines and we focus on one strand at a time. Real math in the real world is not like that. We need to be able to understand what the question is asking us, how we're gonna solve that problem, and to be able to bring all of the tools required in order to solve the problem we have. And it's not just going to be, you know, open up your textbook to page 54, and today we're only going to learn about fractions. That's not real world. So we wanna teach students how to tackle real world type problems and be able to solve them and decide what tools they need, what strategies they need to use, and how they're going to get through that real world. A strong math classroom. Us as teachers, we need to know our students. We need to know our students' ability, which means we need to have lots of opportunities to see our students doing math. We need to have a culture of high expectations and the belief that all students can learn math, but that that learning pathway might be different for different students. And we need to create a math program that is culturally relevant and respons. In a strong math classroom, we have students who are able to take risks, which is going to be huge because taking risks and taking that risk that they might fail is going to be something that we need to accept and embrace within our classroom, because we often are gonna make mistakes when it comes to math, especially when we're learning. So we need students that aren't so super focused on always getting it right, but focused more on the process on how they're going to do it, and taking those risks that they may not get the right answer, but what was their process? We need students to feel empowered and be the belief and the confidence that they can do math. That is something that they're able to do, something they're able to tackle, that they have a strength, and that even though they may not have the same strengths as others, maybe they're not the fastest at math. Maybe they still need to, Maybe they rely more on inefficient strategies at this point in order to solve it. But we need to build the confidence and be very clear with what we value, what is a good math student. And we sometimes have a very narrow understanding of what that is. It's somebody who can. Get the right answer. Somebody that's really fast, um, at, you know, being able to spit out the answer and they have speed. And we prioritize speed over conceptual understanding. Excuse me. And we also want our students to feel valued that their process, that their idea, that their learning style is appreciated inside the classroom. And we want to make sure that they value real math learning and that they feel valued in our classroom as a math student. Okay, that's great, but how So if that's sort of what we need to do at like a 30,000 view, how do we actually make that practically happen in our classrooms? The first is going to be a focus here on the cycle of assessment, and I like to think of this cycle of assessment happening weekly within my classroom. So at the beginning of the week, we establish what is the learning goal in math for the week, What do I want them to be able to do by the end of the week? So it's the beginning of the week what I want them to be able to do at the end of the week. So I want my students to be able to multiply three digit by two digit numbers. That's my learning goal. How? Well, that's the success criteria. How are they going to do that? Well, I'm gonna teach them the partial product strategy. I'm gonna teach them a standard algorithm strategy. We're going to learn different tools. We're gonna figure out which one works for them, which one's most efficient. We're gonna use manipulatives and modeling. How are we going to do it becomes our success criteria, what we're focusing on as our learning goal. That's going to be set throughout the. Then once that is set, there's instruction that is happening this entire time, and from that instruction, I'm able to provide feedback. Now that feedback is not a conference all the time. Sometimes that feedback is simply me walking around the classroom and giving students a check mark because they're on the right track. That feedback is me checking in on them, me asking them questions. In middle of my lesson, asking two students to come and show me what's happening on the board. And we have a discussion about that math feedback is any time I am talking with my students and letting them know, Yeah, you're on the right track. That's a good job way to go. Or, Oh, what if we did this? Or how did we make that error there? How are we making mistakes? Someone share your failure with me. Um, that's one of my favorites to do is, Okay, who got it wrong? Tell me where you got it wrong and how you fixed it. I love that is ability to be able to talk about those errors that were happening in the classroom, provide real time feedback for students. On the flip side of that is we don't just want the feedback only coming from us as teachers. We also want our students to begin to exercise that self assessment muscle and peer assessment muscle. So we don't necessarily need to have any formal structure to give peer assessment or self assessment. It can be as simple as, Hey, we just did a word problem. How did you feel? Do you feel like you got it really strong? Give yourself a five. If you feel like you have no sweet clue what you're doing, give yourself a one. Okay, great. All right. Let's look at everyone's numbers. Okay. We've got some people with ones and some people with fives. Hey, can my fives? Let's pair up with my ones and let's help each other out and give each other feedback. And they walk each other through and coach each other through, and they support one another. Work with a friend who's feeling more c. Let them help you and give you some feedback along the way. It doesn't always have to be just me in the classroom. That can be providing feedback and feedback. Doesn't always have to be a paragraph long, uh, that's something I'm writing on their worksheet. It can be informal. It could be more formal. It could be a check mark. It could be, Hey, you're on the right track. It can be 10 seconds worth of feedback, but we want to have that happen throughout the weeks. We want multiple opportunities where we can check in with our students and provide them feedback from us, from themselves, as well as from their peers. And then to top it all off at the end of the week, we want that assessment to turn into a goal. So if we have a student who's worked really hard at a concept, but they still have a little bit to go, What's your goal next week? Maybe the goal for that student is, Hey, I actually wanna, you know, pay attention more in class, cuz I think that's where I struggled this week. Or maybe I need to focus a little bit more in center's activities because I sort of goofed off this week. Or maybe I want to try harder questions. Maybe I kind of tried easy questions this week, but I wanna try harder questions. Or maybe I wanna practice a little bit more at home because I think I would benefit from it. All of those goals are going to be individualized and should be student driven based on all of the feedback that they've given themselves, the teachers given them, and their peers have given them. And as a reflection of what they've actually learned and how they've accomplished those learning goals. That goal turns back into the next week. What are you going to do this week? And it's this continuous cycle that we go through in our classroom every week, Bo, both formally and informally. It doesn't have to be, you know, this super formal process. But when we look at this is going to generally be how our week will be structured, that's gonna help us ground that idea of what's happening in our classrooms every. Some of the high impact strategies that you want to be using frequently in your classroom is direct instruction. In math, students need their teachers to teach them. We need to give students direct instruction and we need to be giving that direct instruction. To our own style of math learning as well as to the other styles of math learning. Understanding that perhaps as teachers, we were great at math, but we might have students that are struggling in math. So we have to be able to teach to multiple types of students and model different strategies. We want to teach students long division, but we also wanna teach them the box method of division because, and we wanna teach'em how to divide with place value blocks because we may have students that conceptually struggle. With different things and we wanna provide as many opportunities for them to, and many, as many entry points as we possibly can to get them in. When we're creating these lessons, we also wanna develop anchor charts so that we can have an anchor point so that students can reference back to the lesson that we did. So we're gonna create those anchor charts with our students and we're going to display those in our classrooms so that students can refer to them, and it helps to activate the knowledge. Oh yeah, when we did that, the teacher was saying this, and we wanna have checklists and anchor charts. We also want to use different teaching strategies during this direct instruction, such as guided inquiry. We don't always wanna start with showing them all. Sometimes we wanna start with a question and guide our students into their understanding and have that understanding of concepts develop. Great way to think about this is measurement. I could stand up at the front of my room and teach students how to. In a very prescribed way. Or I could ask students, Okay, I wanna measure a pencil and I can grab a meter stick and, and the pencil. And I go, Okay, good. Look. And the kids are like, What are you doing? And. Getting them to sort of develop the understanding that there's some tools that are better for some jobs than other. Maybe I'm gonna measure something like, Oh, I don't know. Mm. Show them with my finger and they're like, That's gonna not be very accurate. And getting them to understand instead of me just always telling them, getting them to discover that, not necessarily like discovery math, but it's just a different way. Hook them into the learning and to activate that by guiding them through, by asking them questions and getting them there. We wanna have opportunities to check for understanding and to be able to communicate how we talk about math and how we talk about our brains that solve math. And that social emotional learning piece is embedded in every single thing we do because we wanna teach students that there is more than one way to solve a math problem. And that different brains solve math in different ways. And ways are valued and always are okay. We wanna move to efficiency. But understanding that just because the standard algorithm doesn't make sense to you doesn't mean you suck at math. So we want to communicate all of that to our students. We also, because problem solving in math is gonna be so important. We wanna teach our students these social emotional learning piece that it's okay to solve math, it's okay to fail. It is okay. We gotta build that grit, that growth mindset, some resiliency here. We wanna teach them what learning actually feels like and. That feeling that sometimes you're encountering something hard and difficult and your brain just wants to run away. Getting students to recognize that that feeling is totally normal and how to process that and how to move through it is an important part of that social emotional learning piece is we're building the resilience and grit. We want our students to be able to reason critically and think, apply the knowledge that they've learned from different parts into that problem solving and really to persevere through challenges. Personally, I love using the chase or the Chase strategy for math solving. I know a lot of people use the cube strategy. I prefer the chase strategy because it doesn't always, it's not just solely focused on underlining and boxing and, and sort of, Decoding of the question, but it is, there are sections of analyzing. There is clues looking for clues, but we're not just looking for, say, keywords all the time. We're looking for the clues. What does it mean? Where are the numbers? Analyzing? What does this mean? Not just, I found the numbers, congratulations, but I want them to analyze what the meaning of those numbers mean, how that relates to the question being asked. Then we want them to solve the problem and finish up with that communication piece. So for me, using this Chase algorithm highlights that second half of the problem solving. It's not just about understanding the question, but it's also about tackling the question and finishing up with the question, explaining what our answer is, how we're gonna solve, show our work, check our work, following a plan, making a plan. And it does help us to sort of sort through those process expectations of problem solving in math class. Another strategy is using manipulatives. For many of us, we didn't use a lot of manipulatives in class, and perhaps using manipulatives in your math class feels strange. And there does seem to be a bit of a theory for many students that if you need to use manipulatives, that must mean you are not good at math because manipulatives aren't the way good math people solve math. And part of our job as teachers is to dismantle this belief. The belief we may hold as well as a belief in our students that using manipulatives is somehow valued less than somebody who can do the math only in their head. Being able for students, especially when they're learning new concepts, to use a manipulative to understand conceptually what is happening as a way to transition between. Something they have no idea what they're doing into being able to do it sort of more automatically. That manipulative is a great way for students to be able to see it. And many of our students need that conceptual bridge to help get them there. And even the students that are strong at their basic math, getting them to just follow the steps and get to the answer is wonderful. But when they don't have that conceptual framework and that understanding and the base built underneath that competent, um, fluency, so they may get it, they may fluent, but we want them to make sure they fully understand it because as the math gets harder, they can't just rely on process alone in order to be able to really understand what's happening. So for example, Um, teaching fractions, conceptually it's difficult for students and using manipulatives is very beneficial as students are learning that fraction piece, especially in Canada. If you're teaching in Canada, which I think many of you are, we are not as reliant, say, on fractions as say, an American student who needs fractions for measurement. Part of their, um, part of their measurement, understanding they're using more fractions more often. We are using more of a base 10 system here in Canada, so our fractions understanding develops a little bit later because it's not used as frequently because we use a Base 10 system for most things. So, for example, I have manipulatives here on the screen to demonstrate the idea of nine fourths converting to two and one fourth, and being able to show students nine one fourths. So if you have the one fourth fraction tiles, I use digital manipulatives to create this, cuz sometimes we don't always have all of the physical manipulatives, digital manipulatives work just as fine. But being able to show students that I have one fourth plus one fourth, how, and I have a hole, then I have two holes, and then I have one fourth leftover that does not fill a hole. They can follow the steps to convert nine fourths to two and one fourth. Many students can just follow the steps and get it, but to really understand it, some students will need to see it. So using manipulatives is a really important way to teach students that conceptual understanding and make the abstract comment or abstract ideas that we are talking about sometimes in math makes them far more concrete and easily understood. Another high impact strategy is small group instruction. S, when I introduced small group instruction in my math classroom, it made a world of difference for me and for my students. The benefit for me was it allowed me opportunities to reteach, reinforce the different concepts, the ability to watch a student solve a problem, see an error happening in real time, and being able to give that feedback as it's happening. Being able to adjust and tweak to say, Hey, I see you're using this strategy, but based on some of the problems you're having. I actually think this strategy might be a more effective one because it seems to fit better, was sort of how your brain is thinking about that math problem. These are conversations that would not happen in a whole group situation. It happens inside a guided math group. Additionally, the benefit for me is in guided math, I actually can take home less marking and I have a much better understanding of my students and their abilities. We love the idea of less marking. I get more information watching my students solve one word problem than I would ever get by taking a math worksheet home that has six word problems on it, and watching a, and just looking at how a student solved the question for me. Being able to see students do their work, being able to have them in front of me and provide that timely feedback makes a much bigger impact on them and on me. It helps to close the gaps and gives me a tremendous amount of observational data so that I really know who my students are as math learners, and it gives me the ability to use flexible grouping so I don't always have to see the same kids at the same time, I can see multiple groups of students and it can be flexible based on need for that week in the moment. We also can't just do all of the higher order thinking time. As much as that is really important, we also just simply need practice time. We need our students to practice, and this is another element that's going to be important. And there's balance that has to happen with the amount of practice we give our students versus the amount of time spent in higher order thinking tasks. So giving our students time. I love using warmup activities, using the practice sheets that they just come into my classroom, spend the first five or 10 minutes really working on this warmup page that's related to our learning goal for the week. It allows them to rehearse and reinforce different concepts, gives routine and consistency, excuse me, to my math classroom, allows for students to communicate and collaborate with themselves. And to practice during that class time. There are a lot of components then. So if all of those are high yield strategies, if we want all of those pieces in place, then we definitely have all of these different components that we need to fit in. Guided math, math journals for reflection, daily math warmups, using anchor charts, having lesson plans and teacher directed lessons, hands on learning math centers, inquiry math and tests and projects. It's a lot to fit in. So if we're looking at 300 minutes, how do we plug that in? You know that you are feeling overwhelmed with trying to fit everything together, and perhaps you're worried about where to even start. Hopefully this presentation is giving you some idea that you can make a plan that helps you get forward. Perhaps you're tired of students just not getting it, or constantly stuck in a cycle of reteaching that prevents you from moving on in your classroom, or you're tired of those disconnected math program that just does not seem to fit together. It comes down to really having two options. One, you can use the tools and strategies that I've talked and put it all together and have a system that's in place for you to follow, that you can streamline what every week looks like and you can plug and play the lessons that you plan into that concept and that format, cuz you know what it should look like so that you can put it all together. And when you have that system, it fits in your other option is that you can follow a proven roadmap that's already been created for you. And that's where I wanna introduce you to Ignited Math. Ignited Math is a full year comprehensive spiraled math program for grades 3, 4, 5, and six. It is a program that will have your weekly lessons organized into spiraled thematic units for the whole year. That includes, Six spiraled units that spiral those concepts and have them reintroduced all throughout the year, whether they are the primary concept being taught or a support strategy that's being used over and over again. It allows you to have resources and materials for each student's grade, whether you are teaching a split grade or a straight grade. So instead of starting from scratch, you get a huge head start, yet you actually have time to take the information you're gathering about students and tailor your math program to actually meet their needs because you have the time to do. It gives you lessons and activities that include your model anchor charts. So why are you here? Well, you know that you are feeling overwhelmed with trying to fit everything together, and perhaps you're worried about where to even start. Hopefully this presentation is giving you some idea that you can make a plan that helps you get forward. Perhaps you're tired of students just not getting it, or constantly stuck in a cycle of reteaching that prevents you from moving on in your classroom, or you're tired of those disconnected math program that just does not seem to fit together. It comes down to really having two options. One, you can use the tools and strategies that I've talked and put it all together and have a system that's in place for you to follow, that you can streamline what every week looks like and you can plug and play the lessons that you plan into that concept and that format, cuz you know what it should look like so that you can put it all together. And when you have that system, it fits in your other option is that you can follow a proven roadmap that's already been created for you. And that's where I wanna introduce you to Ignited Math. Ignited Math is a full year comprehensive spiraled math program for grades 3, 4, 5, and six. It is a program that will have your weekly lessons organized into spiraled thematic units for the whole year. That includes, Six spiraled units that spiral those concepts and have them reintroduced all throughout the year, whether they are the primary concept being taught or a support strategy that's being used over and over again. It allows you to have resources and materials for each student's grade, whether you are teaching a split grade or a straight grade. So instead of starting from scratch, you get a huge head start, yet you actually have time to take the information you're gathering about students and tailor your math program to actually meet their needs because you have the time to do. If you are ready, you can learn more about Ignited Math on our website it is www.ignitedmath.ca again, we are here. If you need anything, if you have any questions, please reach out and we are happy to help in any way possible please email us at info@madlylearning.com or send us messages on Instagram or our Facebook page at madley Learning is where you can find us on all the socials and we cannot wait to, uh, spend more time with you and just help you get ready for what math is gonna look like. Thanks everybody.