Early Mathematics for Pre-K

Editor's note:  This text is an edited transcript of the webinar, Early Mathematics for Pre-K, presented by Caitlin Frazier, MS.

Learning Outcomes

As a result of this course, participants will be able to:

• List three strategies used to plan for integrated and environmental mathematical experiences in various learning contexts.
• List five strategies used to build on children's intuitive, informal notions and encounters relating to math.
• List three indicators of high quality early mathematics classroom environments.

Take a moment to think about your class and your daily schedule. Maybe your schedule used to be a lot more flexible than it was now but it's slowly been filled up with those demands from administrators. In the age of standardized testing these demands are very real and as we all know they often center around language and literacy. They are trying to get kids ready to read as soon as possible and focusing time and effort on letters, letter sounds, beginning sounds, ending sounds, sight words, print awareness, and pre-writing. We know that this has become an early childhood priority and whether we like it or not, it's definitely reflected in our schedules and our philosophies as educators. Figure 1 shows an early childhood schedule from a teacher who has her children for a 3 hour session each day. 

Figure 1.  Early childhood schedule.

Once the overlap between the morning and afternoon session is removed, she ends up having approximately two hours of high quality time to dig into those rich, meaningful experiences and all those high quality preschool things that we want to do to prepare our children for the next grade level. The day is fast, time is minimal, and the priority tends to be language and literacy. You can see this reflected in this schedule with language and literacy in the areas of the read aloud, the critical thinking, the book club, and the SEAL and Project Based Learning areas on the schedule. I know the importance of language and literacy in the early years, but I also know that math has been getting lost in the shuffle and it barely makes an appearance sometimes in our quick days in early childhood settings. Typically when it does make an appearance, it might show up as a whole group calendar time, which you do see on this schedule as well. We know that children learn best with hands-on experiences and depth of knowledge questioning, but we continue to use our very limited time on rogue calendar activities when young children are just repeating those memorized facts that are so often over their heads or not something that they truly grasp and in general, not really contributing to their overall foundational understanding of basic math principles.

Why Early Math Matters

I think it's important that we take a look at our priorities, philosophies, practices, and schedules, to try work on math skills in early childhood settings, beyond calendar activities. We all know the value of math in our lives as adults, and that it is necessary for children to learn math skills. I was introduced to a study that opened my eyes and convinced me to re-evaluate my practices in an early childhood setting. Greg Duncan, an economist and an education professor at the University of California-Irvine, and colleagues did some research showing why early math matters (Duncan et al., 2007). This study examined six longitudinal sets of data and examined links between various school readiness indicators and later academic achievement. The results showed that the strongest predictor of school success was early school entry mathematics, followed by reading and attention skills. The study found that if young children had strong math skills before they even entered kindergarten, they saw it reflected in grades five, six, eight, ten, and later school successes. This study prompted me to re-evaluate my early childhood priorities and to make math more of a priority.

What Can We Do?

There are many things we can do to make sure that we are giving our children a high quality early math experience, making it just as big of a priority as our language and literacy curriculum tends to be. Some of these things include:

• Prioritize early mathematics
• Provide frequent opportunities for exploration and discovery
• Recognize children’s interest in making sense of their world with mathematics
• Build on children’s intuitive, informal notions and encounters relating to mathematics
• Supply mathematical language and procedures

Let's talk about high quality, student-centered math environments in the early childhood setting. Figure 2 is a excellent example of how you need to let children lead in these educational experiences and serve as a facilitator, specifically with mathematics. 

Figure 2.  Early childhood math activity with manipulatives.

In this example, I had set up an activity for children to use the cards pictured in order to take a look at numbers and match hands-on manipulatives with the number and see that quantity relating to the number. I walked away for a few moments and when I returned I had a young child who had taken the manipulatives and decided to build the numbers instead. Following building the numbers one through five they went on to go play with the manipulatives on the other side of the table and were kind of acting out a play-like scenario with these little teddy bears. I thought that creating the quantities and matching it with a number card was most appropriate and what I wanted the objective to be in this activity.  However, after reevaluating and seeing where the children wanted to take it I thought it was a wonderful experience for them to build these numbers and to see how the numbers are formed using the hands-on manipulatives.

High-Quality Student-Centered Math

In a high quality student-centered environment we will see some of the indicators listed in Figure 3. 

Figure 3.  Indicators for teachers and students.

In the left-hand column are some of the things we will see teachers do in high quality early childhood math environments. Teachers will be listening. There's a lot of listening going on in these mathematical discussions. Teachers will also be making sense of children's thinking. They will be listening to what children are saying, making sense of it and then using the sense that they make of it to ask guiding questions of them. Teachers will also be adapting and differentiating. It's not always that we get to just work one-on-one with a child and make it a truly personalized experience. We have to take the time to make sure that we're reaching all learners by adapting and differentiating based on the children's understanding of mathematical principles. Next, we will see a lot of teachers that are assessing and planning. This could happen in the moment and this could also happen down the road after they get a break from that setting where they're actually teaching in the activity, facilitating the activities. This assessment and planning of course will bring them to the next step in deciding what to do next to bring their learners to their highest potential.

In the right-hand column are some of the things we will see students do in high quality early childhood math environments.  We will see students that are using tools to learn. Some of the tools they might be using include ten frames, counting mats, egg cartons to keep track, manipulatives, unifix cubes, and hundreds charts. There are all sorts of tools that can be accessible to students. Another thing that you will see in a high quality environment is that students are using strategies. Some of the strategies they might be using include using the tool of the egg carton and then using the strategy of putting one manipulative in each egg carton hole in order to keep track of their count. Another strategy they might be using is drawing pictures to keep track of their count. They might be making little tally marks to see how many they've counted or circling items to see what they've counted and keep track of that quantity. Another thing we will see in these environments is that students are collaborating. This is not done in isolation. It's often done in partner work, group work, or small group work. There's a lot of discussion going on. This is a lively experience. Math should be fun. Math should be joyful. We will see that in their interactions around the content and with their peers in this collaboration. Another thing we will see here is students that are explaining their thinking.  With this, discussion is going to dig deep into the true understanding of those foundational principles of math. It's not going to be that quick memorized fact. It's not going to be a ROTE regurgitation. It's going to be truly explaining their mathematical understanding.

Preschool Mathematics Learning Contexts

We must help children learn and develop math skills and concepts:

• In an integrated fashion with real world applications
• By finding teachable moments in everyday activities
• During movement activities, songs, stories, indoor/outdoor play & mealtimes
• Using technology

Another way we will help develop this high quality early childhood math environment is by making sure we have math in various learning contexts throughout the day. In Figure 4, you'll see that there are picture cards that have different types of patterns on them, such as ABC and AAB. 

Figure 4. Early childhood math activity with patterns.

This was a fine motor station in a colleague's classroom that she had shared with me. They have young 5 year olds and they make it a point to have fine motor activities every morning. Though fine motor is specifically listed on their schedule that you saw earlier, there's a lot of integration going on here. We have beads and pipe cleaners that the students are using to build those fine motor muscles in their hands and build up that hand strength, but also to create these mathematical patterns and have that mathematical concept tied in to the fine motor learning context. I thought that was such a great example of math in various learning contexts and it shows that we must help children learn and develop math skills and concepts in an integrated fashion with real world applications. We will see those at center time across all the centers. We will see them with those real world applications relating to things that children are interested in. Another way that we will help children learn and develop math skills and concepts is by finding teachable moments in everyday activities. We will make it a point to pay attention to it when they're tying their shoes and talking about the number of shoelaces, just things that are everyday things that we have to do that we can tie in a little bit of math to. We will integrate it with movement activities, songs, stories, indoor play, outdoor play, and mealtimes. These are all wonderful times to bring math into your everyday practices. The last one that I wanted to touch on was through technology. I think that technology is such a huge part of the lives of our children in this modern age. Although we don't want them to sit in front of a screen endlessly and just be passive consumers of technology we want them to really use technology to build their understanding of math and help support it because it's such a meaningful part of their lives as young children these days. A great example of using technology to help children develop these math skills and concepts is by having them go on a number hunt. Many teachers use letter hunts and have children go around the room looking for anything that is the letter L. They may have a shape hunt where children go around the room looking for anything that looks like a square. An idea that I've seen is to use an iPad or an old cell phone or anything to capture a photograph and asking children to find anything around the room that's a quantity or a set of four. Children will go around the room and see if they can count four things or if there's already an arrangement of four things, snap a quick picture, and then they show their peers and their teachers. It's a great way to use technology in a more active fashion and to help them build that understanding of mathematical concepts.

Children will learn and develop math concepts best out of isolation and in various learning contexts such as small groups, large group, individual, exploration and integrated. Again, in Figure 5 you can see a fine motor example similar to the one I mentioned previously where they're using tweezers and a 10 frame to count out quantities. Here they actually have those quantities printed right on the 10 frame, which is a great resource that you could make. They are using the tweezers with pom poms, placing them within the 10 frames one at a time. This is helping them keep track of that one-to-one correspondence to match that number listed on their 10 frame. This is a great example of that integrated context for early math.

Figure 5. Early childhood math activity with 10 frames.

Integrated and Environmental Mathematics

Next we're going to talk a little bit about integrated and environmental mathematics. A play cash register is something that most people have in their classrooms, often in the dramatic play center. I think it's a great example of environmental mathematics. It's in the kitchen, which is supposed to be a play area of course, but we know how much learning happens in the kitchen in the early childhood classroom. I don't know how many times I've had to solve a social emotional crisis with children who are all hoping to get on the cash register and they were having to deal with how to share the time on that cash register. The cash register is a great example of how we can have these toys and games within our preschool classrooms that will help children build those math principles and develop a deeper understanding. In addition to the cash register, you can have fake money. Fake money is a great thing for young children because they think it's real and they think it's really exciting to have that money, to trade with the money, and to make those sales. Fake money is something that I think is a wonderful example of how we can have math in our environment. You could stick labels around your classroom of different items costing different amounts of money. If you're in that preschool setting you might have something that says five on it for the five dollar and you might have something that says one on it for the one dollar or you could get even tricker and say this costs three dollars and see if they can figure out how to spend three dollars on that transaction in the kitchen center. That's a great example of environmental math, having those toys and games around your classroom that are going to build those concepts because they excite children and are engaging. Environmental mathematics is making sure that your classroom environment is rich with resources, toys, and tools and it's just as important as having a print-rich environment to support language and literacy.  Environmental mathematics includes:

• Accessible Maniplatives/Toys/Games
• Accessible Resources
• Accessible Tools

Accessible Maniplatives/Toys/Games. Creating this environment will involve making sure that there are all sorts of accessible manipulatives, toys, and games. The cash register was a great example. Another thing children really enjoy is a stopwatch. It's actually just a kitchen timer, but you could use an actual stopwatch or a kitchen timer that just has those numbers on it and it beeps when it's done. It excites children to no end. They can see the numbers tick down and talk about how long something's going to take them to accomplish. Often times it might turn into a race. You could have those stopwatches outdoors to integrate the outdoor playtime with that early math skill. Stopwatches and kitchen timers are a great example of those manipulatives and toys that integrate math into the environment. I also think of old cell phones that have the punch numbers on them. Children love to play with those and pretend that they're making phone calls. They might even write down those phone numbers and that really helps them develop this use of numbers that might be important to them someday. Also, clocks and watches are fun for children. I know children are thrilled when they get to put a watch on their wrist. Any old watches or child-friendly watches will work, including those with story characters, as they are exciting to children. They display numbers and help children develop those concepts of time and numbers. Measuring tapes, rulers, and any other things that might become toys and games could be used throughout your classroom in different centers and different activities.

Accessible Resources. Another part of environmental mathematics we want to be sure to have is accessible resources. As opposed to manipulatives, toys, and games, when I think of resources I think more specifically about number lines, number words, number charts, number posters, and math books. I think about all these things at the child's level, making sure that it's child friendly and stored right at their height or being accessible on tables, on desks, in cubbies, outside in the outdoor environment, and at mealtimes. Making these resources something that children see all day long in different areas in different environments and in different activities is very important.

Accessible Tools. The last thing about environmental mathematics I wanted to talk about is accessible tools. These tools include the egg cartons that I mentioned, the ten frames, and clip boards. I love having clip boards accessible throughout a classroom as well as having that paper and pencil for them to be able to record and write any of their mathematical findings or anything that they're counting. Having tools accessible to children is a great way to help them build those understandings of concepts.

Integrated Mathematics

Once this environment is crafted to facilitate early mathematical experiences you will find it's so much easier to integrate math daily and throughout the course of each day. There are three ways we can do this. The third way can be integrated into both, but three ways that we can do this is by integrating collections, integrating story problems, and integrating number talks throughout the day. 

• Collections 
• Story Problems
• Number Talks

Collections. When I discuss collections in early math I think about having a group of items to count that the children are interested in such as favorite hobbies, favorite characters, animals, foods, items from nature, items from home, et cetera. Collecting items from nature is really fun because you can bring your collections outdoors. I'm always encouraging getting children and the classroom outside, so going outside to count items is a wonderful way to count collections. Collections can also be tied into any theme, curriculum, or activity. An example of this is if you're studying spring, students can count flowers and seeds. Children will be using tools and resources to help them count and then recording this count on a piece of paper and a clipboard to bring it to another level.

Dinosaurs are something really fun that children love. Maybe there's a young boy in your classroom that's obsessed with dinosaurs, so he brought in some dinosaurs from home to count or you might have some in your classroom they can count. A child can count these dinosaurs - one two three four five. This could be a challenge to a preschool child counting those five dinosaurs, especially at the beginning of the year.  After counting the five dinosaurs he might grab a pencil or a crayon and see if he can draw a picture of what he counted. You might ask, "Can you show me what you counted?" You might see him make some tally marks or circle the items by placing the items down onto the clipboard or wherever he is - whether it's the floor, the table, or a desk. These collections and recordings help children to see that this abstract idea of early math can be very real to them. They see that what they counted can also be written down and recorded in a way that could be explained without the manipulatives or objects. Then they might be able to take it to another level and write down this number. Maybe they can't, maybe you will give them a highlighted version to trace it. Maybe they can find the number in the classroom by knowing that the word five is going to look like this shape. You might find a clipboard that has a ruler on the side of it. I love clipboards that have the ruler on the side, not really for the sake of the ruler in this example, but when a child is recording this collection and this count he is able to look right on the side of that clipboard and say, I know that I'm looking for the number five, one two three four five. This is what the number five looks like. Maybe I can try to write it down. It's not going to look beautiful because we're working on those fine motor skills in early childhood, but it gives them an opportunity to say hey, I can write this number and I can show you what this represents. Another thing with collections that I wanted to touch on briefly before we move onto the next is that the recording part is a really interesting piece of a collection because you'll find that often the recording and the manipulatives aren't going to match perfectly.  A child may have counted five dinosaurs but the recording is going to say that he only counted four.  This is a wonderful opportunity to discuss early math and dig in to how do you know that you counted four if that's what your recording says and seeing if they can match up the manipulatives to each item on the recording and see where this mistake might have been. Did they have more manipulatives? Did they have less on their drawing? It gives them that opportunity to say hey, does this match? Is what I counted and this abstract version of what I recorded the same? Should it be? It gives them the opportunity to reconcile and take the time to understand if it aligns. It's a wonderful way to discuss these mathematical concepts and give children that deeper understanding of math.

Story Problems. Another thing we can integrate throughout the day across the curriculum is story problems. Manipulatives can be used to solve problems about anything. This could be family, age of siblings, number of pets, food, hobbies, sports, thematic content, or outdoor content. If we're studying spring we're going to get some seeds and talk about the seeds and a farmer. You might tell a story about the seeds, such as, We have seven seeds here and we're going to count those seven seeds, but the farmer really wanted to plant some carrots and so he took away one seed. We can take away one seed and hand it to this imaginary farmer. How many seeds do we have left if that farmer took away that one seed? These are really quick little problems that we can get our children to solve in a hands-on way through the day across the curriculum in different activities.  They will be interested in them and they will be really excited about solving these problems with manipulatives, especially if it is things that are relevant to their lives and to their interests. It's giving them all sorts of high-level math experiences. They will do subtraction and addition and do it well.  They will do it with this hands-on experience that's going to give them that foundation that will help bring them to being able to understand higher level addition and subtraction concepts.

Number Talks. Number talks give students the opportunity to:

• Investigate mathematical relationships
• Communicate different ways of making sense of the math they are seeing
• Explore different mathematical strategies
• Listen to & respond to mathematical thinking
• Become engaged in thinking about solutions to everyday situations
• Talk about the problems, become drawn into the process of investigating and solving problems (e.g. balancing a block structure, dividing crackers evenly)

Number talks are taking story problems, collections, and all sorts of mathematical experiences to the next level. I like to compare number talks to a shared writing experience.  I'm sure many of you are familiar with shared writing experiences where you have a group of children (small or large, depending on your environment and your schedule) around you and you write out everything that they say or everything that you're discussing.  They can see how the word translates to paper. I think of a number talk in a similar way because it could start as a collection or a story problem, but then you gather that small group together and discuss all of these different things. You can discuss number sense, counting, cardinality, equivalence, and nonequivalence. You can discuss calculation and place holding, all in a child-friendly and developmentally appropriate way but in a way that helps children to see their thinking mathematically and it's not just writing. You can draw pictures and demonstrate and have many different examples as you talk through these mathematical experiences that children have in a way that gives them a broader understanding. Number talks are going to give students the opportunity to investigate mathematical relationships. It's going to help them communicate different ways of making sense of the math that they're seeing by hearing a teacher modeling this language, by hearing their peers explain some of this thinking that they were doing. It's also going to explore different mathematical strategies.

If a child created a collection or solved a story problem in a really unique way, you can help him help his peers by having a number talk abound that experience.  You might ask the children to come see how Johnny solved this problem. You could gather them around and discuss the strategy that Johnny used to be able to solve that problem. You might say that he was having a really hard time keeping track of his count and he used the egg carton and put one object in each hole to be able to see his count and to come up with the answer at the end. He figured out how many there were. Sharing these strategies with children, talking about it, and putting it at the front and center of the classroom for children to use as a resource and strategy is going to help them develop that deeper understanding of early math concepts. With a number talk, we take the time to listen. That listening is key in the early math environment for depth of understanding. We can listen to what children are saying to know what they truly understand and then we can respond to their mathematical thinking. We can build on it by meeting them at their level and then challenging them just in that zone of proximal development to push them just far enough. Number talks also give students the opportunity to become engaged in thinking about solutions to every day situations. It will help them translate this concept across the day, in school, and out of school. We're showing them that math is not used in isolation. It happens all throughout the day. A number talk shouldn't be something that just happens at your math time. It should be something that could pop up at any point in the day, even at snack time or at outdoor playtime. Number talks should be integrated throughout the day. Number talks also give students the opportunity to talk about the problems as they are drawn into the process of investigating and solving problems. It's kind of like a little mystery. It gives a little bit of detective work to children to say hey, how can I solve this problem? How did you solve this problem? How can we make sense of the world around us using math?

Depth of Understanding in Early Mathematics

Another area that we're going to discuss in high quality math environments is depth of understanding in early mathematics.   FIgure 6 shows students that are counting collections and recording what they counted.  

FIgure 6.  Children counting collections.

This collection was little recyclable materials that I had laying around and they just thought they were very fun. They were squishy and offered a sensory experience as the children were counting and recording their count. You'll see the child on the left has her manipulatives on her recording sheet and was circling them to keep track of her count. The child on the right has her manipulatives off to the side and she was counting using tally marks on that recording sheet. In this example, you can see the differentiation and understanding. The next step after the children count their collection is to sit on the rug with the children or sit at the table and ask them questions, digging into their mathematical thinking, the process that they went through to figure out how many items were in their collection.

No Rote Math. Other ways to increase childrens' depth of understanding in early mathematics include:

• Keeping it open-ended
• Fighting the urge to solve their problems
• Higher order thinking questions
• Supplying mathematical language

An open-ended experience like that lends itself to the true foundational depth of understanding in early mathematics. It's giving children that rich experience to help tie their knowledge to something that's hands-on and meaningful to them. It's important to minimize our focus on rote math. The term "rote math" makes me think of the daily whole group calendar with rote repetition, children memorizing numbers and facts. I can't tell you how many times and how many different young children that I've met in my career that are wonderful children and students and incredibly bright and hard working and can count to 100 at four years old, but really don't have that true understanding of quantity. They don't have that true understanding of number sense. They were just having that content pushed on them, possibly at an early age before it had any personal meaning to them, and they were really good at memorizing.  These children can count to 100 and people often say oh my goodness, they are so good at math. I can't believe that they are going to be mathematical all-stars for their entire lives. It's really a false vision because these children are struggling with those concepts and don't really have anything to attach it to. It's just a memorized sequence that they've been able to regurgitate and repeat. Again, we need to make math more than just the calendar and keep it as far from rote as we can by making it open-ended and constantly trying to keep these experiences child-centered. There's no right or wrong answer. They're just exploring math, discovering math concepts. It's also important to fight the urge to solve their problems.  This is not always easy because they will ask you and you'll want to help them, but we can't help them solve the problems. We need to provide them with higher order thinking questions and get them thinking deeply about math, which might not be easy or quick and they might ask you to solve their problems.  It's imporant to make them persevere. Last, we need to supply them with mathematical language. 

Questioning in Early Mathematics

Teacher as Facilitator - Build on children's intuitive, informational notions and encounters relating to mathematics

With this open-ended hands-on math we need to hold frequent discussions and answer children's questions.  We should ask questions that will get them thinking about math. This will allow us to build on their intuitive, informal notions and encounters relating to mathematics. This will provide the personalized learning experience. It will give them real-time scaffolding, in the moment differentiation that's going to help them help the teachers meet the children at the zone of proximal development to push them to the next level.

Open-ended questions include asking...

• How do you know?
• Why?
• What if?
• Tell me about...

Some of the open-ended questions we're going to ask them include:

• How do you know that this is a square?
• Why is this not a rectangle?
• If it's a square, why is it not a rectangle?
• What if it only had three sides?
• How would that change this shape?
• Tell me about how you counted this set.

All of these questions that we pose to children can prompt a variety of answers and will give you a true look into their understanding of mathematics. It's not just what number is this, what shape is this? A child can just repeat or copy a friend. It might not be a true view into what they understand. But open-ended questions allow them to share their perspective.  When you get to know their perspective it helps you to help them get to the next step in their understanding. With questioning and open-ended math we want to be sure that we're giving children time to explore and understand and that we're not supplying the answers for them.

Perseverance in Problem-Solving

There's such a misunderstanding from the old drill and kill practices and times table math experiences you may remember from when you were a child in school. At that time, children were expected to be really quick with their math and spit out the answers with immediate and automatic responses in math. We all know that this is not the reality of math out in the real world and we need to help our children to develop the perseverance and problem solving that's going to help them throughout their lives in the math experiences that we face daily as adults. The answers don't always come quickly as I'm sure you know and you've experienced and we need to teach children that patience and perseverance is going to help them solve every day problems.

Supplying Mathematical Language

As we provide the high quality math environments that we've been discussing it's really important that we constantly supply the mathematical language and serve as a model as the teacher all day long, not just at math time. Some of the language we can use includes:

• Number words
• Counting on/adding to/joining sets
• Subtracting/taking away from/separating sets
• Fewer/less than
• More/greater than
• Same/equal/match
• How many in all/total/sum
• Shapes- corner, side, curve, straight

We will model mathematical language in the morning at arrival. We will model mathematical language in the restroom when they're counting and washing their hands. We will supply mathematical language at snack time when children are counting out how many crackers they have or how many cookies they have. We will supply mathematical language at recess time when we're discussing how many rocks Johnny had collected that day. Also, we will make sure that this mathematical language is all day long, integrated, and the teachers are modeling it with parallel talk by talking about what they're doing using these mathematical words and this language. Some of this language that we can try to focus on in our daily experiences includes number words. We will tie number words to anything that has any meaning to these children making sure that it's relevant to their lives. We will make sure that numbers and quantities have meaning to them, that they're not just a number on the calendar board. We will also supply mathematical language around counting on, adding to, and joining sets. We wil use this terminology at arrival, snack time, and throughout the day. These are going to be things that we're going to say constantly that supply the true mathematical language in different contexts and in different settings.  Let children know that they can add to their pile of cookies by joining sets with a friend's pile of cookies. They likely won't do this, but you know you're using this language all the time and using it in ways that's meaningful to children. Similarly you will talk about subtracting and use the word subtracting. You will talk about taking from and separating sets. You will say these things throughout the day in those meaningful, real-life experiences. Fewer than, less than, more, greater than, same, equal match, how many, and all. What is the total? What is the sum? It's also important to discuss shapes and geometry with corners, sides, the curve, and straight edges. Using all of these words, phrases, and mathematical language in different contexts is going to help children realize that math doesn't have to be something that's in isolation during math time. It's going to be something that they will see and talk about during the school day, at home, on the school bus, and on the weekends with grandparents and that math is a part of every day real life and these words are a part of every day real life.

Action Steps for Everyday Use

We have covered a wide variety of ways to help improve the math experiences of our little learners.  In order to put it all together and start putting it into action immediately in your classroom settings, here are some of the things that you can do to take the next step in integrating these math ideas into your practices. 

1. Scheduling time
2. Adapting and supplementing curriculum
3. Engaging children in counting and problem solving
4. Selecting and posing story problems
5. Sharing student strategies
6. Eliciting student thinking
7. Using knowledge of student thinking to guide instruction

Number one is scheduling time. We started out this discussion on time. I know there's never enough of it, but I think it's really important that you give math the time that you're giving other content areas in your classroom. While language and literacy are core components of our early childhood curriculum, so is math. We need to schedule time appropriately and reflect that math is a priority in our classrooms. Also with scheduling time we want to make sure that we are scheduling enough time to go in depth with this understanding of early math. As I mentioned before, we're not going to schedule a 20 minute calendar where children are ROTE repeating and regurgitating answers. We want to schedule a 30 minute exploration time where children are counting collections, digging into story problems, and having number talks. All of these things can be a supplement to your curriculum, of course, but we want that time for them to think and explain their thinking and be pushed to the next level. That takes time and we want to schedule an appropriate amount of time.

The second action step is adapting and supplementing curriculum. Everything that we've discussed today can be used with any curriculum, as a supplement to any curriculum, or integrated right into any curriculum. I don't want anyone to think of math as a scripted curriculum that you must do. I think that these mathematical concepts we've discussed today are universal. They could be used in any classroom with any curriculum. You can start to take a look at how you want to add this in and supplement these ideas into your everyday practice, whether it's during your math block or during center time throughout the day.  Think about how you want to start adapting and supplementing your curriculum and your daily practices.

Number three is to constantly engage children in counting and problem solving all day long. It's very simple to start integrating that into your practices. As we mentioned before, it's just making sure that you have the environment prepped with the resources, tools, and strategies available for children to start counting and problem solving all day long.

The fourth action step is to select and pose story problems. It's important to think about story problems ahead of time so you're prepared to do on the fly learning when you see a learning opportunity arise.  For example, you may see children playing with a pile of seeds (part of your springtime theme) and you want them to start talking about story problems. You might have a pile of cards that you keep in your pocket that you can pull out at any time with a few different scenarios.  You can differentiate them by having green cards for an easier level, red cards for a higher level, and yellow cards for a middle level. If you are working with Johnny and see that he needs more of a challenge you could pull out a different color card with a story problem that will challenge him a little bit more. It can be very helpful to have these story problems pre-made so they can be adapted depending on the manipulatives that you're using, the situation, and the activity. These quick, easy prompts are going to help you as a teacher and serve as a reminder that you want to be integrating these story problems throughout the day in your classroom.

The fifth action step is to make sure that we are constantly sharing student strategies. This helps take the learning and teaching away from the teacher and helps the students to teach each other. It helps them to understand the content more because they really tie it to their peer that shared the strategy with them. They might have Johnny show them the egg carton and you could call it the Johnny strategy. Johnny's strategy is to use that one-to-one correspondence to keep track of his count. Sharing student strategies is a way to take the teacher off the stage and help children collaborate and learn together from their experiences.

Number six is eliciting student thinking. All day long we need to elicit student thinking about mathematics. This involves scheduling time and a little bit of prep about what we're going to ask them to get that student thinking to come through.  We will make sure that we're constantly asking children how they know, why this is the way it is, or what if something were different. We need to ask them higher order thinking questions to get to the depth of understanding.

The last action step is to use childrens' knowledge to guide our instruction. It might guide our instruction immediately, for the following day, or for the following week. It's important to take the time to understand what children are thinking, why they're thinking the way they are and then plan and pose for those next steps.

Summary

In summary, today we discussed strategies to plan for integrated and environmental mathematics in various learning contexts. We talked about building on a child's intuitive, informal notions and encounters relating to mathematics. We also talked about quite a few indicators of high quality preschool mathematics classroom environments that help build strong foundations for young children in early mathematics. If you have any questions or comments, please feel free to reach out to me anytime. You can contact me at the email address listed on your handout. 

References

Duncan, G.J., Claessens, A., Huston, A.C., Pagani, L.S., Engel, M., Sexton, H., ... Duckworth, K. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. doi: 10.1037/0012-1649.43.6.1428