Core Decisions
WHAT
In this lesson plan, I want to use the task of “taking inventories” in order to have my lower level math students work on different counting and representing strategies. I also want my students to learn the importance of recounting, using other strategies, in order to double-check their answer. The students will be working in partners in order to count the number of items in their bags. Having the students do group work will encourage the students to communicate the different strategies they are using with one another. The task at hand also encourages the students to use several different tools. The first of these tools are manipulative, the students will be using the items in the bag in order to count. After representing their counting in one way, the students will be asked to double-check their counting by using a ten frame, another tool. The mathematical conversations that will surround the group work and reporting back will also be an important tool. By explaining the different counting strategies each group used, I hope students will be exposed to different ways of counting. While this goal is ambitious, I hope that the ‘residue’ of this lesson is the beginning of a foundational understanding that a ‘teen’ number is made up of a group of tens and some ones. I don’t expect that all of my students will walk out of the lesson with the beginning of this understanding; however, I do think working with ten frames is one way in which to introduce this concept (Hiebert, J. et al. (2007). What are some other more basic counting concepts you can be developing here as well? I’m thinking of 1-to-1 correspondence, improving their understanding of number meanings—how much, understanding ten as an important landmark number, skip counting.
HOW
In order to reach my objectives in this lesson, I will be using Lesson 1.9: Inventories from the Investigations curriculum. In order to have the students practice counting and representing, they will get a bag of a number of items that they will be expected to count and represent. In order to double-check their answer, they will be asked to use a ten frame in order to represent the number in a different way. I will begin by introducing the students to the concept of taking inventories. After this, I will demonstrate the activity with a student partner. Throughout the demonstration, I will ask the students a variety a questions as a way of gauging their understanding. Throughout my lesson plan, I have predicted different student responses to my questions in order to prepare for how I will further explain a misunderstood concept. I will then use the student responses to decide how much understanding of the ten frame counting I will expect to see. After I demonstrate the activity, I will put the students into partners and give them their own inventory bags to count. After the students have worked in partners, we will come back together as a whole group and one partner from each group will be asked to explain how they counted the items in their bag the first time, and then how they chose to represent that number in terms of a ten frame. This will be the more formal assessment of student understanding at the end of the lesson. I have also provided my observers with a checklist to fill out for each student during the course of the lesson.
WHY
There are two specific reasons for why I am teaching this particular lesson. The first is that there is a small group of students in my classroom who need extra practice counting and representing and my teacher has requested that I do a counting lesson specifically with this group of students. Most of the students in this small group tend to only count by ones, even though they have been introduced to several different counting strategies. Furthermore, by introducing the concept of ten frames as a way to double-check, I am also hoping to set up some of the foundation for student to understand that a ‘teen’ number is made up ten ones and some more ones. Counting from 1-20 and representing these numbers, and understanding base ten in terms of ‘teen’ numbers is also a part of the common core standards for Kindergarten.
In this lesson plan, I want to use the task of “taking inventories” in order to have my lower level math students work on different counting and representing strategies. I also want my students to learn the importance of recounting, using other strategies, in order to double-check their answer. The students will be working in partners in order to count the number of items in their bags. Having the students do group work will encourage the students to communicate the different strategies they are using with one another. The task at hand also encourages the students to use several different tools. The first of these tools are manipulative, the students will be using the items in the bag in order to count. After representing their counting in one way, the students will be asked to double-check their counting by using a ten frame, another tool. The mathematical conversations that will surround the group work and reporting back will also be an important tool. By explaining the different counting strategies each group used, I hope students will be exposed to different ways of counting. While this goal is ambitious, I hope that the ‘residue’ of this lesson is the beginning of a foundational understanding that a ‘teen’ number is made up of a group of tens and some ones. I don’t expect that all of my students will walk out of the lesson with the beginning of this understanding; however, I do think working with ten frames is one way in which to introduce this concept (Hiebert, J. et al. (2007). What are some other more basic counting concepts you can be developing here as well? I’m thinking of 1-to-1 correspondence, improving their understanding of number meanings—how much, understanding ten as an important landmark number, skip counting.
HOW
In order to reach my objectives in this lesson, I will be using Lesson 1.9: Inventories from the Investigations curriculum. In order to have the students practice counting and representing, they will get a bag of a number of items that they will be expected to count and represent. In order to double-check their answer, they will be asked to use a ten frame in order to represent the number in a different way. I will begin by introducing the students to the concept of taking inventories. After this, I will demonstrate the activity with a student partner. Throughout the demonstration, I will ask the students a variety a questions as a way of gauging their understanding. Throughout my lesson plan, I have predicted different student responses to my questions in order to prepare for how I will further explain a misunderstood concept. I will then use the student responses to decide how much understanding of the ten frame counting I will expect to see. After I demonstrate the activity, I will put the students into partners and give them their own inventory bags to count. After the students have worked in partners, we will come back together as a whole group and one partner from each group will be asked to explain how they counted the items in their bag the first time, and then how they chose to represent that number in terms of a ten frame. This will be the more formal assessment of student understanding at the end of the lesson. I have also provided my observers with a checklist to fill out for each student during the course of the lesson.
WHY
There are two specific reasons for why I am teaching this particular lesson. The first is that there is a small group of students in my classroom who need extra practice counting and representing and my teacher has requested that I do a counting lesson specifically with this group of students. Most of the students in this small group tend to only count by ones, even though they have been introduced to several different counting strategies. Furthermore, by introducing the concept of ten frames as a way to double-check, I am also hoping to set up some of the foundation for student to understand that a ‘teen’ number is made up ten ones and some more ones. Counting from 1-20 and representing these numbers, and understanding base ten in terms of ‘teen’ numbers is also a part of the common core standards for Kindergarten.
Pedagogical Focuses
- Assessing student understanding through listening to and making sense of student solution strategies and explanations.
- Selecting and using representations through pictures, numbers, words and the Ten Frame to make mathematics meaningful and draw connections between concepts.
- Selecting and using representations through pictures, numbers, words and the Ten Frame to make mathematics meaningful and draw connections between concepts.
Representation
I taught this lesson twice, first to a small group and then to a whole group because it came from the Investigations curriculum. Our math lessons occur sometime after recess at around 12:30pm so I conducted both small and whole group lesson at a similar time in the back of our classroom where our new SmartBoard was set up. Using the SmartBoard was not part of the lesson but my classroom mentor suggested that I use it which I did. The selected four students were primarily ELL students and a student who is struggling with one-to-one correspondence. The student who is struggling with one-to-one correspondence tends to count too fast. She even admits to counting too quickly so I found this lesson a way for her to practice. One of the selected ELL students has a tendency to reverse his numerals especially with numbers such as 2 and 5 so I saw this lesson as an opportunity for him to practice representing his numerals accurately. All of the students were introduced to the Ten Frame via previous math lessons in the classroom. I chose these four students hoping that they will be confident in participating in the same lesson when I teach it to the whole class. I also wanted these students to practice using Ten Frames not so much to focus on place value and teen numbers but to use them as a tool to double-check their counting strategies.
Analysis: Dimensions of Teaching Framework
Task
The first task was to introduce the students what ‘taking an inventory’ meant so I used an out-of-school context, the grocery store. I told them that people at the grocery store have to keep count of what people (like their parents or grandparents) buy so they know when to order more food and other items. I asked them, “What are some things that you buy when you go to the grocery store?” One student (who I’ve noticed rarely raises his hand in class) shot up his hand and when I called on him he replied with an eager smile, “Apples!” By hooking the students with an everyday out-of-school context, they all nodded when I explained to them that was what ‘taking an inventory’ meant. I did not expect them to learn the vocabulary word ‘inventory’ as it was a difficult, lengthy word to remember but introduced it by connecting an out-of-school idea to our mathematical focus.
Following the hook, I demonstrated the first activity by using a student, Mia as my partner to count an Inventory Bag with 10 connecting cubes. I modeled this activity by choosing a student who has a tendency to count fast. I asked her if she could count first and she did exactly as I expected; she counted 11. Then, it was my turn to count as my final count was 10. The next task was to figure out how my partner and I could fix this predicament where we both came up with different numbers. My partner suggested, “We can put the shapes in different places to count them.” I was anticipating the response, “We can recount/double-check” but to no avail most likely because they looked confused as to why we got different answers.
For my next set of instructions, I made the mistake of introducing the Ten-Frames first as opposed to introducing the My Inventory Bag handout. I also realized that I should have cut the Ten-Frame handout [pictured below under Tools] in half to display one Ten-Frame as opposed to two of them because I asked the students why is it called a Ten-Frame where Mia said, “I know, I know. Ten!” Then I checked to see if the students understood the concept that a Ten-Frame will always have ten boxes in it so I asked, “How many do you see here on this Ten-Frame?” where a student replied, “20” to which I understood why he said this because there were two Ten-Frames on the handout. I wish I had done a better job at explaining the Ten-Frame. The students were instructed to use the Ten-Frames as a method to double-check their counting as they placed one manipulative in each box. Both groups had to use two Ten-Frames so I posed the question to both groups, “How many Ten-Frames will you need? How do you know?” One student seemed confused by the question by replying with the number of manipulatives her group had, 12. I had to reiterate the question saying, “How many cubes do you have?”
“12.”
“Ok, you have 12 cubes. When you look at this Ten-Frame mat, how many of these do you need to fill up your 12 cubes?”
The student then went on to place each cube into each box. Once the student filled up the first Ten-Frame and put two cubes onto the second one, she said, “Two”.
The students seemed to have had a stronger understanding of number sense of counting by using one-to-one correspondence through the use of Ten-Frames. I believe that if I had introduced it later in the lesson I could really grasp what their understanding about Ten-Frames are.
The students’ next task was to demonstrate counting an inventory bag along with their partner. Here I wanted the students to develop the ability to accurately keep track of their quantities which did not seem to occur for either group. Mia, who helped me demonstrate the first activity, could not keep track in terms of representing her quantities with symbols onto the My Inventory Bag handout. She kept drawing squares as her manipulatives without counting them accurately. She kept claiming that she thought there were too many squares on her paper. The other group counted their manipulatives just fine until they had to represent them on paper. They both counted the first counter, then drew the first counter on paper, then they counted the second counter “1, 2” then drew the second counter, counted the third counter “1, 2, 3” and drew the third counter, so on and so on. They did this all the way till they drew the 12th counter. Three out of the four students had trouble keeping track of their quantities which might be because the numbers were too high for them. Mia’s quantity was 15 which I realize now that that might have been too high for her to develop the specific skill of accurately counting and keeping track of a quantity.
This task allowed students to see the mathematical idea behind counting, recounting, representation of their final number and the Ten Frame from a different point of view (Hiebert et al., 1997). All of the students counted by ones because the strategy was the one that made the most sense to them. After they counted their inventory bag they were instructed to represent that number onto the graphic organizer with pictures and the written numeral. The students represented their quantity with pictures that made the most sense to them. One group had ice cream sticks but they both drew rectangles as their pictorial representation. The other group had counters in which both pairs drew exactly what they saw as they drew squares with circles inside of them. Each and every student’s visual representation of this task was represented with the intention of what makes sense to the student.
The first task was to introduce the students what ‘taking an inventory’ meant so I used an out-of-school context, the grocery store. I told them that people at the grocery store have to keep count of what people (like their parents or grandparents) buy so they know when to order more food and other items. I asked them, “What are some things that you buy when you go to the grocery store?” One student (who I’ve noticed rarely raises his hand in class) shot up his hand and when I called on him he replied with an eager smile, “Apples!” By hooking the students with an everyday out-of-school context, they all nodded when I explained to them that was what ‘taking an inventory’ meant. I did not expect them to learn the vocabulary word ‘inventory’ as it was a difficult, lengthy word to remember but introduced it by connecting an out-of-school idea to our mathematical focus.
Following the hook, I demonstrated the first activity by using a student, Mia as my partner to count an Inventory Bag with 10 connecting cubes. I modeled this activity by choosing a student who has a tendency to count fast. I asked her if she could count first and she did exactly as I expected; she counted 11. Then, it was my turn to count as my final count was 10. The next task was to figure out how my partner and I could fix this predicament where we both came up with different numbers. My partner suggested, “We can put the shapes in different places to count them.” I was anticipating the response, “We can recount/double-check” but to no avail most likely because they looked confused as to why we got different answers.
For my next set of instructions, I made the mistake of introducing the Ten-Frames first as opposed to introducing the My Inventory Bag handout. I also realized that I should have cut the Ten-Frame handout [pictured below under Tools] in half to display one Ten-Frame as opposed to two of them because I asked the students why is it called a Ten-Frame where Mia said, “I know, I know. Ten!” Then I checked to see if the students understood the concept that a Ten-Frame will always have ten boxes in it so I asked, “How many do you see here on this Ten-Frame?” where a student replied, “20” to which I understood why he said this because there were two Ten-Frames on the handout. I wish I had done a better job at explaining the Ten-Frame. The students were instructed to use the Ten-Frames as a method to double-check their counting as they placed one manipulative in each box. Both groups had to use two Ten-Frames so I posed the question to both groups, “How many Ten-Frames will you need? How do you know?” One student seemed confused by the question by replying with the number of manipulatives her group had, 12. I had to reiterate the question saying, “How many cubes do you have?”
“12.”
“Ok, you have 12 cubes. When you look at this Ten-Frame mat, how many of these do you need to fill up your 12 cubes?”
The student then went on to place each cube into each box. Once the student filled up the first Ten-Frame and put two cubes onto the second one, she said, “Two”.
The students seemed to have had a stronger understanding of number sense of counting by using one-to-one correspondence through the use of Ten-Frames. I believe that if I had introduced it later in the lesson I could really grasp what their understanding about Ten-Frames are.
The students’ next task was to demonstrate counting an inventory bag along with their partner. Here I wanted the students to develop the ability to accurately keep track of their quantities which did not seem to occur for either group. Mia, who helped me demonstrate the first activity, could not keep track in terms of representing her quantities with symbols onto the My Inventory Bag handout. She kept drawing squares as her manipulatives without counting them accurately. She kept claiming that she thought there were too many squares on her paper. The other group counted their manipulatives just fine until they had to represent them on paper. They both counted the first counter, then drew the first counter on paper, then they counted the second counter “1, 2” then drew the second counter, counted the third counter “1, 2, 3” and drew the third counter, so on and so on. They did this all the way till they drew the 12th counter. Three out of the four students had trouble keeping track of their quantities which might be because the numbers were too high for them. Mia’s quantity was 15 which I realize now that that might have been too high for her to develop the specific skill of accurately counting and keeping track of a quantity.
This task allowed students to see the mathematical idea behind counting, recounting, representation of their final number and the Ten Frame from a different point of view (Hiebert et al., 1997). All of the students counted by ones because the strategy was the one that made the most sense to them. After they counted their inventory bag they were instructed to represent that number onto the graphic organizer with pictures and the written numeral. The students represented their quantity with pictures that made the most sense to them. One group had ice cream sticks but they both drew rectangles as their pictorial representation. The other group had counters in which both pairs drew exactly what they saw as they drew squares with circles inside of them. Each and every student’s visual representation of this task was represented with the intention of what makes sense to the student.
Discourse
The main discourse for this lesson was intended for the students to talk to one another. I believe that this type of cooperative learning provides a rich learning experience of accomplishing shared goals through student-to-student interaction (Gillies, 2003). My over-arching question focuses on discourse but the nature of the exchanges during this lesson focused on the student’s making sure they got the right answer. Even though both groups focused on achieving the right answer, both groups had different types of discourse. The group with the sticks, just exchanged the bag of sticks to each other, counted them, represented them onto their graphic organizer and used the Ten Frames-- all of which they did independently. The student who counts too fast was in this group. I noticed that she was drawing more rectangles than she was supposed to so I intervened by asking her to count how many rectangles she was drawing to represent her number. She openly admitted that she might have drawn too many pictures but was not sure [see right picture.] Although there was not much student-to-student discourse in her group, there was a student-to-teacher interaction. I believe that this student-to-teacher discourse monitored her understanding as it helped her realized that she got carried away. Her task of representing quantities encouraged her to reflect as she was aware that she was representing them inaccurately. She reflected on what she was doing and communicated it with me (Hiebert et al., 1997).
The pair who had the cubes [pictured left], both counted and represented their numbers similarly. After they both counted, they proceeded to represent their items onto the graphic organizer drawing what they saw: a square with a hole in the middle. But how they represented them on paper intrigued me. They both counted the first counter, then drew the first counter, then they counted the second counter “1, 2” then drew the second counter, counted the third counter “1, 2, 3” and drew the third counter, so on and so on. They did this all the way till they drew the 12th counter. Due to the fact that both partners used this strategy lead me to believe that one of them used this first, the partner shared his or her understanding and decided to utilize the method as well. I asked Daniel who was using this strategy as he was separating the cubes by drawing one cube and placing it away from the rest of the cubes, “What is this side for and what is that side for?” He replied, “This one I [have to] count and this one I finish[ed].” Asking Daniel why he used this strategy justified his thinking that that was his method of keeping track.
Tools
How do students develop meaning for tools?
Tools used:
- Pre-prepared inventory bags (colored tiles, counters, sticks)
- 3 Ziploc bags
- Inventory Handouts
- Ten Frame mats
- Pencils
- Checklist
- SmartBoard
- Student representations of items in Inventory Bags
The SmartBoard was not in the original lesson plan but my classroom mentor suggested using it because we had just received it the week before. This was my first time using a SmartBoard so I was very eager to implement this for my small group lesson. I used the SmartBoard when I modeled the activity using the My Inventory Bag Handout where I represented my quantity by drawing ten pictures and the written number 10. This supported the student’s learning of a step-by-step procedure through a visual demonstration on a larger scale.
The manipulatives were tools that helped the students focus on the correct answer as they each counted by ones. The students were very familiar with these tools as they know what these manipulatives mean to them. They know that these manipulatives help them count as they immediately began counting once their fingers touched them. The use of Ten Frame mats was another tool that was not part of the Investigations curriculum but I was eager to use it to build an underlying foundation of place value. Even though Ten Frame Mats have place value, number sense and other key mathematical concepts they supported the student’s one-to-one correspondence. As they placed one manipulative in each box, this reinforced their number sense of one-to-one correspondence.
The students used different symbols to represent their quantities. Their representation of their quantities was a tool that they developed meaning of. “In order for students to use tools wisely, they need to develop meaning for the tools… The tools can be used to solve problems and to help students develop meaning for other things. At this point, tools become real supports for learning” (Hiebert et al., 1997). The students constructed symbols that made the most sense to them. One group had popsicle sticks but they both drew rectangles as their pictorial representation. The other group had connecting cubes in which both pairs drew exactly what they saw as they drew squares with circles inside of them. Each and every student’s visual representation was represented with the intention of what made sense to the student.
Tools used:
- Pre-prepared inventory bags (colored tiles, counters, sticks)
- 3 Ziploc bags
- Inventory Handouts
- Ten Frame mats
- Pencils
- Checklist
- SmartBoard
- Student representations of items in Inventory Bags
The SmartBoard was not in the original lesson plan but my classroom mentor suggested using it because we had just received it the week before. This was my first time using a SmartBoard so I was very eager to implement this for my small group lesson. I used the SmartBoard when I modeled the activity using the My Inventory Bag Handout where I represented my quantity by drawing ten pictures and the written number 10. This supported the student’s learning of a step-by-step procedure through a visual demonstration on a larger scale.
The manipulatives were tools that helped the students focus on the correct answer as they each counted by ones. The students were very familiar with these tools as they know what these manipulatives mean to them. They know that these manipulatives help them count as they immediately began counting once their fingers touched them. The use of Ten Frame mats was another tool that was not part of the Investigations curriculum but I was eager to use it to build an underlying foundation of place value. Even though Ten Frame Mats have place value, number sense and other key mathematical concepts they supported the student’s one-to-one correspondence. As they placed one manipulative in each box, this reinforced their number sense of one-to-one correspondence.
The students used different symbols to represent their quantities. Their representation of their quantities was a tool that they developed meaning of. “In order for students to use tools wisely, they need to develop meaning for the tools… The tools can be used to solve problems and to help students develop meaning for other things. At this point, tools become real supports for learning” (Hiebert et al., 1997). The students constructed symbols that made the most sense to them. One group had popsicle sticks but they both drew rectangles as their pictorial representation. The other group had connecting cubes in which both pairs drew exactly what they saw as they drew squares with circles inside of them. Each and every student’s visual representation was represented with the intention of what made sense to the student.
Norms
The students in my classroom generally only come to the math carpet for short direct instruction and then are sent back to their seats to begin their math activity. When I transitioned the four students to the back of the room, I told the students that even though we usually do not work on the math carpet today was an exception because they were helping me with a school project. I also stated that the rules and expectations that applied in the classroom were the same here with me as well. These four students generally do not have any behavioral issues in the classroom so I did not expect to have a problem with management during the lesson.
Some norms that I did expect were for the students to count out loud so I could assess and monitor their mathematical understanding. Each student was well aware that counting aloud is a part of the classroom norm in which me and my classroom mentor assess the different strategies that they use in counting. It is a normative practice for the students to know how to utilize the manipulatives. They were aware of how to use the manipulatives fluently once they received their Inventory Bags. My classroom mentor has introduced to the students different counting strategies such as counting by ones, twos and fives. The students for this small group lesson were comfortable counting by ones which helped me monitor their understanding of one-to-one correspondence. Another norm that I set up for the lesson was that I expected the students to talk to their partner throughout the lesson which they did.
Some norms that I did expect were for the students to count out loud so I could assess and monitor their mathematical understanding. Each student was well aware that counting aloud is a part of the classroom norm in which me and my classroom mentor assess the different strategies that they use in counting. It is a normative practice for the students to know how to utilize the manipulatives. They were aware of how to use the manipulatives fluently once they received their Inventory Bags. My classroom mentor has introduced to the students different counting strategies such as counting by ones, twos and fives. The students for this small group lesson were comfortable counting by ones which helped me monitor their understanding of one-to-one correspondence. Another norm that I set up for the lesson was that I expected the students to talk to their partner throughout the lesson which they did.
Reflections
What did I learn about children’s mathematical thinking, about teaching, or about yourself?
I learned that children’s mathematical thinking is based on what they know and are comfortable with. Using out-of-school contexts and incorporating them into mathematical ideas can help build a stronger understanding as they can see the underlying connections. The students all counted by one’s because it was a strategy that they were familiar with. They also represented their quantities in a way that made sense to them. Learning comes from when students know they are comfortable using what makes sense to them.
When I uttered the first few sentences during the beginning of the lesson, I felt really nervous even though this was not my first time teaching nor was it my first small group lesson. I learned that if I do not know what to say at the start of a lesson, I tend to stammer often which is not a good form of instruction. I learned that I have to really think about what I am going to say when I teach so I do not confuse myself and more importantly the students. That nervous feeling dissipated as I realized midway through the lesson that I remembered what I was supposed to do and say from the written lesson plan. My classroom mentor has even noticed that he can see my thinking process before I teach a lesson as I try to practice what I’m going to do and say.
What questions have emerged from this experience that you would like to explore further?
Some questions that I would like to explore further from this small group lesson is how can I get students to interact with one another to share their counting strategies on their own without being instructed to do so? It being a Kindergarten class, these students tend to do what they are told. Another question from this experience has to do with group work. In what contexts do students benefit from working with partners, small group or a whole group? In this lesson, working with partners seemed to have been the most beneficial in terms of double-checking their work if both partners found different answers. For future math lessons, how can I distinguish when students will learn and benefit from group work as opposed to independent work?
How will you continue to work on the pedagogical focus you chose to focus on?
Just as I had used the Investigations curriculum I hope to continue using this as a guideline with my students. When I conducted this as a whole group, I learned that manipulatives and discourse was a vital tool in learning how students think in terms of counting, representing their quantities through pictures and the Ten Frame. I hope to use the school's math curriculum and tweak it based on my students’ ability along with my personal teaching style. Using classroom discourse throughout my lessons as a communication tool will help me focus on my pedagogical focus of assessing student understanding.
I am deeply intrigued by place value because of some background knowledge on how researchers believe that students understand place value by how their language is organized in the Base 10 system. I hope to use the Ten Frame mats and Rekenreks whenever I see fit when I teach math so I can build a foundation of place value at this age.
References
I learned that children’s mathematical thinking is based on what they know and are comfortable with. Using out-of-school contexts and incorporating them into mathematical ideas can help build a stronger understanding as they can see the underlying connections. The students all counted by one’s because it was a strategy that they were familiar with. They also represented their quantities in a way that made sense to them. Learning comes from when students know they are comfortable using what makes sense to them.
When I uttered the first few sentences during the beginning of the lesson, I felt really nervous even though this was not my first time teaching nor was it my first small group lesson. I learned that if I do not know what to say at the start of a lesson, I tend to stammer often which is not a good form of instruction. I learned that I have to really think about what I am going to say when I teach so I do not confuse myself and more importantly the students. That nervous feeling dissipated as I realized midway through the lesson that I remembered what I was supposed to do and say from the written lesson plan. My classroom mentor has even noticed that he can see my thinking process before I teach a lesson as I try to practice what I’m going to do and say.
What questions have emerged from this experience that you would like to explore further?
Some questions that I would like to explore further from this small group lesson is how can I get students to interact with one another to share their counting strategies on their own without being instructed to do so? It being a Kindergarten class, these students tend to do what they are told. Another question from this experience has to do with group work. In what contexts do students benefit from working with partners, small group or a whole group? In this lesson, working with partners seemed to have been the most beneficial in terms of double-checking their work if both partners found different answers. For future math lessons, how can I distinguish when students will learn and benefit from group work as opposed to independent work?
How will you continue to work on the pedagogical focus you chose to focus on?
Just as I had used the Investigations curriculum I hope to continue using this as a guideline with my students. When I conducted this as a whole group, I learned that manipulatives and discourse was a vital tool in learning how students think in terms of counting, representing their quantities through pictures and the Ten Frame. I hope to use the school's math curriculum and tweak it based on my students’ ability along with my personal teaching style. Using classroom discourse throughout my lessons as a communication tool will help me focus on my pedagogical focus of assessing student understanding.
I am deeply intrigued by place value because of some background knowledge on how researchers believe that students understand place value by how their language is organized in the Base 10 system. I hope to use the Ten Frame mats and Rekenreks whenever I see fit when I teach math so I can build a foundation of place value at this age.
References
- Gillies, R., & Ashman, A. (Eds.). (2003). Cooperative learning: The social and intellectual outcomes of learning in groups. London: RoutledgeFalmer.
- Hiebert et al. (1997). Making Sense: Teaching and learning mathematics with understanding. Portsmouth, ME: Heinemann.