The math lesson I observed this week was a basic counting exercise followed by a game. The teacher warmed up the student by presenting a CCSS objective for kindergarten saying “We can count to 50.” The whole class counted from 0 to 50 together while clapping their hands on each number. Then all the students got out their mini whiteboards while the teacher instructed from the document camera with her own whiteboard. She asked 3 questions which were written on pieces of paper she put under the cam. “Count the turkeys and write the number”, “Count the pilgrims and write the number”, and “Explain how to count these pilgrims” were the three questions. She covered several objectives such as being able to count by 1’s and 2’s as well as verbalizing their rationale. The teacher would present the questions, have students read them aloud, allow time for students to work alone and solve the problem, and then she asked them to show their work as formative assessment. When different students found different ways to count the same objects (by 1’s and 2’s and 3’s) she would write them in number sentence form. For example if J counted by 2 she would write 2+2+2=6 pilgrims on the doc cam, and if R counted by 3’s she would write 3+3=6 pilgrims as R said explained how she counted.
The second part of the lesson was a class math game which helped the students work on greater than and less than understandings. A student thinks of a number between 0 and 20, writes that number on a small board hidden from the group, and the students guess the number. There is a number line on the board and as they guess the student tells the rest of the group if the number is greater than or less than the guessed number.
Student 1’s Perspective:
I wonder what’s next? I had a really fun time at recess today. I wish I could have had time to finish my lunch. Oh it’s time to get out my whiteboard! Yay! I looooveeee whiteboard time! Drawing is my favorite. I think I will draw a mouse. I like mice. [Redirected by teacher] Oh, I guess I should be doing this. I really want to learn, I’m just so tired and bored. I hate sitting unless I can move my hands or pretend to make a rocket. I like rockets and planes. There are 6 turkeys I think. No 16. Wait how do I write 16? Is it 61 or 16? Those teens are tricky! I think I’ll make a really good drawing and Ms. E will think I’m smart! Ms. E! Look at this!!! [Redirected] Oh yah I gotta get back to work. [Move to rug for game] I’m so tired from trick or treating I’m just going to lie down. I don’t like my boots. Hey they make a cool squeaky sound if I take them off and rub them together! Cool!
Student 2’s Perspective:
I like counting! I count all the time at home. I counted 34 pieces of candy from my Halloween bag last night! I know the answer! This is easy when you count by 1s. I might try counting by 2s someday too, but for now I like counting by 1s so I will write that down on my board. Oh Ms. E saw my number sentence and she said I did a good job. I will raise my hand the next time she asks a question because I bet I could figure out the answer. Oh we get to play Monster Squeeze! This is my favorite game ever. I hope I get to be the number guesser. I bet if I sit quietly and raise my hand I will get called on. School is so fun!
Student 1 and Student 2 had very different interactions with this lesson. Student 1 was not very engaged. He did enjoy the drawing aspect of the lesson, but he did not use his drawings to help understand or express his mathematical process. Instead he practiced his own doodles. He wasn’t acting out, but he wasn’t learning either. When he was off task he would doodle silently or stare off into space or lay down on the carpet. My best guess as to why he was not engaged during lesson was because it was the afternoon and he was tired (especially having it be the day after Halloween), he wasn’t sure what to do (perhaps he didn’t think he was good at the lesson), and he wanted to do other things instead of his work. Student 2 in contrast was highly interested. She seemed to really want to please the teacher as well as find out the answer. With each question she asked or response she shared she received positive feedback which made her visibly happier and more excited to share with the class again.
I think Student 2 had great practice with counting discreet objects by 1’s 2’s and 3’s. She was also able to use the terms greater than and less than correctly to figure out an unknown number. Evidence of this learning came primarily through my observations of her participation. The teacher would ask for answers to the problems and she always raised her hand. The teacher would have the students write their responses along with a picture to justify their answer on their mini whiteboards, and Student 2 always had an appropriate, correct response. Student 1 showed little evidence of having learned anything. When he was called upon by the teacher to respond, he had little to offer. Instead of writing the answers or illustrating pictures to try to figure out the problems he would doodle on his whiteboard. He was completely inattentive during the greater than and less than game.
My mentor teacher is excellent at what she does, so it is very difficult to try to think of ways in which I would have better engaged and taught Student 1. I think his inattention came from a place of feeling tired and completely unmotivated. Since this is the case, I could try to work mathematics into the morning lesson time as much as possible. Beyond that I would get to know the things that make Student 1 excited. I know he has an affinity for mice. Perhaps I would try to work in more story problems involving mice in my math lessons. I have also noticed this student loves making tangram and unifix cube creations during free time. I don’t think my mentor teacher has involved these manipulatives in any specific math instruction, so I’d be really curious to see if using these and providing very clear instructions would help this student to engage in the math instruction. I would also try to check in with this student very regularly during class wide instruction so that I could check his progress and answer his specific questions.
This observation taught me that mathematics instruction in particular is only effective when differentiated. Students sitting right next to each other, hearing the exact same lesson, getting the exact same opportunities may learn completely different things throughout the course of the lesson. It is vital to understand each student’s learn style and motivations. When a teacher can engage and differentiate, she can make sure each student is learning what they need to. Our goal is to meet all students’ needs. In order to meet that goal I know I will have to understand what each student needs. In my classroom I foresee a lot of one on one progress checks. If I have the help of in-school tutors or volunteers I will use them to help me differentiate instruction as much as possible and meet students needs on both ends of the spectrum.