1. Describe how your teacher teaches a mathematics lesson. Is there teaching involved or review? Or telling a procedure? Is it a problem-based lesson? Are students learning conceptual knowledge or procedural knowledge. Are any manipulatives used? If so, describe how.
2. Did most of the students grasp the concept? What helped the students learn?
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1. The lesson that I saw my cooperating teacher teach was really great! She used candy hearts (in light of Valentine’s Day) as manipulatives for the students. First they estimated how many they had, then they counted them out. They also used past math skills to count in groups of 2, 3, 4, and 5. The students were able to find the remainder of what was left out of these groups as well. There was a worksheet that accompanied this lesson and helped the students answer questions and keep a record of what they were doing so they could see patterns when the activity was completed.
During this lesson there was not a lot of teaching involved because the students had enough background math knowledge and were also well guided by the worksheet that they were able to learn and work on their own. The students were learning procedural knowledge because they were learning how to grouping numbers which will then lead to an understanding of multiplication.
2. The students I worked with totally grasped the concept of the math they were doing and they could see that there was a connection with what they were doing that could lead to multiplication. I think the activity was really fun for the students and they really liked using the candy hearts. They also used 100’s boards, which were used to show the difference between numbers. Because there were 4 adults in the room the students were able to get 1 on 1 attention and benefited in that way as well.
1. My teacher has just begun to teach place value to her students. She started her mathematics lesson by passing out paper and varying handfuls of macaroni to each student. She then instructs the students to separate the macaroni into groups of ten and glue the groups onto their paper. The remaining noodles are also glued onto the paper. Then she had students place a circle around each group of ten, but not the leftover noodle group. I guess this could be considered problem-based because students started with pieces and had to get to an end result. The teacher went up to the board and demonstrated with a marker what the students’ papers should resemble. Then she showed students how to write the number. For example “3 tens and 4 extra is 34”. She told us she starts out with using the term “extra” at first and then switches to using “ones” when children have grasped the concept. Every student had a different amount of macaroni noodles, so everyone’s answer was different. At first the lesson appeared to just have students going through a procedure of counting and gluing, but writing the number in words and numbers at the bottom showed whether or not students were grasping the concept of place value.
2. It appeared as if all students understood the grouping into tens and the gluing of the noodles. Some students struggled with the actual concept of how the noodles represented a number, and that was evident when students had to write what the noodles represented at the bottom of their paper. Many students understood the tens place, but got confused with what to do with the extra. This lesson really helped to clear up where students were getting lost. When Julia and I went around the room, it was easier to help students because they had a visual right in front of them and we could see exactly where they got confused. The “hands on” noodle counting as well as board visuals for this mathematics lesson helped students get their final answer.
My teacher uses math a ton in her classroom! Her class seems very involved in math. The math I have observed so far incorporates a lot of small group time when students are working on a variety of activities since they are at so many different levels. Manipulatives that have been used include: candy hearts and unifix cubes. The candy hearts were used in a lesson plan incorporating: sorting, adding, subtracting, and multiplying. She uses unifix cubes with her students when working on multiplication facts. For example 3*4, students would use 3 groups of four unifix cubes to solve the problem.
These lessons were both individual lessons where students worked alone at a small group, so not a whole lot of instruction was given by the teacher except for a brief review of the concpets.
The students in class are all at different math levels and they all seem to be grasping the concepts they were working on. Being able to use manipulatives, number lines, and number charts were all very beneficial in their learning.
I observed a first grade place value lesson this last Thursday. The math class started with the first graders doing “math timings.” While I think that they can be good practice for memorizing math facts I am not sure how beneficial they are to first graders. Getting set up and doing the math timings took up about half of the allotted “math” time. After the students finished with the timings they moved into a place value lesson. For this lesson the teacher used macaroni noodles as a manipulative. We handed the students each a small handful of noodles(so each student had a different amount) and they were instructed to glue the noodles into piles of ten and then draw a circle around the pile, and any left over that did not make a full pile of ten were called extras and did not receive a circle around the pile. The teacher demonstrated what their paper should look like by drawing an example on the board. (They have barely been introduced to the place value concept, so that is why the teacher was calling the “ones” extras.)
After they were done grouping their macaroni, they wrote out a sentence, describing their piles and extras that said something along the lines of “2 tens and 6 extras is 26.” Before this point the students did not have any trouble with the lesson at all, as you might expect. About half of the students seemed to do just fine understanding if they have two piles of ten and six extras they have twenty-six, while the other half needed a little more help discovering how they find the final number. During this time Sage and I wandered around throughout the room helping those who needed it. When I was helping the students I tried to ask questions that would lead them to discover the answer, such as “Tell me how many tens piles you have? How many extras? So if I have three piles of ten how many pieces of macaroni do you have? AND then if I have 6 extras? What number does that give me or How much do you have altogether?” I am not sure this was the best way to get them to that answer, but it seemed to work, and they were all able to tell me “why” after they gave me the number, “Cause three piles of ten makes 30 and then 6 more.” By discussing it this way I was relying more on their counting skills and addition skills not necessarily trying to directly teach them place value, but I think this is a first step in helping them to discover place value.
I believe this teacher is just giving the students more experience with making the connection that when you have three piles of ten and six extra it gives us the number 36. While this lesson may not be teaching place value directly, helps prepare them for talking about it in the future, and helps build “place value schemata” in their little brains without them even knowing it! I believe this is a problem-based activity because they are using the manipulative to discover, on their own, the connections between the written number and the objects they were working with, even though it was fairly guided by the teacher and us. I agree with Sage when she said it helped having the macaroni/paper in front of the student because you really could tell exactly what step they were getting confused at.
I know the mind boggles that I could have even more to say...but I just wanted to add, because I realized I wasn't very clear, that while the timings were very much procedural knowledge, I consider the macaroni exercise more conceptual knowledge because they are starting to making that connection between written numbers and what that means.
1. Describe how your teacher teaches a mathematics lesson. Is there teaching involved or review? Or telling a procedure? Is it a problem-based lesson? Are students learning conceptual knowledge or procedural knowledge. Are any manipulatives used? If so, describe how.
2. Did most of the students grasp the concept? What helped the students learn?
I had a chance to talk to a few other teachers at our school and they kept raving about how good our teacher was at teaching math, so I was excited for a chance to get to see her do it. The lesson I got to observe didn't involve any new concepts being taught, so there wasn't very much direct instruction involved. Instead our teacher had her students break up into four small groups at tables in the room. There she has each table working on a different assignment, varying by difficulty depending on which table you were at. I think this works out very well for her when Kylie and I are in the room because she also has another aid that comes in daily, so with the four of us in the room, each on can concentrate on a table. The students use lots of different manipulatives to help them with their calculations. These include unifix cubes and number lines that are placed on each of the tables. An example of how unifix cubes are used is when doing multiplication. If the problem is 5*4, students can take 5 groups of 4 cubes and then count them up to see what they equal. To also help student better understand concepts of multiplication and division, Mrs. Dickey doesn't use the terms "times" and "divided by". Instead she says "groups of" for multiplication and "shared into" for division. For example, "5 groups of 4=20" and "21 shared into 3=7. This helps the students to better understand the reason why 5*4=20 because they can visualize it. She is very big into having students visualize the concept so they aren't getting some abstract number for an answer.
Students seem to understand math very well in Mrs. Dickey's class. The table I was working at with students had them doing algebra. I couldn't believe it! Second graders doing basic algebra! I don't think I ever saw an X in math until 7th grade. They seemed to understand the concept pretty well too. Overall, math is big part of Mrs. Dickey's class and she does a very good job of implementing and teaching it.
I like how your teachers are using fun things to group and allow the students to see that as multiplication and division!
Fun lessons!
I am in a first grade classroom at Hellgate elementary. In our classroom we begin Math lessons when the students arrive back from lunch recess. As the students come into the classroom they sit in a circle or a group on the floor, in front of the smart board. In the lesson I watched, the teacher started the lesson by asking questions to review concepts the class had learned the day before. The students were instructed to raise their hands, when they knew the answer our teacher would call on a student to answer. After a short review, our teacher told the students we were going to work on using different ways to count by two’s and by five’s. The teacher had the students stand up and form a circle. She had all the children put their hands into the middle of the circle. Then the students made predictions on how many fingers they thought were in the circle. Next, the class went around the circle and one by one counted their own fingers while counting by fives. (Example: The first student put up his hands and said “five, ten.” The next student put her hands up and said “fifteen, twenty.”) After counting the fingers in the circle by fives, the class went around the circle counting hands. To find the number of hands in the circle, the students counted by two’s. Then the students sat back down in front of the smart board. Our teacher told the class that there are other ways to count by two’s and by five’s, besides just counting on your fingers. The teacher asked “Does anyone know how to use a table to count by two’s?” She showed the students how to use a table to count by two’s on the smart board. The teacher asked questions such as: “If there are two wheels on one bike, how many wheels do you have with four bikes?” She had the students individually come up to the smartboard and fill in the table to find the answers. She ask multiple questions, where the students found the answers by filling in the table and counted by both two’s and five’s.
When the students went back to their desks, they used unifex cubes to practice counting by two’s and five’s. The students also used a 100’s chart to fill out a worksheet where again they counted by two’s and five’s.
I think that most of the students seemed to grasp the concept, and did a nice job answering questions and filling out a worksheet. I think that the students understood the lesson because there was a review followed by multiple problem-based questions that the students had to work through. I also think the use of manipulatives really helped further their understanding. Overall, I think this lesson went well, but I do think there could be a few more inquiry based questions. I also think that the students could benefit by using the think-pair-share strategy to answer some of the questions, instead of only raising their hands to answer all of the questions.
1. So far I have observed two math lessons and have also administered a test. For the most part each student seems like they really enjoy math!! In my particular class there is a wide range of learning levels so during math and most every subject, my teacher usually uses small groups and stations rather than full class instruction. While I have been there the students have been working on counting by five’s and tens as well as recognizing odd and even numbers.
So far each lesson has been a review for their test. For a review of odd and even numbers my teacher gave each student a number chart and had the students color in the odd and even rows each in a different color. She also gave struggling students unifix cubes to better show the relationship between odd and even numbers. She did this by showing even numbers each had a pair and odd numbers had a left-over cube after each was paired.
During the lesson on counting by tens (forward and backward) she had a review at the beginning in an all class instruction format. She asked the students if they could figure out what ten more or ten less of a various number was. She used a number chart (10 rows of 10 numbers. 1-100) on the Smartboard and called on students to come up and point to the correct answer. She also reminded them that there are ten numbers between the number she picked and the number above (ten less) and the number below (ten more). Each of these lessons apply both problem based and procedural based methods. They also have gained the concept knowledge prior, so during review they are applying the procedure of the concepts.
2. After each of these lessons she had the students complete a worksheet while they rotated between other various (some non-math related) stations. The students seemed to be grasping the material very well and were also very interested in helping the other students around them that were having trouble. Being able to visualize by having the number chart and unifix cubes at their disposal was very beneficial incase they got stuck on a certain problem.
Also, after correcting some of the tests I was able to see that the students only missed 3 problems (at the most) out of 25 total. Though most students only missed 1 or 2.
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