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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While viewing our teachers math lesson I found that he starts out each lesson with a little bit of review. He has the students exlplain or describe what they did they last time they met and what they learned. He also starts out with a hands on approach. He showed the students an angle and they had to decide if it was accut, obtuse, or a right angle. They then had to guess what the measurement of each angle was. After doing this they were asked to come to the overhead and measure the angle themselves to see it their guess was close to the actual measurement. This was a problem-based lesson. He gave them a problem and they had to figure out the right answer from prior knowledge.
This lesson is both procedural and conceptual. The students first use their prior knowledge on what they had learned about angles and their names. They then take that knowledge and actually measure to see if they are correct and if they learned the material correctly.
The students used a protractor in this lesson to measure the angles.
Most of the students didn't have a problem understanding angles and why they were catagorized as acute, obtuse, or right angles. However some students did have a little trouble understanding why there were two sets of numbers on the protractor and ended up reading an acute angle to have a measurement of 130 for example. This was clearly explained to the students as to why he was getting the wrong measurement; however I still feel he was confused as to why this was.
The students prior knowledge about angles and their names really helped the students to review in this lesson. They also found help in using the protractor if they were stuck on a measurement.
1.) Our cooperating teacher taught his students a geometry lesson that was mainly a review on measuring different angles. First, he prepared for the lesson by drawing about six different angles on the overhead. Next, he had the students guess the measurement of each angle and share their estimate with a partner. Then the teacher asked a handful of students what they thought the measurement of the angles were. After the students shared with each other, the teacher chose one student to come up and measure the angles on the overhead with a protractor. After learning the true measurement of the angles, the teacher questioned his students on what each angle was -acute, obtuse, or right and reviewed what each term meant. This was a problem-based lesson because the students were presented with a problem and asked to solve it. The students are using both conceptual knowledge and procedural knowledge because they are taking what they already know about angles and using that knowledge to predict, measure, and name the angles provided by the teacher. The only manipulative that was used was a protractor, when the students measured the angles.
2.) It seemed that most of the students did grasp the concept. Given that the lesson was mostly review, each student had prior knowledge about angles and how to measure them. The hands-on activity seemed to help the students quite a bit and the fact that the students were all working together and collaborating their thoughts and ideas worked well!
1. I have only had the opportunity to watch one math lesson at our placement. The lesson I observed was on division. This was only their second lesson on the topic. She told me that the first division lesson she used candies and had students group the candies for the division problem. So for the problem 15 / 3 she had students set out 15 candies and then group them in 3¡¦s. Then students were to count the groups with an answer of 5.
The lesson I observed was similar, except students drew 15 circles and then circled groups of 3 to arrive at an answer of 5. She did a couple of these problems on the board and then split the class into 3 groups. She took a group and then my block partner and I each took a group. We helped the students complete a worksheet using the same format as the model given to the whole class.
This was basically review for the students and she used both direct instruction where she told them what to she was doing do and then a step-by-step procedure of what to do. No it is not a problem-based lesson. She gives them a division equation and has them use a specific algorithm to solve it. The students are learning procedural knowledge, but some of the students were creating their own conceptual knowledge of division. They understood the connection between multiplication and division and were able to reverse either, with full conceptual knowledge. Most students were just following the procedure and not grasping any connection.
She had used manipulatives (candy) to build experience in the lesson before through grouping.
2. Most students understood how to group the candies/circles to get the correct answer to the division problem. The prior experience using manipulatives helped them to understand the grouping process. However, some students struggled with which number to start with.
3. There is not much in the way of math related posters in the room. There are several posters for language arts and social studies. She has several clocks posted in the room. In addition, she has some signs posted with math terms like vertex, rectangle, square, etc.
Mrs. Fisher uses as combination of review, problem based strategies, and manipulatives to teach the conceptual knowledge of perimeter to her students. To begin her math lessons, our teacher uses what she calls “fast math.” Fast math is worksheets where students practice their multiplication skills as fast and as accurately as they can. Mrs. Fisher uses this type of introduction to warm the kids up and “switch” their brains over from language and reading that they do earlier in the morning to mathematics. After doing fast math, Mrs. Fisher went into a review session of what students had learned the previous day. She reminded students that they learned a little about perimeter the previous day (this was a telling procedure). She asked students to draw a shape using only 20 feet for their total perimeter.(This was the problem based method of her teaching.) She had students come to the board after they had sketched out their idea, and draw it on the board. If they were wrong she had them return to their seat until they had figured out how much can go on each side to add up to 20. As a class, the students would decide if the perimeters were correct on the objects that were drawn. After this activity, students gathered rulers, and were to find 5 objects in the classroom that had a perimeter that they could measure. These were the only manipulatives the children used during this lesson. They were required to write down the measurements of the sides and show each step in their addition process.
The majority of the students grasped the concept of perimeter. There were a few students who struggled to find objects that they could measure, and became frustrated. By showing students that they could measure anything that had sides, such as books, Kleenex boxes, etc they were more motivated to find the perimeter of different objects. What helped students learn more about perimeter was pointing out to them that usually two sides are equal when measuring the square and rectangle objects in the classroom. This made the addition process easier for them
Erin B. pretty much sums it up for me since we were both viewing the same division lesson at Hellgate Elementary. However, there were a few observations I was able to make from working with my small group of students. First, it was very obvious that the students had only grasped the procedural aspects of the division. For example, the students knew to draw the circles and knew to put them in groups but did not know why they were doing what they were doing. So in order to help them build the conceptual knowledge I began introducing the problems as word problems. For example, 15/3 was: If you have 15 chocolate chips to put on 3 cookies, how many chocolate chips can you put on each cookie. The next thing I noticed was that students were making the connection between multiplication and division. Most knew that 15/3 was 5 and 5x3 is 15, I enforced this by challenging the students to check there answers this way. The last thing I noticed was that the grouping of the circles was almost a limiting factor for some the brightest kids. They were able to calculate the answers in their heads very easily, however were unable to make the connection between the answer and the grouping strategy.
Todays math lesson was division. She reviewed the concept but introduced a different way to write a division problem. The kids did not have manipulatives to use. Our teacher used the smartboard to put problems on the board and have different kids come up and solve the problem. While our teacher taught the lesson Sarah and I worked with different students on a worksheet about volume that some did not understand. She reviewed the main concept of how to divide. The students would come to the board and make groups to divide. I have not seen this method before and was not able to make much sense of it because I was working with other students. Most of the kids though seemed to get what she was teaching. Most of what they are doing right now is prep for the test.
Our cooperating teacher takes a pretty traditional approach to teaching math. The lesson began with a brief review...The teacher reads a page or two from the text book, which explains the lesson, the concepts being used, etc, and then the students are assigned homework that the work on in class. Students seem to be learning procedural knowledge, because they're learning how to do the problems, and then apply the procedure to their homework. The teacher did use some manipulatives to help the students gain a better grasp of the some of the questions that were being asked. There was a section of the book about shapes, so she brought out models of the shapes, and they really seemed to help the students. While the students worked on their homework, I used the manipultives to help answer some questions that were asked, and they seemed like a great tool for helping the students understand the concept, rather than just giving them an answer.
On Friday, there was an extension activity assigned, which the students seemed to enjoy. The students were asked to plot Missoula locations on a graph, and then they had to write a list of questions concerning the various points. It was a nice hands-on acitivty, and it seemed like the students enjoyed a break from the normal book work.
Righ now the class is learning multiplication, and some concepts associated with shapes; most of the students have grasped the concept, but a few seem to have a hard time with it. I'm not entirely sure if it's the math they're having a hard time with, or if they just have difficulty staying on task and finishing their homework. I'm sure these questions will be answered, as our observation continues.
My block partner, Norm, and I have not witnessed an actual “teaching” of mathematics in our 3rd grade classroom. We have spent a total of about 10 hours in that class so far and all we have done in math are multiplication timed tests and a few work pages out of the students’ math book on shapes. But, there has been no teaching structure, strategy, or delivery on these math concepts. Our teacher uses a procedure-based teaching method in her classroom. She is very “by the book” and relies on student textbooks for their learning and their practice of math concepts.
On Friday, our teacher broke the class into 3 groups and Norm and I each took one group. The children were studying coordinates and we were to have them graph random points (on graph paper) on a numbered x- and y-axis. For example, a student could plot the “pet store” at (6, 3). After the children plotted 10-12 points with labels, they wrote questions that correlated with those points. For example, a student could ask, “Where is the pet store located?” On Monday, the students will trade graphs and answer each other’s questions. This was a fun extension activity that our teacher employed. Most, if not all, of the students grasped this activity and the concept of plotting coordinate points. No manipulatives were used in this lesson.
According to Norm, our teacher brought out some manipulatives, but I didn't see them. I think she sat at her desk and showed them while kids gathered around??? She should have shown the whole class!
Well, Natalie pretty much hit the nail on the head as far as the math lesson we had the chance to see. I'm not really sure what else to add...
Our teacher has a very relaxed way of teaching, and she is always circulating around the classroom. The students are not scared to give problems a go. Also, she used group work quite a bit. I was amazed at how willing students who understood perimeter were willing to help the others. Also, I was amazed at how lost some students were. This was day two of perimeter and some kids had NO CLUE what was going on. Hopefully all of the students will figure it out this week!
Teaching comes in many forms: small groups and whole class. Telling how to do something is teaching procedures. Having a group figure something out is using a conceptual approach. I think both kinds of teaching were going on here.
We have observed a few math lessons so far in which the main emphasis is on "test prep." The lessons involve students doing worksheets and then correcting them as a class. When students provide an incorrect answer, they are told that they are wrong and do not have the opportunity to really see why. These concepts seem to be review and are very procedural. The only time manipulatives came out was when we were helping students that had trouble finding volume on some worksheets. However, the manipulatives we used did not seem appropriate because they were way too small and the challenge became how to balance such tiny pieces, rather than, how to visually see volume.
Most of the math lessons that I have been able to catch were review. I started observing right at the end of their probablity unit and we've just started geometry. It seemed, in watching the review lessons, that by the end of the probablity unit they were using a combination of conceptual and procedural knowledge. While the students finished their work packets,it was easy to see that many of them understood just exaclty how to work through the problems. Furthermore, in a whole class discussion, the students related what they had learned to things around them. This was neat to see, while some teachers finish one unit and move right on to the next, Mrs. M took a day or two extra to discuss things with the class to make sure everyone was making sense of it. Even now that we have moved on the the next chapter Mrs. M still asks the students questions related to probablitly throughout the day. She also had some great dice games that the kids really got into. You could tell they had learned the game at the beggining of the chapter, and by the end the students really understood and got into the game.
Starting the Geometry chapter we've used many different manipulatives to hook the kids. From foam shapes to geo-boards, the students are not only VERY engaged but they also seem to be taking something out of it. I'm excited to see how the rest of the chapter plays out, and especially what new and different games\manipulatives Mrs. M will come up with.
1. I observed my cooperating teacher teach two geometry lessons. She began each lesson with direct instruction and described the terms they were learning. Each student was given a “Geometry booklet” with blank pages and each term listed on the bottom of a page. As she described the terms (plane figure, polygon, vertex, etc…) the students were instructed to write down the definition, either from the glossary in the back of the book or what they learned from the teacher. Then they were told to draw examples of each term on that page. To complete the lesson, the teacher handed out Geo-boards and the children were allowed to create polygons with a partner. The second lesson was on angles and line segments & rays. The lesson followed a similar format with the teacher defining the terms and the class copying them into their “Geometry booklets.” Again, they were allowed to use Geo-boards to create different angles.
2. Most of the students seemed to grasp the concept of the first lesson. This was evidenced the following day when Josh and I did a similar lesson using the same concepts and terms. The students remembered what each term meant and were able to apply these terms to the activity we did. Although the Geo-boards didn’t teach the concepts to the children, they were good tools for reinforcement. I think working with the subjects they are learning about help the students grasp the concepts better, however, the explanations by the teacher gave them a good place to start.
I have only had one opportunity to watch one math lesson in my 4th grade class. Even then, I walked in about half-way through the lesson. What I did see though seemed like a review on measuring. The students all had their math books out working as a class measuring the objects in the book. She described measurements that weren't exactly to the inch as counting the jumps. (example: an abject was maybe 2.5 inches. well to get the .5 they had to "count the jumps".) So that would be a procedure. The students were using their rulers to measure everything and if they got the answer wrong she had an oversized laminated paper ruler that she could "count the jumps" with the kids. She then turned this lesson into a problem based lesson by asking the students, "if you had to measure from here to your house, what would you use? Inches, feet, or miles?"...and so on.
2. At this point it seemed like the students were still trying to grasp the concept so they had an overall understanding of measurement. They just needed a little practice. I did think it was fun for our teacher to use the term "count the jumps". They knew what that meant and as soon as she said it they could then give her the right answer most of the time.
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