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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When I observed our class doing math, it seemed like teaching/telling. The students sat at their desks with their books open and went through the pages. The students took turns reading the directions, problem-instructions, etc. aloud. Then they came up with their answer and shared it with the class. There was one lesson where each student received a meter stick and were allowed to walk around the classroom and measure things. Then they told the class the favorite thing they measured.
It seemed that most students understood the concepts they were discussing. The teacher is very good about checking with the students to make sure they understand each problem or new concept they go over. However, I feel like the students might be learning procedural knowledge as opposed to conceptual knowledge. They are learning straight from the book, page after page. On their homework they usually make a lot of corrections, which tells me they are not necessarily retaining the information.
I talked to the teacher a little about her feelings on the curriculum. She mentioned that you're basically handed a curriculum and that is what you're stuck with. She said all of the fun went out the window. But because of state standards, it's almost necessary for these students to stick to this curriculum.
When I observed our class doing math, it was a lot of teacher instruction, but she also allowed the students to get involved by showing examples and having the students use the smartboard. This was the first math lesson that I have been able to observe.
It seemed that several of the students were struggling with the concepts and had several questions when they were completing their worksheets. The students actively participated with the smartboard, but it seemed like it left their grasp once they were on their own to do the worksheets.
I observed my teacher introduce her students to the geometric concept of circles. She covered radii, chords, central angles and diameters. She used a smart board and students had their math books open to help themselves find answers. She began by drawing a circle and asked "How do I know it's a circle?", then the class talked about the definition of a circle and wrote the definition in their notes. Based on that beginning definition of a circle, she moved on to ask students what they thought diameter, chord and radius meant. Throughout the lesson she stressed conceptual knowledge, asking for volunteers to go to the smart board and label the parts of the circle. After discussing chords, she went back to the definition of diameters and asked "could a diameter be a chord?". This demonstrated to me that she was really focusing on getting the kids to understand the ideas in a conceptual way, focusing on understanding.
I think the students understood the concepts. The kids were expected to take notes, and after the discussion Ms. McGill gave the kids a worksheet to practice the skills. I think the practice worksheet was pretty necessary, because the kids "got" the definitions, but couldn't see how it applied until they had to answer questions such as "name the circle's radii". I wandered around the room and answered questions, and kids needed some help but after I prompted them to review their notes, I could see the "light bulb" and they didn't need me to re-teach anything.
My teacher teaches mathematics in a telling procedure. His procedure relies primarily on the books instructions. He starts by introducing the lesson and then he demonstrates how to do the assigned task. Following that he gives the students an assignment of about 20 math questions and helps them with the first couple questions to get them started. Following that the class took turns raising their hands and asking the same questions. It seemed after awhile the class seemed to grasp the concepts they were suppose to learn. In the lesson I observed their were no manipulatives used to help there learning. However, since they were on fractions there were ample opportunities.
Most of the students seemed to grasp the concept after the teacher helped them. It seemed as if there one on one experience was the most benificial part of their learning experience.
In our fifth grade classroom, the math lessons are a lot like Heather's experience. The teacher stands up front and writes problems on the board. He has students verbally give him the answers he is looking for on the sample problems. After about two of these examples, he has the students complete the assigned book problems. He definitely provides only procedural instruction without any manipulatives or technological support, and the subsequent lack of conceptual knowledge is seen in many of the students as they try to complete the assigned problems. Many of the students don't grasp the concepts and are simply trying to memorize formulas. Since they are currently learning fractions, which require different problem-solving methods for each problem, many kids struggle. They lack the problem-solving skills necessary to recognize what they are trying to solve, and cannot create their own solutions but rather often need to be told which operation they need to solve the problem. I feel that the students in this classroom need to be made aware of their critical thinking skills and how to use them to solve problems without memorized procedures.
These few examples span the range of teaching! Show and tell vs asking questions about each picture/illustration on the smart board!
Great insights!
In our 5th grade class the students were working by themselves on a series of problems from the book. Our class is the "top level" of 5th grade math so the students seem to of grasped the concepts. When questions come up in class or teacher tries to get them to remember concepts and gets them to work the problems out themselves. From what we have seen there has not been any use of maniputives yet but in talking with our teacher some will be used throughout.
I think it's rather amazing the level of math these kids are doing. It was far more advanced than I remember doing in 5th grade.
We have observed our teacher do a couple of math lessons. She usually does a review of the material covered on the homework. Then she does a problem-based lesson. She shows the students how to solve the problems. She puts up problems on the smart board and has the students work on them independently, while she circulates around the room. After most of the students were finished she calls on students with their hand raised to come up and write the answers on the board. Then she asked the class if they agree or not. She incorporates both procedural knowledge and conceptual knowledge. Right now they are working on fractions. She shows the students how to visualize the fraction with pictures. She also shows them how to use procedural steps to solve certain problems. I have not seen her use any manipulatives in the classroom yet. I think most of the students did grasp the concept, but a few of them did not even try to participate. I think it was really beneficial for some students to have the opportunity to participate in the lesson by writing their answers on the board. This seemed to be a motivational factor for some. Some of the students seem to learn more from their friends sitting next to them during the independent work.
In my fifth grade class we are learning to add fractions. Due to the classroom schedule I have only observed one math class which was in fact a review from the previous days lesson on adding fractions. It seemed to me that approximately 1/3 of the class already had the concept dialed in, 1/3 of the class was increasingly understanding it with practice, and 1/3 of the class seemed to understand nothing (that equals 3/3). At the beginning of the math class the teacher used an example on the overhead projector. Much like Brittany's teacher, my teacher seemed to provide highly procedural instruction. Once the example was worked through the students tried to do similar problems on their worksheets. I can't say for certain that is how she taught it the previous day (strictly procedurally) when the concept was introduced, but I have a feeling it was. I will have to observe a few more lessons before I will know the math teaching strategies of my cooperating teacher. While watching and helping the students work on their worksheets it seem to me that repetition is the way that a majority of the students are learning how to add fractions.
The math lessons I have observed are not really problem-based, instead it seems more like a review. The teacher goes over a concept, then they work on problems as a class, then the teacher writes more problems on the smart board for the students to try by themselves. I think they are learning both procedural knowledge and conceptual knowledge, they are building on their prior knowledge but they are also learning the procedures or steps to complete the problems.
I think most of the students are grasping the concepts. They all seem to be able to solve the problems and if they make mistakes they know what they did for the most part. But I feel since this seemed like review to the kids, most should have it by now.
There were no manipulatives used, but this might also be because it wasn’t the first time the teacher was teaching this concept.
Today I watched math class for the first time. Right when the children walk into the class they are expected to get out there math journals and do the daily oral language question. Today they were supposed to review what they had learned about how you find the value of X to a question. Example: X+4=-6.
Our teacher led a review about how to find the value of X and then she assigned a worksheet for the students to complete. There were many manipulatives provided for the children to use. They used the blue pawns as the positive values and the white pawns as the negative values to manipulate the question. They also were allowed to use an activity that was on the smart board to come to the correct answer.
Most of the class is setup as a student directed approach. I do think that most of the children understood the concept and were confident in their math skills. It was great to see the children help each other out when they were struggling. I think the math class is a great learning experience for the students.
The teacher that I am working with teaches math first thing in the morning. It is a leveled math class so kids from other classes come in during this time and some of her students leave. It seems that everyday is pretty similar. The students open up their books and begin, as a whole class, working through the problems. She gives the students time to think about and try the problem after they read the problem and then they raise their hands to share the answer. Most of the class stays together, but there are some students that fall behind because the rest of the class is moving faster than they are being able to figure out the problems. The math has only come straight out of the book up to this point. So, it does include word problems that may be considered a problem-based question, but the overall lesson is truly just out of the book. Students are learning both procedural knowledge (how to measure items) and conceptual knowledge (formulas for finding perimeter/area. I witnessed those colored shapes being used once, but they seemed more of an afterthought and weren't truly incorporated into the lesson.I am not even sure how they worked into the lesson or how they were used.
I would say that most students grasp the new concepts presented in the classroom, but there are a few kids that seem to get a little left behind. From what I have seen I would say that what helped the students learn was being able to "have a go"at the problems and then check their answers.
I have observed my fifth grade math class twice. Each time has been in a group setting where students are working collaborating to solve problem based work sheets. Ms. Kattell, our cooperating teacher, explained that they had been working on review for the upcoming standardized tests. So because of this, we have not had the opportunity to actually observe her teach a lesson. The students are apart of a leveled math class so, most of the work that they do is above grade standards.
Ms. Kattell also explained that a lot of these students are so smart that they get answers in their heads before even doing any work. This has become an issue since math is all about written work and problem solving. So to actually get the students to write the problems out and how they got them have been a whole other learning process for them. She also noted that because some of these students are so advanced they struggle with just basic multiplication and division.
For the most part the students were grasping the concepts. I will be completely honest; when I was approached by a few of them for help I didn’t know the answers. (Talk about embarrassing) They did struggle with some of the fractions and long division when I was in there. Ms. Kattell walked around the room and made herself available to guide students in finding the answers.
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?
After watching my first math lesson I was excited. The particular math class is full of fifth graders who are advanced at math so they were involved in a lesson with less "copying" and more exploration. Their first task was to answer the Daily Oral Math question reviewing the prior lesson's topic, finding the value of x. The students came to class prepared with math notebooks and their thinking caps on, this class tends to be very competitive because they are all such confident mathematicians!
After completing DOM the class watched a video on the SmartBoard. The video was a child performing similar equations to the equations they have been working on. He used manipulatives such as blue and white pawns to represent the x value and number cubes for the numbers. This demonstration allowed students to see how one of their peers was able to complete the challenge and motivated them to do the same. After the video, students were given a worksheet to complete. Using the same pawn and number cube manipulatives the students successfully worked out the 10 problems. It was fun to see them actually representing different equations and understanding what step needed to come next. If the manipulatives weren't easy enough students were allowed to use an interactive program on the SmartBoard using pictures of the same pawns and cubes. This allowed peers to help each other along with teacher help.
The entire lesson was student-directed. They were all fully engaged and enjoyed solving the equations hands on. It was interesting to watch them explain the equations to each other and listen to their reasoning! Overall I think the lesson was very valuable for this group of students!
In my fifth grade classroom I’m observing, the students have been working on adding fractions and working with improper fractions. Due to our schedule and availability, we’ve only had the chance to see one lesson, which was actually more of a review than a lesson. Our teacher stood up front and wrote problems on the overhead projector. For the first time, she gave each of them a mini white board, marker, and eraser to work on during review. They seemed quite engaged just due to this fact. She said they’d been envious of her mini white board, so she thought she’d give them each one. During the review, our teacher had students verbally give her the answers she was looking for and worked them out on the overhead projector. I noticed the only students to quickly answer her questions are her students who are already doing exceptionally well. After two or three review problems, she had the students complete the assigned book problems.
Like Brittney mentioned, I feel our students also lack the problem-solving skills necessary to recognize what they are trying to solve. They can’t always figure out how to come up with their own solutions, and need to be reminded which operations are needed to solve the problem. I don’t know how my teacher would meet the needs and questions of all her struggling students without Ryan and I there to help. I felt overwhelmed by the amount of students who seemed completely lost. I did however have a few of those moments with students where you see the light bulb come on, and they finally got it. They seemed just as excited as I was that they understood, and that felt really good.
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