Community Picture Profile

1)  You and several of your friends are big Michigan State fans. One of your best friends also loves Ohio State. If tickets for the Spartan football game Vs. Ohio State go on sale July 27th and today is June 15th, how many more days do you have to wait until tickets go on sale?

2) You and your family are planning on going to the Michigan State Football game against Central Michigan. Tickets are expected to be $45 each. If there are 6 people in your family, how much money do you expect you will need to buy everyone a ticket?

Community Picture Poblems

 

1. There are 323 students who attend Mt. Hope Elementary School. 4 buses come to pick up the students from the school at the end of the day. Each bus has 24 seats, each seat holds 2 people. If all the buses are full, how many students were picked up by their parents or stayed after school?

2. There is a full school bus with 48 students on it. There are 7 kindergarteners, 8 1^st graders, 8 2^nd graders, 12 3^rd graders, and 4 4^th graders. How many 5^th graders are on the bus and how many seats do they take up if there are 2 people per seat?

Community Blog

 

1.
In order to get to school next year, you need to drive through this neighborhood. If today is Friday April 20th, in how many weeks does this project need to be finished in in order for you to get to school on Friday September 7th?

2. If this project costs about $200 a week, and the project lasts for 10 weeks, how much money is going to be taken out of the city's budget that could possible be spent on more important things such as a neighborhood park?

Performance Assessments

Reading the "NCTM" article made me think of grading math assessments in different ways. So far, I have had very little instruction on how to use rubrics. I really like the analytic and holistic examples that this article provided. In my field placement, the students do traditional tests and they either get it right or wrong. My mentor teacher gives the students grade based on the percentage of problems that they solved correctly. The tests are always in multiple choice format and the students give their best guesses. The "NCTM" talked about easy ways to get these students to develop their math concepts even further by asking secondary questions such as: "Why did you choose the answer you chose?, "What was not right about the other choices?" "What else would you like to add to the question or answer?" (Allen et al). I think that these questions can help the students explain their thinking and help the teacher get a better understanding of how well the students understand the concepts. If it is just multiple choice, students could correctly guess the answer, yet have no idea how they got it or how to do the problem. I feel like these multiple choice tests are not the best way to assess the students.

The "Gaining Insight into Through Assessment" article gives examples of student solutions for three different questions. These questions are more open-ended and the students are required to show their work. For the first problem with the dots, three different student solutions are examined. There is the correct student solution with the correct work, and incorrect student solution with work that does not make sense, and another incorrect student solution that is incorrect, but the work that they did still makes sense. The article talks about whether or not the incorrect student solution with the correct work is still correct. I feel as though he should be incorrect because he came up with the wrong answer, however I do not know if that is the best thing or not. The question I have is, where do you draw the line and how do you determine whether or not the student should be correct or incorrect? It is clear that the student understands some mathematical concepts, but not the ones that the question is looking for. I liked this article and it was interesting to examine the student work. The article talks about the benefits of having open-ended tasks where students have to show their work. They are forced to communicate their ideas about the math concepts and work through them on paper. It is easy for the teacher to see exactly which strategies and approaches that the student is using. These performance tasks also allow students to work through the problem the way that they want to. We have been learning about how important it is to differentiate in math, and that all students learn and think differently. As long as students get the right answer, I feel as though they can do the task whichever way makes the most sense to them.

I think that performance tasks could be more beneficial for both students and teachers. Students are able to solve problems the way they want and think about problems more than just guessing correct answers. Having students explain their thinking and solutions will further their understanding of math concepts, which will help them in the long run. Students are benefited by performance tasks as well because they can see exactly where the student is having misconceptions, or what students are understanding. I would like to use performance tasks in my future classroom.

For my lesson study, some performance tasks could be used without using paper and pencil. I feel as though orally asking students questions can give the teacher a lot of insight to their thinking. They are put on the spot and have to answer your questions, so there is no way for them to make something up. I feel if they are able to answer the questions, it will show that they understand the concepts, and if they are unable to answer the questions, they still have some misconceptions. For my lesson, students are required to use non-standardized tools to measure objects. I can simply ask students what tool would be the best to measure different objects based on size. I can hear what the students answer and assess their knowledge based on their answers.

Lesson Study Blog

After watching the video on the lesson, I think that main mathematical goal was to try and have students understand what area really is and how it is measured. The teacher/observers are trying to stress the point of square inches. The teacher used modeling to prove what the area of the square was by having a student come up and draw 3 columns  and 3 rows which created 9 squares. The students were forced to think about more than just the algorithm for solving the problem but what they were actually trying to solve and how it is proven. The debriefing video was similar to what I understood our lesson study observers would do. I knew that the observers were going to be looking at how the students approached the problem and how they went about solving it. They had specific topics they were looking for such as if they extended further than the procedure and made connections between what they already knew to what they were trying to learn. Each observer had specific students they were studying which helped them really narrow in on the details of how they were approaching the task.

     The Whitenack article stressed all the important facts and benefits to explaining and justifying students thinking. In the discussion part of our lesson, we are looking for students to share how they approached the task and explain why they solved it the certain way that they did. By having different groups explain their approaches to the task, the class will hopefully see different ways the task can be carried out. This gets students thinking about mathematical reasonings and might bring up arguments about strategies. By having these arguments, strong connections are being made by both the supporter and the arguer. The supporter has to think about ways of defending why they liked the way they solved the task and how it worked. The arguer is learning new approaches and ideas. With our task being very open-ended, it allows for many different way to approach the task. This hopefully will make for a in depth discussion.

     I think the biggest challenge of the lesson study is the observations that are going to be taken. There is a lot to look for and you have to be very prepare on how students might approach the task. The observers have to make sure they are recording every step that the students make and try to think of their reasoning behind their actions. This is a lot to have to do. Total attention has to be carried out throughout the entire lesson. I think the most beneficial aspect of the lesson study will be to say that I was participated in a group that studied how second graders approached measuring with different units. It will be beneficial to say that I was an observer that took a first hand look at how students responded to a task their first time really dealing with measurement. 

Week 12 blog

The two readings that I had to read this week were “Problem solving and At-Risk students” by Margot Robert and “Differentiating the curriculum for elementary gifted mathematics students” by Wilkins, Wilkins and Oliver. In both articles they discussed the importance of allowing the students to feel comfortable in their learning environments and not to make the students feel dumb or overlooked.

In the At-Risk article Robert discusses the importance of modifying tasks for students to not feel left out. She goes through an example of how she approached a problem, which was too extravagant for her at-risk students and modified it by giving select answers in the problem. When the students were able to figure out this problem, she began to see an increase in the students confidence and saw that the students were now able to problem solve.  She discusses the key idea of how to help these at-risk students is to not allow for them to feel incompetent. To help the students in not only mathematics but in their schooling over all Robert found that the students need to feel confident in what they need to do.

I think this issue of confidence can be linked with the gifted math students article as well, in the article the authors discuss how many teachers get annoyed and don’t know what to do with their gifted students when they finish their work earlier then other students. I have often seen this in my own classroom; it gets to a point where the teacher ends up yelling at the student because they tried to advance on new work. I think when these gifted students are asked to do nothing or “go read a book”, the teacher is not allowing the students to advance. Which can allow these students to shut down and not enjoy the subject as much, also relating to confidence issues. The students know that they are good at this subject but do not see how they are being challenged in this area and become frustrated or bored. To help out with these students Wilkins discusses the importance of setting up extra activities or MIC centers. Which are open-ended questions, with a higher-level task that allow the students to explore new ideas. The authors found that the students were not excited and intrigued to be challenged by these tasks. However, once the MIC centers were introduced the students soon began to love math again and loved being challenged.  

Overall, I think that by allowing for many different modifications in your lesson plans and ensuring that students feel confident in their tasks, teachers can make their classroom an open and relaxing environment for all students. 

Measurement in the classroom

In this weeks reading, there was a strong emphasis on how to teach and use measurement in the classroom. From these readings it appears that many teachers do not go over the ideas of measurement thoroughly enough for students to fully comprehend it. In the Thompson reading they discuss how "Measurement is one of the most useful of the mathematical strands for everyday citizens." They then go on to talk about how many middle school students were unable to correctly measure given objects or properly select the correct answer on a standardized test for an estimation of an objects size using measurement. I found this to be very interesting, it seems that teachers are not focusing on the use of measurement because they believe that students should have already learned these basic ideas. In the article they go on further stating that many students have this issue of measurement because they are not familiar with the metric system.
This idea of the importance of understanding measurement in the metric system reminds me of when I was in Australia. Living there for 5 months I had to become familiar with the metric system. At first I had an extremely hard time converting kilos to pounds and kilometers to miles. Ordering meet from the deli and figuring out how far away I was from a given destination became a daily struggle. Growing up I was not exposed to the metric system and if I was I felt like my teachers speed through these ideas and believed that their students would not necessarily need them in the future. I find that focusing on measurement and understanding it to greater level is extremely important.
The readings also discuss the importance of investigations through measurement, If I were to teach measurement in my classroom, I would have the students compare the metric system to the measurement system that is common to the US. The students would also have a chance to ask questions and correlate ideas as to what is similar and what is different in the two systems.
Overall, I think that measurement is a very important concept that many students need to concur. Like the Thompson reading discussed students at the college level are still having difficulties conquering the idea of size and measurement, which is showing that there is not a strong enough focus on this idea.

Measurement and Exploring

This week's reading, "Building a Curriculum Around Big Ideas" by Ron Ritchhart talks about the importance of teaching measurement to students. A few teachers in this article are discussing how they should start teaching measurement to students. They want to make sure that they are teaching measurement the correct way. They don't want to just tell the students measurement formulas. They want them to figure out the real life application of measurement so that the students better understand the concept. One teacher, Carl, talks about how measurement is used in the first place and in the real world (Ritchhart). I think that this is a good place to start when thinking about teaching measurement. The students need to understand why they are doing and learning measurement in the first place. I think that students learn more if they find meaning behind what they're doing, instead of just plugging in formulas and spitting out numbers. Another teacher in this conversation while talking about measuring and using comparisons to measure says, "comparing is still measuring. You're finding out something about the two objects. If you're comparing to see who is taller, then you're dealing with height" (Ritchhart) I think that this person has a good point and comparing two different things is one way to measure. I think that students at a young age would enjoy doing this type of measurement. They would be able to relate it to their own lives, and easily be able to see the importance of measuring height. Teachers could also incorporate teaching about growing and the importance of being a healthy person in order to grow and be strong. Thompson and Lambin's article "Concrete Materials and Teaching for Mathematical Understanding" talks about the importance of using concrete materials to help students understand math concepts. I think that measuring people and comparing heights would be a fun thing for students to do and it would be good to use concrete materials, in this case, people. Students could also use people and peers to measure weight and lengths of body parts such as arms or feet, as well as height. I think that students using concrete materials when learning about measurement will definitely help them understand the importance of learning measurement. I think students should start off with measurement by doing activities such as the one I described. I feel like students will understand the importance and real life application of measurement by exploring for themselves by using concrete objects, making it more important to them.

Week 5 Readings

   I enjoyed this weeks readings on why mistakes are important. The value of them is crucial in the process of learning and understanding the what is being taught. The teacher has to do a good job at setting up the environment of the classroom to make children feel comfortable with making mistakes. It is only natural for people get upset or embarrassed when they are wrong but if the teacher structures the lessons, their teaching, and the the norms of the class to encourage mistakes and learn from them, then students will get more out of what is being taught. One way to address making mistakes and solving them is to let students work together to help each other out. There were multiple examples throughout the readings when children were allowed to work together and communicate between each other to help understand and find an awesome to the question. It can be difficult for teachers to step back and let the students take control for part of the lesson, and even though it might be time consuming, it can have a great outcome. Allowing students to reason why an answer may be right or wrong takes their learning to a whole new level. Students who help others to understand will learn the material better and may be able to teach it in a way that other students will understand it more. Holding whole group discussion and allowing the class to answer each other questions can really help the teacher understand who is thinking what and who is struggling and who is striving. Mistakes are  healthy components to build students awareness. They are the difference between a student learning the material to understanding the material.
     

One way that a teacher can be ready to take on students mistakes and their process of learning is through TTLP. It is important that teachers prepare their lessons and be ready for anything. Using Thinking Through a Lesson Protocol enables teachers to be really think about their lesson before hand and be prepare for how students will take on the lesson. I liked how this type of lesson planning has teachers think about how students will preform and create questions that will help guide their type of learning through the lesson. The article stated how it helps teachers become a better facilitator. I agree because being a good facilitator starts before you are in the role to lead, it starts with the amount of preparation and thought you put in before taking on the role. I can see where other teachers are coming when they said it takes a lot of time. This type of lesson planning might be one that is more of a thought process rather than a written out technique. It maybe something to just add to the steps teachers take while creating their lesson plans that take just teaching the lesson to a whole new level.

Teaching Math, for all to learn By: Molly Heidtke

This weeks reading primarily focused on new ideas to teaching math. In the reading “Children’s understanding of equality: A foundation for Algebra.” The author discusses the importance of having a thorough discussion of the algebraic principle and the placement of the equal sign. I found this article to be very interesting in the sense that my second grade class is learning the idea of the placement of the equal sign and filling out a problem to make it equal on both sides. Unfortunately I was not able to observe my teacher, teach this to the students, but I found it very relatable that students need to learn these ideas at a young age. When I was introduced to algebra in middle school, I was confused on how to balance an equation and I think by introducing this idea to elementary school students, they will be more successful in later years.

The second idea that was based off this weeks reading was the idea of allowing students to come up with their own idea of solving a problem and also using open-ended questions to further trigger their previous knowledge on problem solving. I observed the idea of allowing students to solve their problems their own way last semester in my placement. The students showed several different ways that they came up with how to add 16+7. Some students showed that they used their hands, some drew on their papers and others just showed how they wrote out the problem (horizontally and vertically). I thought it was interesting that the teacher allowed for all students to show their findings of solving problems and found that to be rewarding to all students and the teacher, in the sense that the teacher has a better understanding of how each student solves their problems. Allowing for the teacher to help the student if they get stuck.

Overall, this weeks readings allowed for me to explore new ways in teaching math. I plan to use open-ended questions as a math teacher as well as take most of Reinharts ideas in ways to help students explore how they would want to solve a problem. One main idea from his article that I found it very interesting was when he said not to carry a pencil around, looking back at my mathematic experience, teachers would walk around and basically solve the problems for the students rather then allowing them to figure it out themselves. The next time I am in the classroom I plan to help students without doing the work for them! 

Sheridan- Noteblog Week 2

I see many connections between the readings in the Cognitively Guided Instruction book and the math used in my field placement. The field placement that I am is in a first grade class and I observe math every day that I go in. Math is a huge part of the curriculum in my school because the school that I am in, Colt Elementary is an early education program. The school is kindergarten through first grade. The readings (chapter 4) talked about using counters, or other tangible objects in order to solve multiplication and division problems. The students in my class are mostly working on addition and subtraction programs, but sometimes multiplication or division problems are thrown into their math worksheets. They are used to using their counters and solving problems using this type of manipulative. I feel this is very useful because the students are actually seeing what is happening with the numbers. My class is also starting to use grouping my tens. In chapter 6 they were using larger numbers in their examples than we use in our classroom. For example, an example in chapter 6, page 78 is: “The school bought 6 boxes of markers. There are 24 markers in each box. How many makers are there all together?” Most of the students in my placement do not have enough knowledge to solve a problem like this. They need more work on grouping with groups of tens. Last semester in my placement, students were just starting to use the tens-frame to look at numbers 1-10. This week, they are starting to use two tens-frames to look at numbers 1-20. Some students are struggling with the concept that if one of the tens-frames is completely full, that means that there are ten counters in the spots. Some students still count each individual spot in both frames, instead of counting on from ten and then moving to the second tens-frame. I do feel like most of the students in my placement have basic addition and subtraction problems down, and I’m curious to see how the students do when we move to multiplication and division problems.