Math Applet - Investigating the Concept of Triangle and the Properties of Polygons: Making Triangles

Investigating the Concept of Triangle and the Properties of Polygons: Making Triangles - Geometry (K – 2) http://standards.nctm.org/document/eexamples/chap4/4.2/index.htm

Summary:

In this math applet students take what we all did as children on big wooden boards, and do it on the computer. This applet gives a virtual board with dots representing pegs on it. Students are asked to take the rubber bands on the side of the applet and to make triangles. They are encouraged to make many different triangles all of different shapes and sizes. Students can change the colors of the triangles and shape them in to make colorful geoboards. After they have made their triangles, they are to compare their triangles to a friend’s triangles and explain how their triangles are the same and are different. This lesson could introduce many other shapes as well as students learn more about polygons.

Critique:

I really like this applet. It is easy to use and fun to play with, even for me. If I were to use this applet in my own classroom I would not make it the main lesson. I feel as though students still need that object that can grasp and that physical geoboards are still a great way of teaching shapes. I think that combining the physical geoboards and virtual geoboards would make a much better lesson and give students opportunities to compare the two. This lesson is very easy to advance into learning about shapes with more sides and that makes this applet even more helpful. Students can advance to trickier polygons as they master them.

Math Applet - Spin the Big Wheel!

Spin the Big Wheel! Probability (3 - 5) http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=1015

Summary:

This applet gives third through fifth graders a very brief introduction to the way probability works. Students are told to “spin the wheel” to see what they win. They are also told the probability of getting a big prize. This resembles a carnival game that many of us see at a fair or picnic. Students spin the wheel to see what they get while a box on the side of the applet keeps track of what they land on and how many times. After several turns, students can compare results and see which part of the wheel was favored, or if they came out mostly even. Students can also put the data into a circle graph to see it more visually. This is a simply way to introduce probability and is a great way to start students at an early age.

Critique:

This applet has the potential to offer a lot and it has a lot of pros and cons in my opinion. Some pros would be that it is visually appealing for students. Students are going to be more inclined to do this sort of lesson because it is hands on and can become a game for them. They are learning and they do not even know it; which is the best kind of learning. Some cons is that this is a very basic explanation of probability; So basic that I feel it is good for third graders but might come off on the easy side for fifth graders. This applet could bring in more options to land on to make it more challenging. It could also be more interactive and ask students problems and equations rather than leaving it as is. Overall, the applet opened my eyes to the benefits this could add to my classroom to get students thinking about mathematics in a positive way.

MTMS Article - Rubrics as Formative Assessment Tools

Summary:

In this article I learned all about rubrics. Rubrics are one of the best formative assessment tools out there for classrooms because they benefit not only the teacher, but the student as well. There are four types of rubrics and all of these incorporate different approaches to assessing students. The different kinds are; holistic, analytic, specific, or general. Each rubric is explained of how it is created and how it is used, there are also examples listed of each rubric. Teachers gave great information on how they came to creating their own rubrics and the thought process they had to go through to get a well working rubric. There are two ways to make a rubric, by using students work or by using the assessment task. Both of these ways are helpful and can give the end result a teacher needs for assessment.

Application:

This article is very helpful for any new or upcoming teaching, including myself. At Bradley, I feel we learn a lot about different assessment tools but it is always nice to hear it from someone else's perspective. I think one of the most beneficial parts of the article was explaining how to create a rubric. I love the idea of making a rubric based on students work and their understanding of a task. It just makes sense to grade based on what students know rather than a correct set answer. I think I will use this technique in my classroom because it seems fair for all students. I feel more confident in my understanding of rubrics, especially the different kinds and what is put into each of them. In general, this will help me use rubrics to their full potential rather than plopping a letter grade on a students paper without an explanation.

McGatha, M, & Darcy, P. (2010). Rubrics as formative assessment tools. Mathematics Teaching in the Middle School, 15(6), Retrieved from http://www.nctm.org/eresources/view_media.asp?article_id=9096

Teaching Children Mathematics

Summary:

This article deals with preschoolers and there computation of numbers. Children work with an assessor on counting skill and comparing techniques. One on one students and assessors with count with cards and teddy bears determining amounts and corresponding teddy bears to dots. Teachers will have the student pull out however many bears they need to match up with how many dots they have on their card. They continue this process by adding another card and also comparing their amount of bears to the assessors bears. This type of skill is one that is important to assess at this age. Assessors ask questions and from students answers they are able to determine where they are in their counting abilities as well as their number sense. This type of assessment works for students at all ability levels and can be easily adapted to all students.

Application:

This article really helped me get a better sense of how to assess younger students. I feel that a lot of times when students are first brought into school they are at all different ability levels. This technique is a great way of figuring out what that ability level is and ways to help the student later. I feel that being one on one with an assessor is the best way to get correct results for a students number ability and it allows them to be the focus for awhile. I think this is a good technique for any classroom and can be incorporated into different age levels and content subjects. Applying this is easy and beneficial for both student and teacher.

Moomaw, S, Carr, V, Boat, M, & Barnett, D. (2010). Preschoolers' number sense. Teaching Children Mathematics, 16(6), Retrieved from http://nctm.org/eresources/view_media.asp?article_id=9130

PBL Samples Critique

PBL #1 Lounging Around - In the first PBL, students are presented with the problem of creating a new student lounge for the middle school. They are given a set budget and deadline to get it completed by. The activity becomes in depth throughout the process while students have to decide of fabrics and furnitures as well as creating advertisements. Students will create lists throughout the project and holding a debate for the cost and funding for the new student lounge. This PBL takes 16 days and covers many content areas.

PBL #2 Operation "Redo the Zoo" - This PBL is for 5th and 6th graders. Within it students face the problem of redoing the local zoo. Students get to decide what the zoo will look like, what kind of plants and animals are in it, and what building will be in the zoo. This PBL will take 15 days; during those days students will journal about their zoos and keep math logs for the money they spend. By the end of the project students will have a completed portfolio explaining all the work that goes into the zoo.

The Lounging Around PBL has a lot of strengths. I like this PBL because it states a problem that students can relate to extremely well. It goes into specific detail about what needs to be accomplished without getting to wordy and making it confusing. Everything is laid out in a good form that is easy to understand. One weakness I saw in my opinion is that some of the lessons could have held more detail. I felt that a few of them left me hanging and a little confused about what I was suppose to do with my classroom. Operation "Redo the Zoo" has a good general idea; students are interested in the zoo. I also feel that adding journaling is a strength because that is the best way to see students thoughts. One of the biggest weaknesses I see with this PBL is that it seems that there is a lot of unnecessary wordage. I feel like I am being told a lot but not really getting the entire point of the lesson or what the students are actually all going to be doing.

Overall, both PBLs will interest students at the grade level set. I feel like they both can be incorporated into many content areas and take about the same length in time. Also, both require collaboration and work everyday. Some differences are that Lounging Around is more realistic then Operation "Redo the Zoo. " Students could have the opportunity to help create their student lounge but it is a lot less likely that they can completely redesign a local zoo. Also, I feel that Operation "Redo the Zoo" went into a lot more detail than Lounging Around did.

An example of Lounging Around being clear and concise would be when the authors wrote the "description of the problem" it is very short and to the point making it easy for everyone to understand. An example of a lesson being to short is having a "work day" on day 11. I feel that's very broad and should explain better exactly what the students should be doing. In Operation "Redo the Zoo" journaling is mentioned when the authors wrote "Students will have a 15-minute time period to write in their journals about how they think they will apply concepts learned in the previous mini lessons, to their project." This is a great way to get students brainstorming. I see unnecessary wordage in the "brief description," it seems to be to long to be considered brief and many statements can be removed.

In both PLBs I feel that math is a main focus of the project. Students are given budgets and need to keep records of how much money they spend. They also need to measure various items and do algebraic math problems. The level of math expected from both problem based learning projects is right on task with the grade level it is presented to.

I feel that there is a wide range assessment throughout both of the PBLs I have looked over. Not only do the teachers assess the students but the students get to assess each other as well using checklists and rubrics. Teachers use rubrics to grade students which makes it easier for students to see what tasks they need to accomplish. Also, students are assessed both formally and informally. Like I have previously stated, I feel that parts of both lessons have clarity at different parts. Lounging Around has great clarity in describing the overall project and lacks it when going over what is going on each day. Operation "Redo the Zoo" is the exact opposite. It gives far to much detail in the overall description but makes a lot of sense when the daily processes are described. Both PBLs are great about making math more enjoyable. When realating the content to real life examples students are less likely to realize they are doing math and think of it more as an exciting project. This is a great way for students to effectively learn mathematics skills and it is incorporated into both PBLs.

PBL Article Review

I found the webpage "In the Classroom - Problem Based Learning" from the Center for Educational Technologies website. I was very impressed with the page they have set up for problem based learning. The information is very general, but it is great information for someone just starting to experience problem based learning. The webpage began by giving an introduction to problem based learning along with a simple definition. It goes into how a PBL works and what concepts all go into one. It then talks about what the teachers role is in a PBL and ways teachers can overstep their boundaries. Lastly, the webpage gave some great sites to look into for more information on developing a Problem based learning project.

When reading the information the webpage gives, I noticed that it is all very general. What they are explaining is great and very useful but, I think more information would have been better. There is a link to a PBL model which is very helpful, it creates a to-do-list for a PBL. I thought the learning listed made a lot of sense and was accurate. It says that the idea of problem based learning is to teacher students how to learn. Students learn meaningful information that is relevant to their life rather than just memorizing facts.

The strengths of the article include the way it is written and the topics it covers. The article is very easy to understand and provides valuable knowledge about problem based learning and how it strengthens a classroom. The article also covers both students and teachers which is beneficial to everyone involved. A weakness of the article would have to be that it does not provide as much depth as needed to fully understand problem based learning. It simply goes over the basics and leaves it at that.

Problem-based learning. (2002). Retrieved from http://www.cotf.edu/earthinfo/classroom/teachers/FTtopic1.html

PLB Reading/Review

Problem based learning focuses on hands on, student centered learning that involves real world everyday problems. It is a widely used method of teaching and when used correctly, it can be very beneficial for all involved. An essential for creating a PBL is to involve an ill-structured problem. These problems are messy and confusing at first, which is what students are trying to figure out. The problem needs to be create enough to keep students interested and get them hooked into learning about the problem.

During a PBL, students are given roles within their groups. These roles help to maintain students interest and also make sure every student is doing some work on the problem. In the end, the point of a PBL is to get students thinking at a higher level. To apply skills from all areas and apply it to a problem that students need to work through together. Students will work through a thought process and use the scientific method to determine outcomes and guesses. Students will also go through each step one at a time rather than looking for an overall answer.

Problem based learning is used in the classroom over any topic that is challenging to teach or for students to grasp. These problems can be done in groups to establish more peer collaboration and communication. In general, PBLs are important in every classroom