Summary: This applet is all about money. The first setting of the applet is titled "how much money". In this setting a certain amount of money is shown visually through actual pictures of bills and change. The student will type in how much money is shown. The apple will say if it is too much money, not enough money, or if the answer is correct. The next setting is called "pay exact amount". In this setting there is a title that says to pay exact amount in a certain amount of money. For example "pay $60". At the top of the applet there are pictures of bills and change and you have to move the exact correct amount of money into the box. The applet will tell you if you are correct or not. The next setting is called "make a dollar". This is where the applet gives you pictures of change and asks you to make a dollar using the change.
Critique: I find this applet to be extremely beneficial. This applet would be great for younger children. It is very visual and hands on. Students get the opportunity to see actual pictures of money. When students learn about money it is important that they know what it really looks like, and not just the plastic and fake paper stuff. Students may become confused when presented with real money if they have been learning about money using plastic money. The three different settings for this applet are also very beneficial. The different settings are all very different but are all teaching the same general concept of money. This applet allows students to not only count money, but to make change into a dollar, and also learn how to give exact change when asked for it. These are all very important concepts for children to learn early on.
http://www.nlvm.usu.edu/en/nav/frames_asid_325_g_1_t_4.html?from=category_g_1_t_4.html
Monday, February 15, 2010
Math Applet- Percent Grids
Summary: This applet is all about teaching percentages using a grid. This applet has three settings in which you can use to figure out percentages. The first setting is an explore setting. Through this setting you fill in box's on the grid, and then write what percentage that shows. This applet will tell you if you are correct or not. The next setting is the "show" setting. In this a percent will be listed such as 50%. You will have to fill in 50% of the box's on the grid. At the top of the applet shows what percent you are filling in so you know if you are correct. The third setting is called "name". This is where the applet presents you with a picture of a grid with a certain amount of box's shaded in. You have to type in the correct percent that is shown, and the applet will tell you if it is correct or not. The applet uses a neon green color to make it visually appealing.
Critique: I really enjoyed this applet. I feel that it is very hands on which can be very beneficial to students. There is also a variety of methods used to show percentages. The thing I really enjoy is that with this applet it gives the opportunity for students to be able to explore percentages and see what a certain percent really means and what it looks like. This applet also allows students to test their knowledge of percentages as well. This applet would be a great tool to introduce percentages (in the explore setting) and also to test knowledge or review knowledge of percentages (in the show and name settings). The standards that are listed for this applet directly correlate to the applet as well. This tool can be very beneficial for students, especially if they are visual or hands on learners.
http://www.nlvm.usu.edu/en/nav/frames_asid_333_g_2_t_1.html?from=category_g_2_t_1.html
Critique: I really enjoyed this applet. I feel that it is very hands on which can be very beneficial to students. There is also a variety of methods used to show percentages. The thing I really enjoy is that with this applet it gives the opportunity for students to be able to explore percentages and see what a certain percent really means and what it looks like. This applet also allows students to test their knowledge of percentages as well. This applet would be a great tool to introduce percentages (in the explore setting) and also to test knowledge or review knowledge of percentages (in the show and name settings). The standards that are listed for this applet directly correlate to the applet as well. This tool can be very beneficial for students, especially if they are visual or hands on learners.
http://www.nlvm.usu.edu/en/nav/frames_asid_333_g_2_t_1.html?from=category_g_2_t_1.html
Monday, February 8, 2010
Journal Article- Preschoolers' Number Sense
SUMMARY
The article started off with an example of a teacher evaluating on their students number senses. The student and teacher would each pick a card and take the corresponding number of small plastic bears that match the card. The teacher would then ask the student questions like "who has more bears?" or "how many bears do you have?" She was doing this to asses her students number sense. This simple understand can be a predictor for how the student will do in the future with mathematics. The preschool age is very critical in learning mathematics so teachers need to make sure to asses their students to make sure that they are understanding the concepts.
Teachers need to use different types of assessment, especially with preschool age children. Children at this age usually become bored with the traditional types of assessment. Teachers should try to incorporate "play" into their assessments and also their teaching because this will keep their young students involved and paying attention.
APPLICATION
I have learned a lot through this short article. One of the most important things that I learned about was equity. In a classroom all students deserve an equal opportunity to learn and grow. As a teacher we will have classrooms with many diverse students. These classrooms will have students with disabilities, students who may be advanced, and also students who are learning English as their second language.
When it comes to teaching my young students a good way to do this is through play. This allows students to actually see how the math can fit in with their everyday lives. It also helps them stay on task, stay involved, and want to participate.
Teaching students the core mathematical concepts at an early age is very important. A student who does well at math in the beginning of school usually continues do excel in math throughout all of their schooling. This same idea goes with students who may not be doing as well with mathematics in the beginning of their schooling. This is why it is important to continually assess your students. When working with children who are at the preschool age, I should vary up my types of assessment. Young students can get very bored with the traditional question yields answer assessments. For my students I will need to provide different assessments. For example I can assess them through the actual process's or by doing examples with them.
The article started off with an example of a teacher evaluating on their students number senses. The student and teacher would each pick a card and take the corresponding number of small plastic bears that match the card. The teacher would then ask the student questions like "who has more bears?" or "how many bears do you have?" She was doing this to asses her students number sense. This simple understand can be a predictor for how the student will do in the future with mathematics. The preschool age is very critical in learning mathematics so teachers need to make sure to asses their students to make sure that they are understanding the concepts.
Teachers need to use different types of assessment, especially with preschool age children. Children at this age usually become bored with the traditional types of assessment. Teachers should try to incorporate "play" into their assessments and also their teaching because this will keep their young students involved and paying attention.
APPLICATION
I have learned a lot through this short article. One of the most important things that I learned about was equity. In a classroom all students deserve an equal opportunity to learn and grow. As a teacher we will have classrooms with many diverse students. These classrooms will have students with disabilities, students who may be advanced, and also students who are learning English as their second language.
When it comes to teaching my young students a good way to do this is through play. This allows students to actually see how the math can fit in with their everyday lives. It also helps them stay on task, stay involved, and want to participate.
Teaching students the core mathematical concepts at an early age is very important. A student who does well at math in the beginning of school usually continues do excel in math throughout all of their schooling. This same idea goes with students who may not be doing as well with mathematics in the beginning of their schooling. This is why it is important to continually assess your students. When working with children who are at the preschool age, I should vary up my types of assessment. Young students can get very bored with the traditional question yields answer assessments. For my students I will need to provide different assessments. For example I can assess them through the actual process's or by doing examples with them.
Journal Article- Calculus in Middle Schools?
SUMMARY
This article was all about how calculus can be seen throughout all different grade levels. Calculus can often scare students, and make them dislike math because they see it as too challenging. Students do not understand however that the work they are doing at a middle school level directly correlates to work that is done at a high school or even college level. This article provided many examples to teaching students calculus. Such examples include looking at various representations of a problem and also creating a story about how certain graphs provided to the students go together. The article also emphasized that middle school is a very important time to prepare students for higher level mathematics. In conclusion, as teachers at any level we want to provide foundations for our students to be able to grow and prosper. We want to provide opportunities that cause our students to think and have to work hard. However, we do not want to scare our students.
APPLICATION
I do not want my students be afraid of math. I need to make sure that I provide my students with a solid foundation of math during the elementary level so that by the time they get to middle school so that they are not overwhelmed and scared. In the elementary school level you want your students to be familiar with the algebraic way of thinking. Than as a middle school teacher we will need to provide our students a foundation on of calculus to get them ready for high school. Middle school is were as a teacher you want to provide the foundation of calculus for your students for future learning. A good way to teach students about calculus is to provide them with about five graphs. Have your students write a story to explain the graphs and how they fit together. This well help students gain understanding. As a teacher I will want to show my students the connection with what there doing to actual problems that can be found in their mathematics textbook. I want to prepare my students so that they can actually take the higher, more advanced math classes and not be scared away.
This article was all about how calculus can be seen throughout all different grade levels. Calculus can often scare students, and make them dislike math because they see it as too challenging. Students do not understand however that the work they are doing at a middle school level directly correlates to work that is done at a high school or even college level. This article provided many examples to teaching students calculus. Such examples include looking at various representations of a problem and also creating a story about how certain graphs provided to the students go together. The article also emphasized that middle school is a very important time to prepare students for higher level mathematics. In conclusion, as teachers at any level we want to provide foundations for our students to be able to grow and prosper. We want to provide opportunities that cause our students to think and have to work hard. However, we do not want to scare our students.
APPLICATION
I do not want my students be afraid of math. I need to make sure that I provide my students with a solid foundation of math during the elementary level so that by the time they get to middle school so that they are not overwhelmed and scared. In the elementary school level you want your students to be familiar with the algebraic way of thinking. Than as a middle school teacher we will need to provide our students a foundation on of calculus to get them ready for high school. Middle school is were as a teacher you want to provide the foundation of calculus for your students for future learning. A good way to teach students about calculus is to provide them with about five graphs. Have your students write a story to explain the graphs and how they fit together. This well help students gain understanding. As a teacher I will want to show my students the connection with what there doing to actual problems that can be found in their mathematics textbook. I want to prepare my students so that they can actually take the higher, more advanced math classes and not be scared away.
Wednesday, February 3, 2010
Example PBL's Log
1) Operation: “Redo the Zoo” PBL for 5th & 6th grades PBL EXAMPLE ONE
This PBL is all about the Zoo, at the beginning of the unit students take a trip to the zoo. By the end of the unit students will be able to make their own zoo, or "redo the zoo". By taking a tour and walking around the zoo students will be able to see what aspects of the zoo that they like, and which aspects they do not like. This PBL allows students to show their creative side. Their final project will be in form of a visual display board and a written proposal. Students will show reasoning and proof through calculations, conjectures, and also journals which they will be keeping.
The students will be broken up into groups, where each group member gets a different position. Such as one person is the zoologist and one is the builder. Each member of the group will work together to create a new zoo. After fifteen days of working together and also mini lessons, students will comprise a final project and present it to the class.
Adopt-A-Lot Problem Based Learning PBL EXAMPLE TWO
This example is about students adopting a lot or park because it relates to the students interests. This PBL allows the students to sort of become involved with their community. The students will be divided into groups of four to five randomly. However, each student does not have their own role. The students were given a problem were they were design a park on a given budget. When the ran out of their budget they had to come up with ways that they could fund raise the extra money in which they needed.
2) Strengths and Weakness's of This Activity
I have learned a lot about PBL's through this activity. This activity really strengthened my knowledge on the subject. By actually being able to see two different examples I could sort of see which example was a better one. I learned that with a PBL you must be extremely detail orientated. In a PBL you want to make sure that you include everything that is needed and more. I also learned that the rational should help you learn what the whole PBL is going to be about. I'm really glad that we were given the opportunity to do this blogging about PBL's before we started our own PBL's. I now know what we are going to be completing, how detailed we have to be, and what we need to do to get it done.
3) Compare and Contrast the Two PBL's
These two PBLs are very different from each other. The first PBL is very organized, has pictures, great descriptions, and also a ton of extra information such as many student pages, teacher pages, and resources. The second PBL has the main information, however it is lacking the extra information that really make the first PBL great. The PBL on "redo a zoo" also seems that it would be a lot more interesting to students. In this PBL students get to travel to a Zoo, which can be very exciting for some students. The PBL's are different because the first example seems to show more student involvement and inquiry.
4) Critique the strengths and weakness's
I really enjoyed the first PBL because it pointed out very thoroughly how each of the process standards were going to be shown throughout the lesson. In the second PBL they did not explain at all how they were going to incorporate each process standard. For example in the first PBL, "A connection is made to the area of language arts when students write in their journals and give their oral presentations at the end of the project." They stated how they were going to show connections through other subjects. They also showed how they were going to show connections with other subjects later in the PBL. However in the 2nd example, they only showed it in the end. Another strength of the first PBL is their student pages. These student pages seem perfect for a 6th grade student. They have a good amount of pictures to get the students involved, but also the information learned on the student pages is very beneficial. One thing that I really liked about the 2nd example was that they had well thought out guided questions for each day of their daily schedule. For example a question was "Are you frequently reviewing your budget?". This is an example of many of their questions that all seem to be about keeping the students on track with the PBL. Another strength of the first PBL example was that their rationale and brief description of their PBL. This let me know exactly what there lessons and what there overall unit was going to be. However, with the second example of the PBL I was left confused after reading their rationale and had to continue reading the rest of the PBL before I understood what they were trying to do. In the first PBL each student had their own role "The students will have the opportunity to choose from the following roles: architect, zoologist, horticulturalist, builder, and an accountant", however in the 2nd PBL example the student were not any specific position.
5) Is math the main focus? 1st PBL example
At first for the first PBL example I was not quite sure on how they were going to relate building a zoo back to 6th grade math. However, when I continued to read the PBL I realized that it had a lot to do with math. Through this PBL students are going to be doing numbering and operations, geometry, measurement and algebra. Through this they will be using prior knowledge and will gain a lot of new knowledge, For example, by the end of this unit students will be able to calculate percentages when computing a budget. The level of math that is expected through their objectives and the new knowledge that they will gain directly correlates with the Illinois state standards that they listed.
Is math the main focus?2nd PBL example
This example does have to do with math. The students will need to budget their money. However, in this PBL example the way math is related is not as clear as it was in the first. In the first example they stated numerous times how math was to be incorporated however I did not really see that much in this example. They did have math objectives where it said things that students would be learning such as proportions, budgeting, and graphing.
6) Assessment - 1st PBL example
Throughout the entire unit there will be multiple assessments. There will be informal assessments consisting of journals and also observation. There will also be a formal assessment through quiz's throughout the unit. The final assessment will be on a portfolio that they make and also through a final presentation. I find these ways of assessment very beneficial. Some students work better with formal assessment and other work better with informal assessments, this gives students equal opportunities of both types throughout the unit. The actual assessment part of the PBL however did not address specifically how they were going to asses the students involving math. Throughout the PBL you could clearly see how the math was going to be assessed.
Assessment - 2nd PBL example
This example did a really good job with their assessment. There were examples of informal assessments; journals, student teacher conferences, and direct observation. There were also formal assessments such as a written proposal, notes, and a fund raising plan. There is also a assessment on a portfolio in which they will complete. One thing that that really stuck out was their rubric for the portfolio, these rubrics were extremely detailed which would really benefit the students. Even though the math assesment was not clearly explained in the assessment portion of the PBL, throughout the entire lesson you could see where and what math topics were being assessed.
This PBL is all about the Zoo, at the beginning of the unit students take a trip to the zoo. By the end of the unit students will be able to make their own zoo, or "redo the zoo". By taking a tour and walking around the zoo students will be able to see what aspects of the zoo that they like, and which aspects they do not like. This PBL allows students to show their creative side. Their final project will be in form of a visual display board and a written proposal. Students will show reasoning and proof through calculations, conjectures, and also journals which they will be keeping.
The students will be broken up into groups, where each group member gets a different position. Such as one person is the zoologist and one is the builder. Each member of the group will work together to create a new zoo. After fifteen days of working together and also mini lessons, students will comprise a final project and present it to the class.
Adopt-A-Lot Problem Based Learning PBL EXAMPLE TWO
This example is about students adopting a lot or park because it relates to the students interests. This PBL allows the students to sort of become involved with their community. The students will be divided into groups of four to five randomly. However, each student does not have their own role. The students were given a problem were they were design a park on a given budget. When the ran out of their budget they had to come up with ways that they could fund raise the extra money in which they needed.
2) Strengths and Weakness's of This Activity
I have learned a lot about PBL's through this activity. This activity really strengthened my knowledge on the subject. By actually being able to see two different examples I could sort of see which example was a better one. I learned that with a PBL you must be extremely detail orientated. In a PBL you want to make sure that you include everything that is needed and more. I also learned that the rational should help you learn what the whole PBL is going to be about. I'm really glad that we were given the opportunity to do this blogging about PBL's before we started our own PBL's. I now know what we are going to be completing, how detailed we have to be, and what we need to do to get it done.
3) Compare and Contrast the Two PBL's
These two PBLs are very different from each other. The first PBL is very organized, has pictures, great descriptions, and also a ton of extra information such as many student pages, teacher pages, and resources. The second PBL has the main information, however it is lacking the extra information that really make the first PBL great. The PBL on "redo a zoo" also seems that it would be a lot more interesting to students. In this PBL students get to travel to a Zoo, which can be very exciting for some students. The PBL's are different because the first example seems to show more student involvement and inquiry.
4) Critique the strengths and weakness's
I really enjoyed the first PBL because it pointed out very thoroughly how each of the process standards were going to be shown throughout the lesson. In the second PBL they did not explain at all how they were going to incorporate each process standard. For example in the first PBL, "A connection is made to the area of language arts when students write in their journals and give their oral presentations at the end of the project." They stated how they were going to show connections through other subjects. They also showed how they were going to show connections with other subjects later in the PBL. However in the 2nd example, they only showed it in the end. Another strength of the first PBL is their student pages. These student pages seem perfect for a 6th grade student. They have a good amount of pictures to get the students involved, but also the information learned on the student pages is very beneficial. One thing that I really liked about the 2nd example was that they had well thought out guided questions for each day of their daily schedule. For example a question was "Are you frequently reviewing your budget?". This is an example of many of their questions that all seem to be about keeping the students on track with the PBL. Another strength of the first PBL example was that their rationale and brief description of their PBL. This let me know exactly what there lessons and what there overall unit was going to be. However, with the second example of the PBL I was left confused after reading their rationale and had to continue reading the rest of the PBL before I understood what they were trying to do. In the first PBL each student had their own role "The students will have the opportunity to choose from the following roles: architect, zoologist, horticulturalist, builder, and an accountant", however in the 2nd PBL example the student were not any specific position.
5) Is math the main focus? 1st PBL example
At first for the first PBL example I was not quite sure on how they were going to relate building a zoo back to 6th grade math. However, when I continued to read the PBL I realized that it had a lot to do with math. Through this PBL students are going to be doing numbering and operations, geometry, measurement and algebra. Through this they will be using prior knowledge and will gain a lot of new knowledge, For example, by the end of this unit students will be able to calculate percentages when computing a budget. The level of math that is expected through their objectives and the new knowledge that they will gain directly correlates with the Illinois state standards that they listed.
Is math the main focus?2nd PBL example
This example does have to do with math. The students will need to budget their money. However, in this PBL example the way math is related is not as clear as it was in the first. In the first example they stated numerous times how math was to be incorporated however I did not really see that much in this example. They did have math objectives where it said things that students would be learning such as proportions, budgeting, and graphing.
6) Assessment - 1st PBL example
Throughout the entire unit there will be multiple assessments. There will be informal assessments consisting of journals and also observation. There will also be a formal assessment through quiz's throughout the unit. The final assessment will be on a portfolio that they make and also through a final presentation. I find these ways of assessment very beneficial. Some students work better with formal assessment and other work better with informal assessments, this gives students equal opportunities of both types throughout the unit. The actual assessment part of the PBL however did not address specifically how they were going to asses the students involving math. Throughout the PBL you could clearly see how the math was going to be assessed.
Assessment - 2nd PBL example
This example did a really good job with their assessment. There were examples of informal assessments; journals, student teacher conferences, and direct observation. There were also formal assessments such as a written proposal, notes, and a fund raising plan. There is also a assessment on a portfolio in which they will complete. One thing that that really stuck out was their rubric for the portfolio, these rubrics were extremely detailed which would really benefit the students. Even though the math assesment was not clearly explained in the assessment portion of the PBL, throughout the entire lesson you could see where and what math topics were being assessed.
Article about PBL
I was looking around for websites and I came across a very interesting website called IMSA's PBL Network. This website is about what a PBL is. From this site I learned a lot of information. "Problem-based learning (PBL) is focused experiential learning organized around the investigation and resolution of messy, real-world problems." (Gerdes, 2009). Problem based learning is focused on hands on experiences for students to solve real life problems. Through this type of learning students are able to solve problems through the guidance and facilitation of a teacher. PBL is a type of learning in which students are more in charge and the teacher acts as more of a guide, and helps the students along the process. Throughout the PBL the teacher will monitor students and also pose questions to get the students to think. Problem based learning helps students make learning relevant to the real world and also promotes critical thinking. PBL is effective because students as both the learners and problem solvers and teachers act more as a facilitator.
I find this website to be very affective to teach about problem based learning. This is especially true if you are a visual learner. The IMSA website provides many diagrams and pictures to help explain what a PBL is and how it works. There is a whole section on the intro to PBL page that takes you through what a PBL is, how it works, why it works, and what roles each person plays who is involved. This intro page breaks down problem based learning to the tee and explains every single aspect of it. Another thing that I have not yet seen through other PBL resources was a page that compared problem based learning to other types of learning. There are also tutorials in which you can act as student and follow a PBL example. A thing that I did not like so much about this website is that even though there was a lot of beneficial information, it seemed to be a little cluttered. The website could be more organized into more specific sections. The intro section had almost ten different sub sections. This could make it hard for someone who wanted to find a specific fact about problem based learning. Overall, I really enjoyed this website and would recommend it to anyone who is trying to learn about this learning process.
Gerdes, D. (n.d.). IMSA's PBLNetwork. IMSA's PBLNetwork. Retrieved February 3, 2010, from http://pbln.imsa.edu/index.html
I find this website to be very affective to teach about problem based learning. This is especially true if you are a visual learner. The IMSA website provides many diagrams and pictures to help explain what a PBL is and how it works. There is a whole section on the intro to PBL page that takes you through what a PBL is, how it works, why it works, and what roles each person plays who is involved. This intro page breaks down problem based learning to the tee and explains every single aspect of it. Another thing that I have not yet seen through other PBL resources was a page that compared problem based learning to other types of learning. There are also tutorials in which you can act as student and follow a PBL example. A thing that I did not like so much about this website is that even though there was a lot of beneficial information, it seemed to be a little cluttered. The website could be more organized into more specific sections. The intro section had almost ten different sub sections. This could make it hard for someone who wanted to find a specific fact about problem based learning. Overall, I really enjoyed this website and would recommend it to anyone who is trying to learn about this learning process.
Gerdes, D. (n.d.). IMSA's PBLNetwork. IMSA's PBLNetwork. Retrieved February 3, 2010, from http://pbln.imsa.edu/index.html
What is a PBL and where is it used?
Problem based learning is a learner centered approach that is facilitated by a teacher. Problem based learning helps with critical thinking, decision making, reasoning, and much more! PBL promotes higher learning and really causes a student to think. A teacher is very involved in problem based learning. They act sort of like a coach. They ask questions, provide advice, keep students on track with time, and are also a major support for the students. The teacher also decides what role students will play in the problem based learning. In problem based learning students work together to solve problems. This type of learning usually involves current events or the students interests. Students are encouraged to take their own responsibilities for their group based upon their specific roles in the group. KWL charts (Know, want to know, what we learned) can also be used in PBL, this helps students keep track of what they knew before the PBL, what they want to learn (questions that they will answer) and than once the lesson is over, what they have learned.
Problem based learning can be used as a unit. Within this unit class's should be taking field trips, having mini lessons, labs, and sometime speakers. Throughout the unit teachers should also every so often asses their students. Students can also asses themselves as well. It is important for students to be able to asses their self and also their group members.
Using problem based learning is very beneficial in a mathematics classroom because students can work together to solve problems. They can help each other out and also feed off of what the other students know. Problem based learning is important because it also promotes students to find the answers. Instead of giving students a question and telling them to find the answer, students are given the opportunity to form their own questions and find the answers. One of the most important parts of problem based learning is that it lets students see why math is important to the "real world". Students need to see and understand how math is, and will be, a part of their everyday lives.
Problem based learning can be used as a unit. Within this unit class's should be taking field trips, having mini lessons, labs, and sometime speakers. Throughout the unit teachers should also every so often asses their students. Students can also asses themselves as well. It is important for students to be able to asses their self and also their group members.
Using problem based learning is very beneficial in a mathematics classroom because students can work together to solve problems. They can help each other out and also feed off of what the other students know. Problem based learning is important because it also promotes students to find the answers. Instead of giving students a question and telling them to find the answer, students are given the opportunity to form their own questions and find the answers. One of the most important parts of problem based learning is that it lets students see why math is important to the "real world". Students need to see and understand how math is, and will be, a part of their everyday lives.
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