Get the Turtle to the Pond
K-2
http://illuminations.nctm.org/LessonDetail.aspx?id=L396
Summary: This is an application geared for grades K-2. This is a simple game developed to help students apply measurement and basic geometry knowledge. The students are given directional buttons which include moving forwards, backwards, rotating the turtle 90 degrees left or right. The students get to choose how many units to move their turtle. They have to get the turtle to the pond, and then the turtle splashes in the pond. The students could also document their paths on paper by drawing the turtle and his journey to the pond and writing our the steps including the measurement units. The students will be able to write directional words including right, left, forwards, backwards. They will also be able to use the applet to create an appropriate path to the pond.
Critique:
I think this is a really great applet for K-2. It is very age appropriate with a good amount of challenge. This has the strength of letting learners have interaction with what they are learning. They can also determine the level of difficulty by pushing different buttons that put barriers in the way and also that take the grid off of the page. This could be difficult for students who are directionally challenged. This would be a good use for students as an extension to what they are already learning in class.
Sunday, February 14, 2010
Pan Balance - Applet Review
Pan Balance - Numbers
3-5
http://illuminations.nctm.org/ActivityDetail.aspx?ID=26
Summary:
This is an application that is geared towards grades 3-5 dealing with number operations. In the applet, the students are given a balance with one pan on each side of the balance. A simple problem is entered into the red pan such as 7+3 and it will show the sum of 10. Then in the blue pan the student should enter something that will be it's equivalent such as 5x2 and the answer 10 will appear. The problems with solutions will then appear on the right hand column called the balanced equations area because it was equivalent. If a student does not enter problems that yield the same answer, the equation with the higher number will appear heavier causing the balance to tilt one side; then it will not go into the balanced equations area. Students will be able to type mathematical equations that are equivalent. Students will also be able to recognize the difference between equivalent and non equivalent equations.
Critique:
I think that this application would be an effective use in the classroom to reinforce lessons done in class about equivalent equations. This application could be used for one person or as a two person game. This is good for those who are fluent in numbers because they don't give you any numbers to start of. The student enters their own equations without any prompting from the applet. The weakness of this is that students who need help with numbers and operations may not know where to begin, so extra help would be needed. This could be a good tool for those who are gifted/talented because it would give an extra challenge.
Critique:
3-5
http://illuminations.nctm.org/ActivityDetail.aspx?ID=26
Summary:
This is an application that is geared towards grades 3-5 dealing with number operations. In the applet, the students are given a balance with one pan on each side of the balance. A simple problem is entered into the red pan such as 7+3 and it will show the sum of 10. Then in the blue pan the student should enter something that will be it's equivalent such as 5x2 and the answer 10 will appear. The problems with solutions will then appear on the right hand column called the balanced equations area because it was equivalent. If a student does not enter problems that yield the same answer, the equation with the higher number will appear heavier causing the balance to tilt one side; then it will not go into the balanced equations area. Students will be able to type mathematical equations that are equivalent. Students will also be able to recognize the difference between equivalent and non equivalent equations.
Critique:
I think that this application would be an effective use in the classroom to reinforce lessons done in class about equivalent equations. This application could be used for one person or as a two person game. This is good for those who are fluent in numbers because they don't give you any numbers to start of. The student enters their own equations without any prompting from the applet. The weakness of this is that students who need help with numbers and operations may not know where to begin, so extra help would be needed. This could be a good tool for those who are gifted/talented because it would give an extra challenge.
Critique:
Wednesday, February 10, 2010
Article Review: Techniques for small-group DISCOURSE
I chose the article, Techniques for small-group DISCOURSE, taken from the Teaching Children Mathematics Journal. This article featured the importance of reasoning and critical thinking in mathematics through group discourse or discussion. Too many of students develop a negative disposition because of the way instructors teach mathematics. In order for mathematical instruction to be effective, the teacher must apply various methods which include: critical thinking, reasoning, open communication, question asking, making conjectures, constructing and assessing mathematical arguments.
According to this article, there are many things a teacher can do to keep the students actively engaged in learning math. The teacher's effectiveness in group discourse can either make or break a student's disposition towards math. One of the techniques teachers can use is asking questions. Teachers need to master the art of question asking. They need to ask thought-provoking, guided questions that will yield critical thinking, and the sharing of learners' own ideas as well as listening to others.
The authors of this article took the reader through some examples of students engaging in small group discourse. The small group discussions were then evaluated to come up with techniques that work and to assess things that the teacher did that didn't work so well.
It was found that when teachers require the students to give explanations for their work, students become more fluent in mathematical ideas and are more open to other ways of justifying the answer. Students should be redirected from just giving a final answer and encouraged to think through the process. It would be advantageous for the learner to consider multiple ways of arriving at a solution instead of having one particular way of doing things in mind and shutting out other creative approaches.
I think that this approach to instruction within mathematics is a very useful tool. I believe that students would learn better by internalizing through critical thinking and justification.
Kilic, H., Cross, D., Ersoz, F., Mewborn, D., Swanagan, D. and Kim, J. (2010). Techniques for small-group Discourse. Teaching Children Mathematics 16 (6), 350-357
According to this article, there are many things a teacher can do to keep the students actively engaged in learning math. The teacher's effectiveness in group discourse can either make or break a student's disposition towards math. One of the techniques teachers can use is asking questions. Teachers need to master the art of question asking. They need to ask thought-provoking, guided questions that will yield critical thinking, and the sharing of learners' own ideas as well as listening to others.
The authors of this article took the reader through some examples of students engaging in small group discourse. The small group discussions were then evaluated to come up with techniques that work and to assess things that the teacher did that didn't work so well.
It was found that when teachers require the students to give explanations for their work, students become more fluent in mathematical ideas and are more open to other ways of justifying the answer. Students should be redirected from just giving a final answer and encouraged to think through the process. It would be advantageous for the learner to consider multiple ways of arriving at a solution instead of having one particular way of doing things in mind and shutting out other creative approaches.
I think that this approach to instruction within mathematics is a very useful tool. I believe that students would learn better by internalizing through critical thinking and justification.
Kilic, H., Cross, D., Ersoz, F., Mewborn, D., Swanagan, D. and Kim, J. (2010). Techniques for small-group Discourse. Teaching Children Mathematics 16 (6), 350-357
Article Review: Calculus in the Middle School?
I read the article entitled Calculus in the Middle School? found in the Mathematics Teaching In the Middle School journal. The authors of this article were presenting the idea of incorporating calculus earlier in a learner's education. Just as Algebra is being taught at earlier academic levels, so should calculus. It has been proven successful to teach algebra as a way of thinking to elementary students as a way of preparing them for Middle School. Just as Algebra is viewed as an introductory course to ready young learner's minds for higher level math, Calculus is viewed in the same way. Calculus is used in High School to prepare individuals for College level math. It is also used to weed out those who would not be successful for particular fields of study based on their performance in these types of math courses.
The article presents two main ideas in Calculus that should be taught in Middle School math called differentiation and derivative. They suggest that calculus needs one strong basis of competency in order to be strong in these classes. That baseline content area is the study of mathematical change. If students understood mathematical change, they would be set up for success upon entering these calculus classes.
In the article, the authors pose a hypothetical situation in a classroom where the teacher introduces calculus to the students without their knowing. The students work the problem step by step together while activating mathematical discourse and reasoning. Through their discourse, they come to a working knowledge of each step until they complete the last step of the calculus problem that is found in a calculus textbook. The teacher then tells the class what they have done.
REFLECTION:
I think that this is a good idea; however, since the article uses a pretend scenario, it's hard for me to imagine how the classroom discussion would actually occur. I could see this being very strategic and effective, but I would be interested to see how the students respond in a real life setting. I think that the article poses an excellent point and idea which should be entertained.
Barger, R., McCoy, A. (2010). Calculus in the Middle School? Mathematics Teaching in the Middle School 15(6), 348-353
The article presents two main ideas in Calculus that should be taught in Middle School math called differentiation and derivative. They suggest that calculus needs one strong basis of competency in order to be strong in these classes. That baseline content area is the study of mathematical change. If students understood mathematical change, they would be set up for success upon entering these calculus classes.
In the article, the authors pose a hypothetical situation in a classroom where the teacher introduces calculus to the students without their knowing. The students work the problem step by step together while activating mathematical discourse and reasoning. Through their discourse, they come to a working knowledge of each step until they complete the last step of the calculus problem that is found in a calculus textbook. The teacher then tells the class what they have done.
REFLECTION:
I think that this is a good idea; however, since the article uses a pretend scenario, it's hard for me to imagine how the classroom discussion would actually occur. I could see this being very strategic and effective, but I would be interested to see how the students respond in a real life setting. I think that the article poses an excellent point and idea which should be entertained.
Barger, R., McCoy, A. (2010). Calculus in the Middle School? Mathematics Teaching in the Middle School 15(6), 348-353
Sunday, February 7, 2010
Wednesday, February 3, 2010
PBL Article Review
I chose the article, How to buy a car 101, in which a 7th grade class does a PBL on buying cars. They are given a set of guidelinesfor the project and parameters for the type of car needed. The students are given 2 weeks to do research by looking at dealerships and cars online, contacting banks and dealerships, etc. The students had an opportunity to take mathematics and get their hands dirty in a real life situation in which they could apply what they had learned and learn new ideas and concepts.
I thought that the teacher who put this PBL together did an excellent job of adhering to the content standards that were set forth. He/she also did a great job of making the problem both interesting and applicable to the students as they are at the age of dreaming about driving and owning their very own car. I liked how the teacher set the boundaries and guidelines for the learners, had an example of the final product, and let the students take control of the rest. The article emphasized the importance of letting the learners take over in the classroom in taking initiative.
In learning through PBL, students get a better understanding of the material they are learning because they are applying it to their everyday lives or real life situations.
Flores, C. (2006). How to buy a car 101. The National Council of Teachers of Mathematics. 12(3), 161-164.
I thought that the teacher who put this PBL together did an excellent job of adhering to the content standards that were set forth. He/she also did a great job of making the problem both interesting and applicable to the students as they are at the age of dreaming about driving and owning their very own car. I liked how the teacher set the boundaries and guidelines for the learners, had an example of the final product, and let the students take control of the rest. The article emphasized the importance of letting the learners take over in the classroom in taking initiative.
In learning through PBL, students get a better understanding of the material they are learning because they are applying it to their everyday lives or real life situations.
Flores, C. (2006). How to buy a car 101. The National Council of Teachers of Mathematics. 12(3), 161-164.
Problem-Based Learning Review
After much study and review, I have found that problem-based learning is an instructional method that helps teachers to adhere to the standards. PBL is also heavily concentrated on real life situations and problems that are interesting and relevant to the student. Problem based learning is student centered and allows students to take a problem and work with it making necessary changes or additions as they see fit. There is no particular outcome or one right answer. The goal of this type of instruction is to have many different possible outcomes so that students can grapple with mathematics methods.
Problem Based Learning has a lot of benefits. This technique of instruction includes integrating knowledge not just in mathematics but in other situations which allows the learner to think critically through reasoning. Through using PBL, students feel equipped to take on tasks that may be a challenge. This also allows students to think through the small practical steps leading up to the solution.
Problem Based Learning has a lot of benefits. This technique of instruction includes integrating knowledge not just in mathematics but in other situations which allows the learner to think critically through reasoning. Through using PBL, students feel equipped to take on tasks that may be a challenge. This also allows students to think through the small practical steps leading up to the solution.
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