Thursday, December 8, 2011
Sunday, October 23, 2011
Inquiry and CMP Research
Inquiry Based Learning
When I googled “Inquiry based learning” one of the very first hits to appear is the link to the website described below. They describe Inquiry-based learning as a learning process through questions generated from the interests, curiosities, and perspectives/experiences of the learner. When investigations grow from our own questions, curiosities, and experiences, learning is an organic and motivating process that is intrinsically enjoyable.
I am very happy with the way they explain it in their diagram:
What a great way to learn right? Being able to ask the questions that you want to know, create your own personal hypothesis of those questions, investigate them, find some new knowledge that you have gained from it, discuss with others on what you found, and then apply it in real life? What an extremely attractive way to learn!
Connected Mathematics Project (CMP)
When visiting the Connected Mathematics Project Homepage their overarching goal is that “All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness and proficiency.”
Sounds like a pretty awesome goal to me, so how are we going to get there?
The CMP instructional model follows the design of “Launch, Explore, and Summarize”. The basic idea is that the teacher launches a discussion and helps the students understand the nature of the question. The next stage is to explore the questions you might have about the topic individually, in pairs, or even in larger groups. Finally, once these groups have had sufficient time to discuss, all of the parts of the classroom come back to a whole to summarize what they have found.
The question is : “How does the CMP Instructional Model (Launch -> Explore -> Summarize) compare to the more traditional direct instruction -> guided practice -> independent work model? Is the CMP model inquiry based?”
Through the research that we have all put together the CMP model definitely seems to be an inquiry based method that completely differs from the direction instruction method and allows students to learn the topics in a much more dynamic fashion while really challenging them to think rather than posing the questions for them. Id say that this would be a pretty powerful way to teach math if you set it all up correctly!
When prompted with the following questions, Loran Sell, a former middle school math instructor and now professor described his thoughts on the CMP:
When I googled “Inquiry based learning” one of the very first hits to appear is the link to the website described below. They describe Inquiry-based learning as a learning process through questions generated from the interests, curiosities, and perspectives/experiences of the learner. When investigations grow from our own questions, curiosities, and experiences, learning is an organic and motivating process that is intrinsically enjoyable.
I am very happy with the way they explain it in their diagram:
What a great way to learn right? Being able to ask the questions that you want to know, create your own personal hypothesis of those questions, investigate them, find some new knowledge that you have gained from it, discuss with others on what you found, and then apply it in real life? What an extremely attractive way to learn!
Connected Mathematics Project (CMP)
When visiting the Connected Mathematics Project Homepage their overarching goal is that “All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness and proficiency.”
Sounds like a pretty awesome goal to me, so how are we going to get there?
The CMP instructional model follows the design of “Launch, Explore, and Summarize”. The basic idea is that the teacher launches a discussion and helps the students understand the nature of the question. The next stage is to explore the questions you might have about the topic individually, in pairs, or even in larger groups. Finally, once these groups have had sufficient time to discuss, all of the parts of the classroom come back to a whole to summarize what they have found.
The question is : “How does the CMP Instructional Model (Launch -> Explore -> Summarize) compare to the more traditional direct instruction -> guided practice -> independent work model? Is the CMP model inquiry based?”
Through the research that we have all put together the CMP model definitely seems to be an inquiry based method that completely differs from the direction instruction method and allows students to learn the topics in a much more dynamic fashion while really challenging them to think rather than posing the questions for them. Id say that this would be a pretty powerful way to teach math if you set it all up correctly!
When prompted with the following questions, Loran Sell, a former middle school math instructor and now professor described his thoughts on the CMP:
- How does the CMP curriculum align with the national Common Core and NCTM standards? Very well, in fact it was designed to fit the standards.
- Numerous students are a year or more behind in the basics. How does one address the needs of these students on a daily basis so they can get up to grade level and also experience success in the inquiry to investigation philosophy of the CMP? This is a difficult problem that, in my experience, is not addressed adequately in CMP. What I see most teachers doing is filling in the basics with drill and practice. Without devoting extra time to reteaching basics, students who are lacking in skills are either retaught at the cost of the CMP objective, or continue to flounder and often become dependent on other members of their group.
- What is the role of homework (and accountability) in the CMP? Teachers who are training in CMP and make the most of the class time may not need homework to accomplish the objectives. Unfortunately there are far too many teachers teaching CMP who are not trained and/or do not buy into this style of teaching. For homework to be effective, it most have a meaningful connection to the lesson that enriches or reinforces the lesson. What I see is often homework is " finish the assignment."
- CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning).
- Describe several classroom management techniques that ensure all students are actively engaged. Eg, how are individual roles established? Accountability (Group, individual)? Ongoing assessment(s) and checking for understanding? For small group work to be effective it most have both group and individual accountability. This is where the training of teachers is vital. Without it many teachers forget one or the other. Individual scores have both a group and individual component. ie
- a. Your grade on today's activity will be 50% on the work and answer that your group obtains, and 50% on your explanation of the process used to arrive at this answer.
- b. EAch group member has an individual responsibility in the final product. - Tom will show the mathematical solution of the problem - Amy will write an explanation of the process that the group used to solve the problem - Alice will show the check of the solution using an alternate method. - Shawn will flowchart the process
Monday, October 17, 2011
Research about Closure and Anticipatory Set
Closure:
What is closure and why is it important? Closure is what you do at the end of a lesson to summarize the lesson that was taught and is also a last chance to check for understanding. As a group, some research that we found on closure stated that it is also a chance for you as an educator to see if additional practice is needed, whether you actually need to re-teach a topic or if it is ok for you to move on to the next lesson. The specific types of closure activities that we spoke about and considered for our lesson were the ideas of journaling or using exit cards. A journal can be used as a piece that stays in the classroom that at the end of each class or period a student has to journal about two or three things that they learned for the day and then the teacher can review those journals each day to make sure that your messages are getting across. The idea of the exit card is to pass out index cards to each student, have them put away all materials from the day and then give them a few questions pertaining to the topic to see how much actually sank in. Once these things have been finished, you as an educator now can see where each student stands in comprehending the subject at hand.
Anticipatory Set:
The research that we used for the idea of the anticipatory set basically stated that it is your introduction and hook into the lesson that you are about to teach. It also is a time that you have the opportunity to link to previous knowledge, the last lesson you taught or whatever information that has already been discussed that helps to understand the lesson that is about to be introduced. An anticipatory set basically gives you the chance to get your students interested in the topic by relating it to something that they already know in an interesting way. An example of an anticipatory set for introducing how to figure out a discount at a clothing store (using percents) may be to say “How many of you have bought something on sale before? Do you remember when we talked about decimals yesterday? Well today, I am going to show you how to figure out how to use decimals to figure out how much money you will save when stores are having sales on merchandise”.
How did we use this research in our lesson plan?
We used prior knowledge that students have about things around them in the world that may be real life examples of decimals, fractions or percents. By asking students to recognize which of those concepts tied to the examples in the anticipatory set it got them thinking about the subject by linking with their previous experiences, just like described above when asking about how many students had bought something on sale before. For closure, we used the idea of the exit card to make sure that they understood the concept that we taught and if they didn’t or wanted more explanation they could also write questions on the card. We discussed and agreed that these examples worked best for our anticipatory sets and closure.
Below are a few of the websites we visited and that we think are good resources for the topics that I just discussed!
http://edc448uri.wikispaces.com/file/view/40_ways_to_leave_a_lesson.pdf
Thursday, October 13, 2011
Practicum-Sharing a Lesson
During my practicum I was able to stand in for my mentor teacher to teach a lesson in rounding for his 5th grade students. The objective of the lesson was for the students to recognize the place value that we were asking them to round, and then to correctly round up or down depending on the value of the number to the right of the place value they were to round to. The students reacted very well to using two distinct tools to help them round, the first step was to underline the number that was to stay the same or to be rounded up, and then to put an arrow over the top of the number that determined whether to round up or not. The only real issue that came up was that students repeatedly stated that the number in the first place to the right of the decimal was the "oneths place", I then wrote on the board and asked them to take a note in their composition notebooks that the one "trick" to remember with place values after the decimals is that there are no "oneths" and the place value to the right of the decimal starts with tenths and goes up from there just like it does to the right of the decimal place.
Throughout the lesson I was able to walk around the room to check for understanding by looking at their notebooks to check on the correctness of their rounding of the example problems on the board. Also, during the warm up section I was able to have students get into groups and have a representative come up and answer their assigned problems and then have their peers agree or disagree with their answers.
Overall I feel like the class went very well, if I had a chance to teach it again I would introduce the "trick" about place values at the very beginning because that was supposed to be a prerequisite skill for the lesson that obviously was not something that all of the students were aware of.
Throughout the lesson I was able to walk around the room to check for understanding by looking at their notebooks to check on the correctness of their rounding of the example problems on the board. Also, during the warm up section I was able to have students get into groups and have a representative come up and answer their assigned problems and then have their peers agree or disagree with their answers.
Overall I feel like the class went very well, if I had a chance to teach it again I would introduce the "trick" about place values at the very beginning because that was supposed to be a prerequisite skill for the lesson that obviously was not something that all of the students were aware of.
Saturday, October 1, 2011
Warm-ups in Math Education
Warm ups in math education have long been a debated topic, are they really useful? Research states that daily warm ups are a useful tool given to students at the beginning of the period to review a previous topic or to introduce new material. I believe that warm ups are a great way to start a class because they give students something to accomplish of an educational nature while allowing the teacher time to take roll and perform other housekeeping duties. By providing a warm up the students now have the opportunity to independently get their minds geared towards the topic and section of math that is being reviewed or introduced. Not only can a warm up help review material, it can also check for understanding, or even assess knowledge of a new topic. I do believe that warm ups are something that every math teacher should have in their everyday lesson plans.
Monday, September 26, 2011
Task 2-3 Appropriate Use of Technology
The tool that I chose to use for the Appropriate use of Technology assignment, Task 2-3 from the Illuminations Website is called the “Fraction game”. It is listed under one of the Activities for students from 6th-8th grade.
Click here to play the game
The activity is designed to allow students to individually practice working with relationships among fractions and ways of combining fractions.
1. What mathematics does it teach or reinforce? Finding multiple paths to adding fractions together to get a desired result.
2. Is this effective? Absolutely! This is a great tool for students that shows that there is more than one way to add fractions together to get the same number. For instance if the desired result is to find all combinations listed that will add together to get 4/5. The sliding scale on the game will allow you to move the fifths marker to 3/5 and the tenths marker to 2/10, thus adding together to make 4/5. It would also allow you to slide the markers to 2/5 and 4/10 and so on.
3. Does the technology offer something that other tools would not? I think so, even though the scope of the tool is really just finding ways to add fractions together there aren’t many tools that are this easy to use that shows the different possibilities and values of adding these fractions.
4. Are there other effective ways to teach or reinforce this same content? Of course, this is only one way to practice adding fractions, probably not a tool you would use to initially teach how to add fractions together.
5. If you were to teach this same lesson, what might you change about the delivery or example(s)? I think specifically for this level, I might use a little more student friendly language when initially explaining the model. Also, I would want to also provide a way to subtract the fractions also to get the same desired result so that more extensive learning can happen when using the tool.
Click here to play the game
The activity is designed to allow students to individually practice working with relationships among fractions and ways of combining fractions.
1. What mathematics does it teach or reinforce? Finding multiple paths to adding fractions together to get a desired result.
2. Is this effective? Absolutely! This is a great tool for students that shows that there is more than one way to add fractions together to get the same number. For instance if the desired result is to find all combinations listed that will add together to get 4/5. The sliding scale on the game will allow you to move the fifths marker to 3/5 and the tenths marker to 2/10, thus adding together to make 4/5. It would also allow you to slide the markers to 2/5 and 4/10 and so on.
3. Does the technology offer something that other tools would not? I think so, even though the scope of the tool is really just finding ways to add fractions together there aren’t many tools that are this easy to use that shows the different possibilities and values of adding these fractions.
4. Are there other effective ways to teach or reinforce this same content? Of course, this is only one way to practice adding fractions, probably not a tool you would use to initially teach how to add fractions together.
5. If you were to teach this same lesson, what might you change about the delivery or example(s)? I think specifically for this level, I might use a little more student friendly language when initially explaining the model. Also, I would want to also provide a way to subtract the fractions also to get the same desired result so that more extensive learning can happen when using the tool.
Friday, September 23, 2011
Standards harmoniously blending?
The following statements are the standards expressed by the NCTM, common core, and CMP websites on the topic of 6th-8th grade math respectively:
In grades 6-8, all students will work flexibly with fractions, decimals, and percents to solve problems.
Compare numbers in a variety of ways, including differences, rates, ratios, and percents and choose when each comparison is appropriate (6, 7, 8)
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
In grades 6-8, all students will work flexibly with fractions, decimals, and percents to solve problems.
Compare numbers in a variety of ways, including differences, rates, ratios, and percents and choose when each comparison is appropriate (6, 7, 8)
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
The question at hand is "How, if, or when do these sets of standards harmoniously blend together?". All three of these sets seem to have the focus on the topic be in different places, whether it be working flexibly with these numbers, choosing when to use the numbers appropriately, and then how to apply or recognize them on one of the number lines or diagrams. The point of all three of the standards is for these students to understand how to correctly use and apply fractions, decimals, percents and ratios. I honestly think that they each compliment each other very well, and together make a very comprehensive goal for 6th-8th grade students to reach.
Subscribe to:
Posts (Atom)