Essential Question: As you proceed with the following research, do you feel the CMP program is more direct instruction, or more inquiry based instruction?
The Connected Mathematics Project is considered an inquiry-based method as it centers around the problem that students need to solve, rather than the strategy.
How does the CMP Instructional Model (Launch -> Explore -> Summarize) compare to the more traditional direct instruction -> guided practice -> independent work model?
The Launch -> Explore -> Summarize model puts a lot more of the foot work in the students hand. The question is asked, then the students work to try and find ways to solve the problem - this can be independently or in groups - then the students come back to the board with their ideas and summarize the best ways found to solve the problem. In the traditional model, the teacher provides the strategies during direct instruction, then allows students to see how the strategy is applied (and scaffolding is used) during guided practice, and finally students work alone to solve problems using the given and practiced strategies.
I was able to watch a lesson using the CMP model here: http://www.mmmproject.org/ls/mainframeS.htm
The teacher launches the lesson by allowing the students to look for as many squares as possible within a given paper using the dots. The teacher refers a lot to making connections with past material, at times using their journals to look back at what they've already learned (to answer the question, can the square be slanted?). The students work in partners and small groups to discuss ideas with each other. Using this tactic, students were able help each other and direct each other towards the right idea. Different students could bring different things to the table and share knowledge. This lesson was a lot more of students helping and teaching students.
There would have been benefit to accessing a Smart Board in order to show this lesson, but I recognize those aren't available everywhere. As the students help each other, sometimes they are misinforming each other; this is a concern, and I think that there are times when a more solid definition or a more formal explanation are necessary for some students to catch on.
In this teacher's classroom, she has students who are eager to learn and it seems as though they have fairly high levels of self efficacy; there aren't any students complaining that it's too hard or that they don't know how to do it - students are working together and figuring it out.
Wednesday, October 19, 2011
Saturday, October 15, 2011
Closure and Anticipatory Set
What is the purpose of the Closure component in a lesson plan?
The closure component of a lesson plan can have several purposes. The closure piece wraps up any loose-ends of the lesson and reviews what the students have learned today. I think that the anticipatory set and the closure are a lot like the introduction and conclusion of a story. I remember my high school language arts teacher saying it like this: First, you tell them what you're going to tell them, then you tell them, then you tell them what you told them. We are doing much the same with this - we preface the lesson and give them a heads up for what is coming, then we wind-up the lesson, re-covering what we've told them, as well as gearing them up for the next day, all the while checking in and making sure students are relatively up to speed. This is also a time to clarify anything that might have been confusing to students.
While I was googling, I found this succinct "Purposes of Closure". They clarified that the closing piece of a lesson could cover a couple of these purposes, but not necessarily all of them.
• Reviewing the key points of the lesson.
• Giving students opportunities to draw conclusions from the lesson.
• Describing when the students can use this new information.
• Previewing future lessons.
• Demonstrating student’s problem-solving process.
• Exhibiting student learning.
• Creating a smooth transition from one lesson to the next lesson.
Strategies and Examples:
Journaling or quickwrites are one way to close up a lesson, which allows students to independently reflect on what they've covered that day. I've also seen a 3-2-1 prompt given, where the students write three things they've learned or discovered, two things they found interesting, and one question they may still have.
Another example is having students do the same thing on an index card to be turned in, or solve a few sample problems as their ticket out of class.
A pair and share time could be taken for students to discuss with each other what they have learned.
What is the purpose of an Anticipatory Set in a typical lesson plan?
The anticipatory set in a lesson plan pulls into play prior knowledge that the students hold about the relevant subject. This is a lead-in time to prepare students for what they are about to learn, and to hopefully grab their attention. This would also be a time to introduce the learning objectives written in kid-friendly language.
Examples of this might be journaling in their notebook what they remember about fractions/decimals/percents, or it may be a prompt asking where we see these symbols in our world. Many of the examples that I found through google were short one or two sentence phrases just reminding students what they talked about in a previous lesson or what will be coming up in the next lesson.
http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm
edc448uri.wikispaces.com/file/view/40_ways_to_leave_a_lesson.pdf
The closure component of a lesson plan can have several purposes. The closure piece wraps up any loose-ends of the lesson and reviews what the students have learned today. I think that the anticipatory set and the closure are a lot like the introduction and conclusion of a story. I remember my high school language arts teacher saying it like this: First, you tell them what you're going to tell them, then you tell them, then you tell them what you told them. We are doing much the same with this - we preface the lesson and give them a heads up for what is coming, then we wind-up the lesson, re-covering what we've told them, as well as gearing them up for the next day, all the while checking in and making sure students are relatively up to speed. This is also a time to clarify anything that might have been confusing to students.
While I was googling, I found this succinct "Purposes of Closure". They clarified that the closing piece of a lesson could cover a couple of these purposes, but not necessarily all of them.
• Reviewing the key points of the lesson.
• Giving students opportunities to draw conclusions from the lesson.
• Describing when the students can use this new information.
• Previewing future lessons.
• Demonstrating student’s problem-solving process.
• Exhibiting student learning.
• Creating a smooth transition from one lesson to the next lesson.
Strategies and Examples:
Journaling or quickwrites are one way to close up a lesson, which allows students to independently reflect on what they've covered that day. I've also seen a 3-2-1 prompt given, where the students write three things they've learned or discovered, two things they found interesting, and one question they may still have.
Another example is having students do the same thing on an index card to be turned in, or solve a few sample problems as their ticket out of class.
A pair and share time could be taken for students to discuss with each other what they have learned.
What is the purpose of an Anticipatory Set in a typical lesson plan?
The anticipatory set in a lesson plan pulls into play prior knowledge that the students hold about the relevant subject. This is a lead-in time to prepare students for what they are about to learn, and to hopefully grab their attention. This would also be a time to introduce the learning objectives written in kid-friendly language.
Examples of this might be journaling in their notebook what they remember about fractions/decimals/percents, or it may be a prompt asking where we see these symbols in our world. Many of the examples that I found through google were short one or two sentence phrases just reminding students what they talked about in a previous lesson or what will be coming up in the next lesson.
http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm
edc448uri.wikispaces.com/file/view/40_ways_to_leave_a_lesson.pdf
Sunday, October 9, 2011
Practicum- sharing a Lesson
I have not yet started a practicum, however I am an aid in a special education classroom, so I am able to reflect on what I've seen from the teacher I work under.
The teacher most often follows the Language! program, and she did a study in idioms. Her objectives were something along the line of understand the meaning of an idiom and it's uses. She found a book that had a page of idioms, and read through them with the students. She then had them draw a picture to describe the idiom meaning of the word.
While in theory this sounds great, it was difficult even for me to figure out how to draw something that was a "piece of cake" that wasn't an actual piece of cake! Many of the idioms were fairly obscure, and I hadn't heard of them. In part because of the disability level of students in the class, the students really struggled with idioms such as "pass the hat" and they weren't broken down to the level they needed to be.
She checked for understanding by looking at their drawings, but their artwork is at a pretty low (scribbly) level that it's hard to distinguish.
As the lesson went along, I would have stopped it and adjusted it on the spot. The student with autism was going to really struggle with this, and I would have found a new approach, or perhaps a different activity. If I were to teach the lesson, I would have the students draw the literal meaning of the phrase "apple of my eye" and then DISCUSS the idiom meaning.
The teacher most often follows the Language! program, and she did a study in idioms. Her objectives were something along the line of understand the meaning of an idiom and it's uses. She found a book that had a page of idioms, and read through them with the students. She then had them draw a picture to describe the idiom meaning of the word.
While in theory this sounds great, it was difficult even for me to figure out how to draw something that was a "piece of cake" that wasn't an actual piece of cake! Many of the idioms were fairly obscure, and I hadn't heard of them. In part because of the disability level of students in the class, the students really struggled with idioms such as "pass the hat" and they weren't broken down to the level they needed to be.
She checked for understanding by looking at their drawings, but their artwork is at a pretty low (scribbly) level that it's hard to distinguish.
As the lesson went along, I would have stopped it and adjusted it on the spot. The student with autism was going to really struggle with this, and I would have found a new approach, or perhaps a different activity. If I were to teach the lesson, I would have the students draw the literal meaning of the phrase "apple of my eye" and then DISCUSS the idiom meaning.
Sunday, October 2, 2011
Warm-Ups in Math Education
I think Math Warm-Ups are great tools to reinforce skills that were learned previously; it can be a form of assessment to measure retention of material and understanding. Some times that time from one day to the next can be crucial; students who did not get enough sleep may not have stored what they learned in their long term memory and truly may not remember what had been taught the day before. Giving students who did retain the material the quick practice and review sets them up for the rest of the day. Creating that basic foundation of mathematical concepts is important for them to move on and be successful in math.
Students can also gain a sense of accomplishment and success if they are able to conquer the first part of their day. Sometimes providing that success for students can encourage them to not give up. Completing a short simple warm up can give them confidence and put them in a great spot for the rest of the period to learn.
Warm-ups can also be used to introduce new content or material.
Students can also gain a sense of accomplishment and success if they are able to conquer the first part of their day. Sometimes providing that success for students can encourage them to not give up. Completing a short simple warm up can give them confidence and put them in a great spot for the rest of the period to learn.
Warm-ups can also be used to introduce new content or material.
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