Inquiry Learning Model and The CMP Model

The goal of the CMP Model of learning is very similar to the Inquiry Learning Model in that it aims to produce reasoning students. The classical sources of inquiry learning date back to Aristotle but more recently was introduced into modern education by John Dewey with the notion of constructivist education. The CMP model takes a functional approach to teaching mathematics as apposed to a structural approach. This aligns it more with the Inquiry Learning Model and centers it around the student. Rather than focusing on learning the procedures of solving equations it helps students to understand the function of the equations and to "uncover" equations as part of problem solving. This is directly apposed to the direct instruction model of education where the teacher is the primary source of information. Instead using CMP as an inquiry based learning model, students discover and put into contact mathematical principles and thus internalize the importance and properties of what is being studied. The traditional or Glencoe Mathematics system relies heavily on completely modeled examples with clear explanations that are accompanied by guided practice. Although this seems to be a good way to teach, it is the epitome of direct instruction and works very well for only students who thrive in this sort of environment. In order to reach a wider range of student, I feel inquiry based learning supported by a knowledgeable teacher with bits of direct instruction would do a better job of teaching higher order reasoning students. It would also make math more interesting to students who learning styles differ from the teachers teaching style.

Resources:

http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI1804_3

http://www.discover.tased.edu.au/sose/inquimod.htm

http://www.ehow.com/way_5862807_inquiry_based-math-learning.html

http://en.wikipedia.org/wiki/Inquiry#Classical_sources

http://www.thirteen.org/edonline/concept2class/inquiry/index_sub4.html

http://connectedmath.msu.edu/

http://www.math.udel.edu/LIECAL/papers/LieCalEquationSolvingPaper.pdf

The Teaching of Equation Solving: Approaches in Standards-Based and Traditional Curricula in the United States, Pedagogies: An International Journal.

Closure and Anticipatory Set

Closure
Closure is the release of students the ability to demonstrate their ability to use the material. It can be the conclusion but also could be further questions that you give the student to think about. Maybe something you want them to think about for the next lesson? It should have obvious clues for students to understand they have successfully completed the lesson. or make account if students need to revisit it. It can also have a component that connects this lesson to previous lessons for the students.

Anticipatory Set
Anticipatory Set is the question you pose to your students to get them interested in the material. It grabs their attention and sets them up for the lesson. It's purpose is to focus the students attention on the subject. One important aspect of the anticipatory set is the outline or objectives you give a student so they have a clear idea of the goals for the lesson. It can make connections to previous learning.

Sources:

http://www.okbu.net/ed/398/set.htm

http://members.tripod.com/teaching_is_reaching/lesson_design.htm

3-4 Assignment

My micro teaching lesson last semester on using nets to produce cubs and other 3D shapes was taught to 3 other people in my cohort. I started with a short demonstration on how a cardboard box was put together. I thought the visuals worked well and the worksheets worked out ok. One student caught on very well but I had I don't think my instruction helped one of the students. I think a more in-depth group discussion as well as being more explicit with my instructions would have been better. I should have written some of the key elements of a cube net on the board as they where discovered and I think that I could have been clearer with my expectations. I thought that having the majority of the work a hands-on activity was the best part of the lesson and being able to adapt it to several different learning levels also worked well. I also think that the translation from three students to a classroom full of students might be challenging for this lesson but if I worked more on the board and had more description written down I could effectively reach 30 or so students. 

2 of 3 My classroom

• Preview and reflect on each of the following mini-presentations.

• Math is not linear  |  A Better Way to Teach Math  |  The Flipped Classroom

Math is not Linear is my favorite of the three presentations. First I think Prezi is brilliant and second I agree that math touches so many facets of our day to day life and is so expansive that to teach it without context is like learning to use a computer without having one to work with (this has been done). Connecting previous knowledge is the obvious part of the equation, but I really appreciated that she talked about making connections to future learning. I think this is great. It gets students to think ahead in life and make connections to the fact that it does get easier and more obvious. 

The Jump model of teaching math made a lot of sense to me and I have tried to use something similar when helping students with math work in classes I have volunteered in. Breaking every problem up into smaller problems helps show how working on even the hardest problem can be simplified. I also recently used an iPad app called AlgebraTouch that shows you how to break up algebra problems into different components using simple “one-touch” demonstrations. It makes these problems very easy and is very fun to work with. This video didn’t go into as much detail about the Jump method but I did download one of the free sample worksheets and it looks like it demonstrates this strategy very well.

The flip classroom is a good way to set up any classroom that would normally be lecture centered. It gives students a chance to have access to the teacher when working on real problems. It does let students watch the lectures at their own pace but I worry about students who don’t have access to computers or simply don’t do their homework. You would have to lecture to them anyway or set aside time for them to watch the video in class. It also doesn’t give students a chance to ask questions as the lecture goes along. Maybe some sort of hybrid with a teacher available in a forum while students watch the videos at home would be more appropriate. You could use it in bridged classrooms where multiple levels are being taught at once, letting students watch Kahn Academy to get a second perspective on the lesson would in my opinion be a good idea.

The talent code is an interesting statement and I have often heard that practice makes perfect. I have also heard second hand that if you do anything for 10,000 hours before you become an adult, you will reach genius level in that subject. Both point out that it is possible for every kid to be an allstar if they just put their mind to it and practice. I also like the idea of breaking up the subject, especially math, into chunks and practicing pieces individually. I hope to use this method in my teaching.

Together these techniques would help to foster a better learning environment for many students. I will use elements of all of them in my classroom.

Warm-ups in the Math Class

My first question about warm-ups is why are they used primarily in math and not other subjects? I think they can be very effective to get your mind thinking in the mode of the class. Writing classes I think could benefit from this especially creative writing or poetry. In math it serves to get students to focus and think mathematically. It can also have a calming or focusing effect for students who are coming in from lunch or from other frantic activities. It can also be a sort of brainstorm activity instead of the common questions. A quick chat within small groups about yesterdays lesson serves to refresh the previous lesson. It can also be a recap by the teacher, specifically about the expectations you have of them or the direction your unit is headed. This would help keep students on track after maybe the third or fourth day on the same subject. They could also be used to take the "temperature" of the class and to determine if students are following along. Except for a very informal formative assessment I don't think this is very practical because you would have set aside grading time for each warm-up and track every piece of paper turned in. 

Middle School Geometry Standards

The standards from the three different organizations are fairly similar with a few being more specific and others being more general. For instance the Common Core Standards ask a student to be able to draw a geometric shape and the NCTM standards call on a student to be able to analyze characteristics of shapes. The three standards together, in my opinion, cover almost every aspect of geometry and bring it down to a middle school level. Connected Math goes further to requiring specific vocabulary that students would know. My favorite standard is from the CC standards, 7.G.6. involves solving real-world problems involving two and three dimensional objects. This goes to the very heart of why we teach math, so that our students can solve real-world problems. 

My matrix of middle school geometry standards.

Appropriate Use of Technology

• Task 2-2:  Standards, standards everywhere.    

http://www.khanacademy.org/video/similar-triangles?playlist=Geometry 

This lesson defiantly addresses some of the standards for 7th grade geometry. It shows how to draw triangles and the unique properties of triangles including sum of all angles will equal 180 degrees. It also describes sizes, orientations and transformations of triangles and the properties of similar triangles and how similar triangles may be different sizes due to scaling but the angles remain the same. It also touches on rotational symmetry.

I think this was effective for refreshing my memory about similar triangles and would be a good demonstration to begin a class with. However I think that a better lesson would be one where 7th graders could follow along with. Giving them a hands-on opportunity to see how similar triangles interact. It also would need to build on previous knowledge about the properties of triangles. He is very clear and concise which makes him easy to understand and follow.

This technology does offer a way for students to access lessons from home if they have computers. It also would be available to parents who are trying to help their children with homework.

It does lack some sort of hands on element that I think is essential to this kind of lesson. Maybe different size similar triangle blocks or paper cut outs. I also would include rotational symmetry in more depth. Showing how the same triangle can be resized or rotated and still have the same angles. 

I would include a hands on element to this lesson. Blocks, paper cutouts or an online application would help to reach students who have a hard time following along or are tactile learners. I would also include examples for the real world such as the Eiffel Tower or bridges that use triangles to increase strength. There are also some really cool resources out their to illustrate geometric properties like this one from Wolfram (http://demonstrations.wolfram.com/GoldilocksAndThe3SimilarTriangles/).

The standard share a few harmonious similarities but are in some cases vague and disconnected. The NCTM Standards seemed very concrete. They are worded in a more real world situation and I can see connecting them to real life situation easier.