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. 

Task 1-3

The best practices in education that stand out for me are Differentiation, Ecology, Problem Development, Clear and Common Focus, High Standards and Supportive Learning in no particular order. Differentiation refers to attacking problems from different points of view and different levels of understanding. Not all students learn at the same rate or have the same learning styles. Offering students different ways to show they their understanding or to learn a lesson is critical. Ecology might be my favorite. It is taking math or any other material out of the vacuum of the text book and applying it to real-world problems or situations.  Making those connections are key to answer that age old question of “why do I need to know this”. It also helps when trying to engage students. Using their interests as learning experiences helps them to internalize the information. Along with this Problem Development gets students to think backwards and reflect on where the instruction can be used. It forces them to make the connections and allows for critical thinking. Having a Clear and Common Focus, from teacher, student, parents, administrator and staff makes sure everyone effected is on the same page. Teachers as well as Students need commitment from parents and administrators because they are the support system that reinforces learning. High Standards ensures that not only is everyone held to the same standard but that each person, teachers included, are working at their best level. Students who are challenged within their Zone of Proximal Development achieve at a higher rate than students who are not. Supportive Learning provides a positive, safe environment for all students to participate and learn.


“Practice can not be separated from theory” in that what we learn must be what we teach. As we as educators teach we must constantly be learning as well. This seemingly simple idea sometimes get lost as we set into our day to day routine. Learning about our students, and their worlds, learning new strategies, learning new ways to connect our lessons to the outside world, these are ways we can continue to develop as educators. Several principles for instruction that I think are important are: Allowing for errors, provide students to learn as they go. Provide for immediate relevance and make it obvious, the connections between your lesson and the your students future. And make Instruction learner centered so that students drive the learning and hopefully demand a high quality education.

About Me

My first choice for teaching would be middle school geometry teacher. This is mostly covered in 7th grade. My back ground in design and construction lend itself very well to this subject. I think this allows me to make connections between geometry and the real world application fairly easy. I have also workedein business for the past 11 years and can connect some basic business practices to mathematics.

In my free time I enjoy camping, hiking, fishing and being outdoors when the weather is nice. I am not a huge sports fan but baseball is fun to go see. My graphic design experience makes me fairly fluent on a computer and I prefer the Mac platform. I spend to much of my free time playing video games. Mostly FPS style games although sometimes a good RPG adventure game comes along. I have a dog and two cats and live with 3.5 other people.

DC Evaluations makes me wonder?

This article "D.C. Evaluations Target Hundreds for Firing or Bonuses" brings very specific questions to my mind... How does someone become a bad teacher? Where they always ineffective? Did they become complacent? Did they get burned out? How does anyone survive while being ineffective at their job? Are their these same problems in other fields? How can we as educators do a better job at helping students be successful and not go down a path that leads to unhappiness?

My point is that after 17 or more years of school young adults should be on a path to success. If a teacher enters the system ineffective then somewhere along the way the educational system has failed miserably. It's not enough as a teacher to teach their subject I feel that they should be helping students to find their strengths and weaknesses. To find their hidden talents and to get them excited about the subject they are good at and to help them find their path to happiness.

For those teachers that started out successful and became complacent or disgruntled maybe it is time for a change. I know first hand what it is like to become set in a job that you feel is ineffective and was fortunate to have the opportunity to try something new. People are living longer these days and is only natural that they go through these transitions. The higher education system has done a good job of offering programs for people such as me. It almost seams like it is too easy. But then again I don't have a family to support or am overwhelmed with bills and expenses.

Maybe moving more students into the higher education system sooner would enable them to explore more opportunities and to better find that first career and be more effective as citizens. If only we could afford it?