Last night I had the amazing opportunity to watch Sir Ken Robinson speak at Millersville University. I left speechless. If you are unfamiliar with his work, please go here and here and here.

There are so many thoughts running through my head at the moment I'm not exactly sure I can write anything that will do his talk justice. I'm wishing I would've wrote this post last night when I got home instead of sleeping. I do want to highlight just a few points that Sir Ken made that stuck with me and will cause me to rethink my classroom and department.

1. How do you run an organization that is adaptable to change and flexible? One that is creative? One that keeps up with change and stimulates change? Public education needs to be this way. One point that he made, and that I agree with, is that schools are all about conformity. All students take the same classes at the relatively the same time and are expected to get the same grade. Schools need to allow students to explore their interests and creativity so that they can find their element. This will require schools to adapt to the students it educates rather than the students adapting to the schools they attend. There are many steps that need to be taken for this to happen, and its certainly not something that will happen overnight. Can we as individual teachers do anything to support this process, even if the governing bodies do not officially embrace it? Sure.

2. NCLB is actually leaving everyone behind. Standardized testing is causing teachers across the country to mold their students into machines, learning processes but not thinking about what is going on. Usually, this is done in the most boring way possible. When students are looked at as data, they revolt. When they are looked at as individuals, they succeed. A political policy that was supposed to help education and increase our students knowledge is, in reality, taking away from their education because they are being forced to learn about things that they see no value in. They are not able to express their creativity because they are limited to what's on the test. Combine this with the decrease in public education funding and you lose those courses that engage students and stimulate their creativity and you keep the courses that are cut and dry.

3. We are reducing our funding for education increasing our funding for the correctional institutions. 1 in 31 people are in, waiting for sentencing, or being rehabilitated by a correctional facility. Not that those two statistics are directly related, but its interesting to think about.

4. Personalizing education helps people realize their talents. Every attempt to personalize education has failed. Standardized tests de-personalize the educational experience. This was really the subject of his entire talk.

5. By narrowing the curriculum, we are implying that life is linear; that we all will follow the same path. In truth, life is organic; its constantly changing and adapting to surroundings. Let's teach our students how to make these adaptations rather than telling them what to do and where they should be. Let them discover what they are good at and what they are interested in, and let's foster it. If we tell them what to learn and how to learn it and don't move off of the curriculum that is set for 'everyone,' how will they ever learn their place in life? There are plenty of people in the world that are good at what they do, but don't truly enjoy it. Let's have our students graduate ready to pursue a career that they are good at AND love.

6. Myths - 1. Only special people are creative. 2. You are either creative or your not. 3. Special things are required to be creative. 4. You can't teach creativity.

7. As teachers, we are like gardeners and our students are our plants. Gardeners don't grow plants; plants grow themselves. Our job is to provide the optimal conditions for growth. Beautiful analogy.

8. The risk we take in margenalizing our students is greater than the risk of letting them be creative and grow.

9. "I'm not what's happened to me, I'm what I chose to become" - Carl Young

Of course, these are not my original thoughts. They are all from the great Sir Ken Robinson. He said so much more and was extremely informative and insightful, but these are just a few of the points that stuck with me and will guide my classroom from now on.

## Friday, September 21, 2012

## Friday, September 14, 2012

### Mistake?

I was grading some student work today and came upon this mistake.

In the class, we are currently studying problem solving strategies. This particular problem came from the 'Look For A Pattern' lesson. The problem asks the student to find the next four rows in Pascal's Triangle. Now, the majority of my students have not seen or worked with Pascal's Triangle before, so to them this is a seemingly random set of rows of numbers. I did not give them the background knowledge of the Triangle beforehand either because I wanted to see what they came up with as their answer. Usually students get it correct right away. This, however, was new to me. Because I only gave the first five rows, if you look at them as whole numbers rather than individual digits, they are all powers of 11. Pretty neat. This student went with that and continued. Unfortunately, Pascal's Triangle differs from this point on. She did find a pattern, thinking outside the box. Now, I did mention specifically in the problem that it is Pascal's Triangle, but she found a pattern.

Does she have an understanding of finding patterns? I believe so. Do I mark her wrong because her answer is different than what I've got on my answer key? If I'm grading on finding patterns (which I am), then no. If I'm grading on their understanding of Pascal's Triangle (which they may have never seen before), then yes. But then again, why would I grade on something they've never been exposed to?

I thought this solution was interesting; thought I would share.

## Tuesday, September 11, 2012

### Lil' Help

I need some guidance, help, advice, etc. The first unit in my geometry class was big on vocab to set the pace for the rest of the course. It focused on all of the different types of angles, polygons, and quadrilaterals. We explored each to their fullest, expanding on and making connections to every characteristic possible. In the past I've given an exam with problems and the students have done fine. Recently I started giving this as a quiz instead...

My students have to find all of the angles that I've labeled (36 of them total) in this regular dodecagon. I give them one right angle, but that's it. They need to find everything else on their own. I like this because they need to use the properties we talked about throughout the unit to arrive at the answers. Its a nice, different type of assessment that gets them to apply their knowledge.

I'm having trouble because I don't know how to grade it. Obviously, if they get one angle wrong that is going to through off other angles as well. I can't take points off for every wrong angle because then I'm potentially subtracting points for the same mistake multiple times, which isn't really fair. I need to find a way that assesses them fairly. I've thought about having them write an explanation of how they arrived at their answers, but that would be a ridiculous amount of writing, even if I made a simpler figure with less angles. I've also though about having them list their answers in the order they calculate them so I can try to follow their thought process, but I'm not sure if that would give me the full picture of their understanding.

Could I evaluate it in some type of standards-based grading system? Are there any other ways that I could use this to assess my students, or do I just simply not grade it but make it a class activity?

Lil' help?

Note: as I type this I'm listening to the Dark Knight Rises soundtrack and I'm now totally pumped to teach for the day, although my lessons may be slightly darker than usual.

## Monday, September 10, 2012

### SDC (day 5)

Today a fear of mine happened: I lost track of what I've covered so far in my two geometry classes. I started to plan for the day this morning and couldn't figure it out for the life of me. I prepared some extra material, probably enough for 3 days in reality, but I started both classes with some info we've already discussed. Overall, this wasn't a big deal; a little review never hurts. It kind of messed with the flow we had going in both classes though. Last week the students were directing the curriculum (see previous posts) and then today I found myself moving back to old habits and directing more. I realized it about half-way through my second block but it was tough to get back to the questioning. I found the downfall in this plan that I didn't plan out: when it gets to the end of the unit, there is certain info I need to cover and it gets increasingly difficult to ask questions that will guide the students thought there. And I guess if I'm asking the questions to guide in a specific direction, its not totally student-directed. So, this is going to be tough to organize. I loved the way last week went. The students were into it, I was into it, everything was going awesome. Now, being limited by units, its getting tough as we finish up the first one. Ideally, as I said before, I would like to have the entire course's material planned ahead of time to really let the students run with the material instead of me leading the way. We shall see.

The good news is that I got everything covered in both classes within the same time frame. I had a few students notice that between classes they had differing homework assignments, but it didn't bother anyone.

I did end the day with a lil' bit o' problem solving. Got my students thinking, motivated, and I'm slowly turning them into super geniuses. More on that problem tomorrow...

The good news is that I got everything covered in both classes within the same time frame. I had a few students notice that between classes they had differing homework assignments, but it didn't bother anyone.

I did end the day with a lil' bit o' problem solving. Got my students thinking, motivated, and I'm slowly turning them into super geniuses. More on that problem tomorrow...

## Thursday, September 6, 2012

### Student Directed Curriculum (Day 2)

Day 2 of my experimental student curriculum has come and gone, and I must say, it went quite well. Here's how it went down: On the first day I gave them this paper and gave them 5 minutes to calculate as many angle measures as they could as well as find any polygons that jumped out at them.

Obviously, everyone found the right angles, the majority were able to do the vertical angles, and a couple went as far as making the connection to corresponding angles. After the five minutes, I asked for a volunteer to put something they found on the board. Both of my classes started with angles, so I went with that. We started with the angles the students gave me, I asked them how they knew what the measures were, and we connected it to other types of angles and found examples. I was greatly impressed with the discussions we had and reasoning I got from students. This was the first real lesson we've had where I've asked them to explain themselves and they went for it. It was awesome! That was day one.

On day 2, we came back to this same paper, only this time I asked for polygons since we already exhausted all of the angles. This is where it got interesting. I had a student in both classes come up and highlight a few polygons. Both classes pretty much gave me the same list: rectangle, triangle, trapezoid, parallelogram, rhombus, pentagon. I asked where they wanted to start. My second block class voted for the trapezoid; we dove in. I showed them a trapezoid in comparison to an isosceles trapezoid and they commented on what they thought were the differences. We talked about consecutive angles between the bases and related it to corresponding angles. There wasn't a single aspect of trapezoids that we didn't discuss. For the most part, they were able to toss out the ideas and then we explored them; I did very little nudging. We ended the day talking about the reflection symmetry of an isosceles trapezoid, and the relationship to the perpendicular bisector of the bases. I thoroughly enjoyed it.

Then block three came, and oh boy it just got better. Same routine as above, however, they wanted to start with pentagons instead. Game on. The student that highlighted the pentagon was unsure if it really was one because it wasn't regular (only he didn't say regular). Discussion started, we came to a consensus that it doesn't have to be regular to be a pentagon. Great. So I drew a regular pentagon on the board and said, "What's the measure of each of these angles?" *confused/thoughtful looks/blank stares* "Ok, how many degrees are in a pentagon?" 360? 540? 720? Awesome, these students have an idea of where I'm going with this. I drew a triangle. "180 degrees!" someone said. I added a triangle to it and showed them the quadrilateral formed. "360 degrees.?" someone hesitated. So far so good. I add another triangle to form the pentagon. The pattern? "540 degrees!" confidence building. I kept going: another triangle, six sides, 720, another triangle, seven sides, 900, another triangle, eight sides, 1080. What's the pattern? "Oh, I get it!" "How many degrees in a polygon with 100 sides?" "You would take 98 times 180." "Why 98?" "Because the number of triangles is always two less than the number of sides."

"Sah-weet! So back to my original question. What is the measure of each angle in the regular pentagon?" "108. 540 divided by the 5 equal angles." Needless to say, I was excited. Everyone was paying attention. Multiple students were participating (the above conversation included many students). We discussed a few more pentagonal items, and then I guided them toward the symmetrical nature of the polygon. Reflection symmetry was discussed in a similar matter as my previous class, but here I had time to move on to rotational symmetry. No problem. They were good to go even though this was a relatively new concept for them. The only issue I had (or think I'll have) is the phrasing, 'five-fold rotation symmetry.' My students always have trouble with that, knowing what it means, using it correctly, etc. I have yet to find a good way to explain it. Any ideas?

So, yeah, I'm excited about this whole freedom of curriculum concept so far. After my third block class, I realized its going to get tough to keep track of what I taught from day to day. I guess its time I figure out some kind of organization skills past post-it notes.

The students seem to be with me too. Everyone was listening, involved, engaged. Questions were being asked both by me and them, and answers were the same. We're both learning, and I don't think it gets much better than that.

Here's the kicker: I only have this plan 'planned' for these first two units on quadrilaterals and triangles. After that, I'm still trying to figure out how to get it to work. My next units are area/perimeter, surface area/volume, similarity, reflections, proofs, and circles. Theoretically, it would be easy to mix and match units and make all kinds of connections, however, that would almost require me to planned for the ENTIRE SEMESTER since I'll never know what's going to come up in class. Maybe in the spring? Ugh... that'll be tough. We shall see.

On day 2, we came back to this same paper, only this time I asked for polygons since we already exhausted all of the angles. This is where it got interesting. I had a student in both classes come up and highlight a few polygons. Both classes pretty much gave me the same list: rectangle, triangle, trapezoid, parallelogram, rhombus, pentagon. I asked where they wanted to start. My second block class voted for the trapezoid; we dove in. I showed them a trapezoid in comparison to an isosceles trapezoid and they commented on what they thought were the differences. We talked about consecutive angles between the bases and related it to corresponding angles. There wasn't a single aspect of trapezoids that we didn't discuss. For the most part, they were able to toss out the ideas and then we explored them; I did very little nudging. We ended the day talking about the reflection symmetry of an isosceles trapezoid, and the relationship to the perpendicular bisector of the bases. I thoroughly enjoyed it.

Then block three came, and oh boy it just got better. Same routine as above, however, they wanted to start with pentagons instead. Game on. The student that highlighted the pentagon was unsure if it really was one because it wasn't regular (only he didn't say regular). Discussion started, we came to a consensus that it doesn't have to be regular to be a pentagon. Great. So I drew a regular pentagon on the board and said, "What's the measure of each of these angles?" *confused/thoughtful looks/blank stares* "Ok, how many degrees are in a pentagon?" 360? 540? 720? Awesome, these students have an idea of where I'm going with this. I drew a triangle. "180 degrees!" someone said. I added a triangle to it and showed them the quadrilateral formed. "360 degrees.?" someone hesitated. So far so good. I add another triangle to form the pentagon. The pattern? "540 degrees!" confidence building. I kept going: another triangle, six sides, 720, another triangle, seven sides, 900, another triangle, eight sides, 1080. What's the pattern? "Oh, I get it!" "How many degrees in a polygon with 100 sides?" "You would take 98 times 180." "Why 98?" "Because the number of triangles is always two less than the number of sides."

"Sah-weet! So back to my original question. What is the measure of each angle in the regular pentagon?" "108. 540 divided by the 5 equal angles." Needless to say, I was excited. Everyone was paying attention. Multiple students were participating (the above conversation included many students). We discussed a few more pentagonal items, and then I guided them toward the symmetrical nature of the polygon. Reflection symmetry was discussed in a similar matter as my previous class, but here I had time to move on to rotational symmetry. No problem. They were good to go even though this was a relatively new concept for them. The only issue I had (or think I'll have) is the phrasing, 'five-fold rotation symmetry.' My students always have trouble with that, knowing what it means, using it correctly, etc. I have yet to find a good way to explain it. Any ideas?

So, yeah, I'm excited about this whole freedom of curriculum concept so far. After my third block class, I realized its going to get tough to keep track of what I taught from day to day. I guess its time I figure out some kind of organization skills past post-it notes.

The students seem to be with me too. Everyone was listening, involved, engaged. Questions were being asked both by me and them, and answers were the same. We're both learning, and I don't think it gets much better than that.

Here's the kicker: I only have this plan 'planned' for these first two units on quadrilaterals and triangles. After that, I'm still trying to figure out how to get it to work. My next units are area/perimeter, surface area/volume, similarity, reflections, proofs, and circles. Theoretically, it would be easy to mix and match units and make all kinds of connections, however, that would almost require me to planned for the ENTIRE SEMESTER since I'll never know what's going to come up in class. Maybe in the spring? Ugh... that'll be tough. We shall see.

## Tuesday, September 4, 2012

### Student Directed Curriculum (kind of)

I teach geometry. This is my sixth time teaching it. I think I'm the only person in my department that hasn't changed what they've taught for the past six years. The perks: overall, less planning! The downside: more planning? trying to reinvent the same material so it doesn't seem like the same old thang, while still keeping it effective and relevant for the students.

I always push for questioning in my class. I do stand in front of the class and explain some things, but their questioning fills in some of the holes and also covers the curriculum. In the past, I've followed the set curriculum I helped to write a few years back. Just like any other typical class, I started at unit one and plowed through to unit 13 or 14, following the lessons in the order they appeared. I thought I would try something new this year: let the students decide.

My plan is to start with unit 1, the basics of geometry (terms, notation, polygons) and go from there. I have a paper that I made up with all kinds of lines on it and I provided three or four angle measures. With this, I'll let the students calculate as many angles as they can and find as many polygons as possible in 5 or 10 minutes. From there, they can share what they've discovered and we'll discuss in great detail everything they bring up. For example, if a student give me an angle measure, we'll talk about whether or not its correct and why its calculated that way and how it will lead to other answers. If someone points out a polygon first, say a kite, then we will explore every aspect of kites (angles, segments, symmetry, area, etc.) before we move on. Theoretically, the entire beginning of the course will be based upon this one worksheet. Unfortunately, I don't think I'll be able to give them complete freedom and follow wherever they lead me (not sure its physically possible to be that planned out) (now that I think of it, in order for my students to 'run' the curriculum, you would think it wouldn't require much planning since I'm not doing the work, turns out it might require more, hmmm...).

The downside is that my two geometry classes will potentially be at different points in the curriculum all the time. Its probably going to be tough to keep track of what I taught and what I didn't. The upside is, the students are thinking, their guiding themselves, we're working together, they're engaged. Now, as I type this a question arises, how do I handle assessment? I'll need to provide a certain amount of structure for this to work so it doesn't turn into complete chaos. Do I still keep the unit in the same order so as tests/projects can be used consistently between classes? I realize the exams should not be the motivation for such a decision, but how else would I handle it? If I let the units get criss-crossed and the previous order changes, do I allow it and move to project based assessment instead of exams? Or, do I simply evaluate when enough material is enough and write up new assessments, different for each class?

I probably should've thought this through a little more before the second week of school. Oops.

I always push for questioning in my class. I do stand in front of the class and explain some things, but their questioning fills in some of the holes and also covers the curriculum. In the past, I've followed the set curriculum I helped to write a few years back. Just like any other typical class, I started at unit one and plowed through to unit 13 or 14, following the lessons in the order they appeared. I thought I would try something new this year: let the students decide.

My plan is to start with unit 1, the basics of geometry (terms, notation, polygons) and go from there. I have a paper that I made up with all kinds of lines on it and I provided three or four angle measures. With this, I'll let the students calculate as many angles as they can and find as many polygons as possible in 5 or 10 minutes. From there, they can share what they've discovered and we'll discuss in great detail everything they bring up. For example, if a student give me an angle measure, we'll talk about whether or not its correct and why its calculated that way and how it will lead to other answers. If someone points out a polygon first, say a kite, then we will explore every aspect of kites (angles, segments, symmetry, area, etc.) before we move on. Theoretically, the entire beginning of the course will be based upon this one worksheet. Unfortunately, I don't think I'll be able to give them complete freedom and follow wherever they lead me (not sure its physically possible to be that planned out) (now that I think of it, in order for my students to 'run' the curriculum, you would think it wouldn't require much planning since I'm not doing the work, turns out it might require more, hmmm...).

The downside is that my two geometry classes will potentially be at different points in the curriculum all the time. Its probably going to be tough to keep track of what I taught and what I didn't. The upside is, the students are thinking, their guiding themselves, we're working together, they're engaged. Now, as I type this a question arises, how do I handle assessment? I'll need to provide a certain amount of structure for this to work so it doesn't turn into complete chaos. Do I still keep the unit in the same order so as tests/projects can be used consistently between classes? I realize the exams should not be the motivation for such a decision, but how else would I handle it? If I let the units get criss-crossed and the previous order changes, do I allow it and move to project based assessment instead of exams? Or, do I simply evaluate when enough material is enough and write up new assessments, different for each class?

I probably should've thought this through a little more before the second week of school. Oops.

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