At the end of the first unit of this adventure, I'm happy I finally pushed myself to do it. I was really unsatisfied with the old method of pre-printed notes with blanks that I would just talk through while students copied down the important info. I used that method for 4 years because when I started teaching I had 4 preps and didn't have the energy to focus on Geometry, so I used the lesson plans handed down from other teachers in the building.

Regardless of the method (which I still support wholeheartedly), I'm more satisfied with how I've re-sequenced the course and what I envision that will do for what we can accomplish as a class. Spending this much time on equations of a line will enable us to actually put it into practice and study shapes graphically which (I hope) will make conclusions easier to see than the traditional, more abstract approach.

Let's see how hopeful I am come Monday after grading 100 tests though.

## Friday, September 28, 2012

## Thursday, September 27, 2012

### Day 17: Online Practice

Maybe it's just my school, but I feel like any time I try to use school technology on a class wise scale, it feels like it's more hassle than it's worth. That's especially true when we're using it for the first time of the year.

Case in point: My district requires math teachers to use the Carnegie Learning software as part of our curriculum. I'm OK with that, but there's usually not enough working computers in a lab for as many students as I have, and there's always something going on with a Java update or some such thing.

So I lost all of 2nd hour yesterday when I scheduled us to use a lab that hadn't updated Java, so they couldn't run Carnegie. Oof. I then got to spend my plan hour in a frenzied panic trying to find a backup plan for my remaining classes which amounted to links to Khan Academy videos and practice problems. No worries, as the lab I had for the later classes had been updated and worked out fine once they kids learned how to log in (another headache).

There's a broader issue to discuss with online practice - does it help foster learning? Personally I think it's no different than any other tool, it can be used responsibility or not. Students who take it seriously will get something out of it and those and refuse to engage won't see any benefit.

Case in point: My district requires math teachers to use the Carnegie Learning software as part of our curriculum. I'm OK with that, but there's usually not enough working computers in a lab for as many students as I have, and there's always something going on with a Java update or some such thing.

So I lost all of 2nd hour yesterday when I scheduled us to use a lab that hadn't updated Java, so they couldn't run Carnegie. Oof. I then got to spend my plan hour in a frenzied panic trying to find a backup plan for my remaining classes which amounted to links to Khan Academy videos and practice problems. No worries, as the lab I had for the later classes had been updated and worked out fine once they kids learned how to log in (another headache).

There's a broader issue to discuss with online practice - does it help foster learning? Personally I think it's no different than any other tool, it can be used responsibility or not. Students who take it seriously will get something out of it and those and refuse to engage won't see any benefit.

## Wednesday, September 26, 2012

### Day 16: Unit 1 Quiz 3 & Review

Nothing major - simple 4 question quiz on solving systems of linear equations. My streak of "assessments without a typo" ended at 2, oh well. At least I caught it while they were still taking it so it was addressed in a timely fashion.

I'm still amazed at the differences in behavior between the honors and regular classes. It's really the only major difference - racial & gender makeup is the same, they're almost all 10th graders, etc, but the regular Geo class just can't physically sit still, stop talking and pay attention. It's sad because knowing that, we still put 35 of them in a room. If some kids are more distractable than others, why don't we make smaller classes with more teachers for them? What? Distractable isn't a word? Psshaw.

We used the time after the quiz to go over some examples of S1.5 - writing the equation of a line parallel/perpendicular to another line, through a given point.

I did try to emphasize that with SBG, you can't "fail" a quiz or a test. For starters, quizzes & tests don't get entered as such into ActiveGrade, only the standards go in. In my view, when I assess students, I'm asking to know where they're at. Maybe they're finished learning, maybe they're still at the starting line. If they're not done yet, that's ok - we're not even done with the unit yet. If they're still not done when we take the test, that's ok too, but the responsibility to continue learning will shift onto their shoulders at that point. Really, the only point at which they *have* to be done is the end of the semester. If nothing else, I really hope I can get students to think along those lines.

Tomorrow is online practice with the Carnegie Learning Tutor and Friday is the Unit 1 Assessment.

I'm still amazed at the differences in behavior between the honors and regular classes. It's really the only major difference - racial & gender makeup is the same, they're almost all 10th graders, etc, but the regular Geo class just can't physically sit still, stop talking and pay attention. It's sad because knowing that, we still put 35 of them in a room. If some kids are more distractable than others, why don't we make smaller classes with more teachers for them? What? Distractable isn't a word? Psshaw.

We used the time after the quiz to go over some examples of S1.5 - writing the equation of a line parallel/perpendicular to another line, through a given point.

I did try to emphasize that with SBG, you can't "fail" a quiz or a test. For starters, quizzes & tests don't get entered as such into ActiveGrade, only the standards go in. In my view, when I assess students, I'm asking to know where they're at. Maybe they're finished learning, maybe they're still at the starting line. If they're not done yet, that's ok - we're not even done with the unit yet. If they're still not done when we take the test, that's ok too, but the responsibility to continue learning will shift onto their shoulders at that point. Really, the only point at which they *have* to be done is the end of the semester. If nothing else, I really hope I can get students to think along those lines.

Tomorrow is online practice with the Carnegie Learning Tutor and Friday is the Unit 1 Assessment.

## Tuesday, September 25, 2012

### Day 15: Discussion of solving linear equations

Things are getting better. This material seemed more familiar to the students, so there was less fight about whichever method I used.

I used the traditional modeling approach to the discussion in 2nd hour and it went OK. It didn't blow the doors off the room or anything, but we got through most of the worksheet, kids were generally respectful and there were some solid questions asked. One of the presenting groups asked if they could purposely put a mistake in their board to see if the class would catch it. That was pretty cool.

Both for time and behavioral concerns, I took more control over 5th hour. I still had groups whiteboard problems, but instead of turning them loose to carry on a class discussion, I walked around the room myself and stopped to interpret what I saw on each board. This took the load off students who may be afraid to present and it also gave students a chance to see how I think. I made a point to emphasize that I was still not giving out correct answers, I was simply acting as a medium between the presenters and the class. That seemed to be a compromise they would accept.

Tomorrow is the quiz on solving systems both graphically and algebraically. I don't emphasize elimination as a method because I feel that if you give students with a shaky foundation too many choices, they'll start mixing and matching pieces of each approach. KISS - if you can graph it, do that. If not, use the magic of algebra.

The major thing that's struck me through this unit is that regardless of how familiar the students are with this content they've all seen before, they have no idea what they're really doing. What I mean is that they might be able to follow the steps needed to calculate slope, but they have no real concept of what slope is and why it's relevant. I think I've already noted this here, but it popped up again with solving lines graphically. "Where's the solution?" "it's right there (pointing)." They could graph the lines OK, but too many struggled with a) knowing what a solution is and 2) correctly identifying the coordinates of a point from a graph. How can students graph lines and not be able to label the coordinates of a point?

I used the traditional modeling approach to the discussion in 2nd hour and it went OK. It didn't blow the doors off the room or anything, but we got through most of the worksheet, kids were generally respectful and there were some solid questions asked. One of the presenting groups asked if they could purposely put a mistake in their board to see if the class would catch it. That was pretty cool.

Both for time and behavioral concerns, I took more control over 5th hour. I still had groups whiteboard problems, but instead of turning them loose to carry on a class discussion, I walked around the room myself and stopped to interpret what I saw on each board. This took the load off students who may be afraid to present and it also gave students a chance to see how I think. I made a point to emphasize that I was still not giving out correct answers, I was simply acting as a medium between the presenters and the class. That seemed to be a compromise they would accept.

Tomorrow is the quiz on solving systems both graphically and algebraically. I don't emphasize elimination as a method because I feel that if you give students with a shaky foundation too many choices, they'll start mixing and matching pieces of each approach. KISS - if you can graph it, do that. If not, use the magic of algebra.

The major thing that's struck me through this unit is that regardless of how familiar the students are with this content they've all seen before, they have no idea what they're really doing. What I mean is that they might be able to follow the steps needed to calculate slope, but they have no real concept of what slope is and why it's relevant. I think I've already noted this here, but it popped up again with solving lines graphically. "Where's the solution?" "it's right there (pointing)." They could graph the lines OK, but too many struggled with a) knowing what a solution is and 2) correctly identifying the coordinates of a point from a graph. How can students graph lines and not be able to label the coordinates of a point?

## Monday, September 24, 2012

### Day 14: Solving Systems of Equations

New approach. I needed to remember that this first unit is skill-based. Students are not "discovering" this content (although it was supposed to be review), so I did deviate more than I would have liked and demo the skills required to solve systems of equations graphically and algebraically. I still did so in a very socratic way - I had students guide the class through graphing the lines as well as the steps needed to manipulate equations for substitution.

Overall, the lesson was extremely successful and kids seemed more positive about their abilities.

It's possible I tried to implement too much too quickly, especially will skill-related content that students weren't entirely comfortable with. I have no plans to abandon my plans, but I'm ok with adjustments as long as the class remains student-centered.

Overall, the lesson was extremely successful and kids seemed more positive about their abilities.

It's possible I tried to implement too much too quickly, especially will skill-related content that students weren't entirely comfortable with. I have no plans to abandon my plans, but I'm ok with adjustments as long as the class remains student-centered.

## Friday, September 21, 2012

### Day 13 - Unit 1 Quiz 2

Simple day: Assess standards 1.2 & 1.5 - distinguish between parallel/perpendicular/oblique lines and write the equation of a line parallel/perpendicular to a given line through a given point.

Students were visibly frustrated, even though the quiz was open notes. There were only 6 questions, but I did insist on a time limit because we also had to set up accounts for the class website and ActiveGrade.

Assessment results: 1.2 was OK, 1.5 was an utter disaster. Right now the schedule has us finishing Unit 1 this week with a test on Friday. I've set aside some time on Wednesday to readdress 1.5 in preparation for the unit assessment.

Students were visibly frustrated, even though the quiz was open notes. There were only 6 questions, but I did insist on a time limit because we also had to set up accounts for the class website and ActiveGrade.

Assessment results: 1.2 was OK, 1.5 was an utter disaster. Right now the schedule has us finishing Unit 1 this week with a test on Friday. I've set aside some time on Wednesday to readdress 1.5 in preparation for the unit assessment.

## Thursday, September 20, 2012

### Day 12: Progress?

The Honors classes continued with a traditional-ish modeling style whiteboard discussion. One of the classes is still fighting me a little, but we're at least moving forward.

In my regular class, I had intended to just take over and work through some problems on my tablet connected to the projector. I wasn't going to just do the work and have students follow - my goal was an audience participation work through. And then when the kids saw the tablet, they oohed and ahhed and all wanted a piece (I forget how cool they think a 5 year old beat up convertible notebook computer is). So I found a student that had at least attempted a problem and gave them the tablet to let them work it through on the screen. Then we'd go over it as a class, catch any mistakes that might have been made, and repeat.

The major upside is that almost everyone wants to participate if it means using the cool toy. The downside is that the crowd gets a little restless a) while waiting for someone to write out their answer and 2) when they don't get their turn to play.

In any event, U1 Quiz 2 is today on parallel, perpendicular, & oblique lines. I'm a little wary of how they're going to perform, but it's already been a full week on old material, and I'll try to stress the importance of remediation and reassessment next week.

In my regular class, I had intended to just take over and work through some problems on my tablet connected to the projector. I wasn't going to just do the work and have students follow - my goal was an audience participation work through. And then when the kids saw the tablet, they oohed and ahhed and all wanted a piece (I forget how cool they think a 5 year old beat up convertible notebook computer is). So I found a student that had at least attempted a problem and gave them the tablet to let them work it through on the screen. Then we'd go over it as a class, catch any mistakes that might have been made, and repeat.

The major upside is that almost everyone wants to participate if it means using the cool toy. The downside is that the crowd gets a little restless a) while waiting for someone to write out their answer and 2) when they don't get their turn to play.

In any event, U1 Quiz 2 is today on parallel, perpendicular, & oblique lines. I'm a little wary of how they're going to perform, but it's already been a full week on old material, and I'll try to stress the importance of remediation and reassessment next week.

## Wednesday, September 19, 2012

### Day 11 - This is taking forever

Still working on getting the problems from WS2 on a whiteboard. Attitude was a little better today, but progress is still slow.

Generally I don't pay much attention to pace as long as we're moving forward, but linear equations are all things that were taught in 9th grade. I had hoped that this would serve as an easy intro to the structure of the class so that we could adjust to modeling while simply reviewing old material. Instead, we're spending 4 days interpreting slope-intercept form of a line while stubborn teenagers insist a) they've never learned this before and 2) they "shouldn't have to learn from other students."

*sigh*

Hopefully we can get through a discussion of the worksheet tomorrow and take a quiz either tomorrow or Friday. We're quickly approaching the point of "when do I take the reins to get us moving forward?"

Generally I don't pay much attention to pace as long as we're moving forward, but linear equations are all things that were taught in 9th grade. I had hoped that this would serve as an easy intro to the structure of the class so that we could adjust to modeling while simply reviewing old material. Instead, we're spending 4 days interpreting slope-intercept form of a line while stubborn teenagers insist a) they've never learned this before and 2) they "shouldn't have to learn from other students."

*sigh*

Hopefully we can get through a discussion of the worksheet tomorrow and take a quiz either tomorrow or Friday. We're quickly approaching the point of "when do I take the reins to get us moving forward?"

## Tuesday, September 18, 2012

### Day 10: Practice w/ U1 WS2

We began the class with a quick recap of the concepts we derived yesterday (notes). We then talked as a group about how to approach the bulk of the problems on the worksheet (I didn't explicitly work out any examples) and I left them to work.

The big point I had to stress today was the idea of collaboration and asking other students for help. Most struggling students are convinced that me, the teacher, is the only person appropriate to ask for help.

I've noticed that I have to approach each class with a slightly different tactic. My 2nd hour class is amazing and they don't really put up much of a fight, my 5th hour (the only "regular" class) needs a little more coaching; both emotionally and academically, and my 6th hour class is becoming very adversarial. I toyed with the idea of playing up that animosity and their hatred of the modeling approach / socratic questioning to act more like the Emperor "let the hate flow through you, feel it make you stronger, etc" but that's a dangerous game to play with 10th graders.

Here's my thought for tomorrow (adapted from an experience I had in physics at the end of last year, my first as a modeler):

Me: "Why do hate my methods?"

Them: "Because you never give us the answer - you only ask more questions!"

Me: "Ok, the answer is 12 (for example). Why do you believe me?"

Them: "Because you're the teacher! Obviously you know the answers!"

Me: "Says who? Teachers can't be wrong? We don't make mistakes?"

Them: "Well, they might, but they're going to be right most of the time."

Me: "Ok fine, but where did *I* get the answers?"

Them: "You went to college right? Don't you have degrees in this stuff?"

Me: "Yep - I have a B.S.E. in Engineering Physics from UM (I'm not trying to brag online, just detailing what I'm going to say to them), a Certification of Teaching from EMU in secondary math & physics, and a M.S.T. in Teaching Astronomy. Are those degrees enough to earn your trust that I know the "right" answers?"

Them: "Well, duh."

Me: "Notice, TWO of those degrees are specialized in TEACHING. Do you trust me that I know the best way to TEACH you? To get you to LEARN?"

Them: "..." (I hope)

No joke, I had this conversation with one of my physics students last year. That last line stopped him dead in his tracks. The conversation stemmed from his comment that he "hated" (he was mostly kidding) my class because I made him think. That might be the greatest compliment I've ever gotten from a student.

The big point I had to stress today was the idea of collaboration and asking other students for help. Most struggling students are convinced that me, the teacher, is the only person appropriate to ask for help.

I've noticed that I have to approach each class with a slightly different tactic. My 2nd hour class is amazing and they don't really put up much of a fight, my 5th hour (the only "regular" class) needs a little more coaching; both emotionally and academically, and my 6th hour class is becoming very adversarial. I toyed with the idea of playing up that animosity and their hatred of the modeling approach / socratic questioning to act more like the Emperor "let the hate flow through you, feel it make you stronger, etc" but that's a dangerous game to play with 10th graders.

Here's my thought for tomorrow (adapted from an experience I had in physics at the end of last year, my first as a modeler):

Me: "Why do hate my methods?"

Them: "Because you never give us the answer - you only ask more questions!"

Me: "Ok, the answer is 12 (for example). Why do you believe me?"

Them: "Because you're the teacher! Obviously you know the answers!"

Me: "Says who? Teachers can't be wrong? We don't make mistakes?"

Them: "Well, they might, but they're going to be right most of the time."

Me: "Ok fine, but where did *I* get the answers?"

Them: "You went to college right? Don't you have degrees in this stuff?"

Me: "Yep - I have a B.S.E. in Engineering Physics from UM (I'm not trying to brag online, just detailing what I'm going to say to them), a Certification of Teaching from EMU in secondary math & physics, and a M.S.T. in Teaching Astronomy. Are those degrees enough to earn your trust that I know the "right" answers?"

Them: "Well, duh."

Me: "Notice, TWO of those degrees are specialized in TEACHING. Do you trust me that I know the best way to TEACH you? To get you to LEARN?"

Them: "..." (I hope)

No joke, I had this conversation with one of my physics students last year. That last line stopped him dead in his tracks. The conversation stemmed from his comment that he "hated" (he was mostly kidding) my class because I made him think. That might be the greatest compliment I've ever gotten from a student.

## Monday, September 17, 2012

### Day 9: Describing Pairs of Lines

Ok, I'm going to make a rule for myself and this blog. I'm not going to describe difficulties that arise from student behavior if I think it's unrelated to the modeling format. I say that because things appear to be going well in my two honors classes, and failing miserably in my regular class.

Today's goal: get students to make connections between things they already know about lines (parallel, perpendicular, etc) and what those concepts actually mean. That might be my single biggest surprise teaching math - even kids who have been successful in their math careers generally have little to no idea how to explain math concepts without using math vocab. In other words, they can't apply math to non-obviously-math scenarios.

I had 2 volunteers stand at their own starting points (taped on the floor). I then asked a random student from the class to make up a slope. Surprisingly, most responses came of the form "2, 6" (not 2 over 6), so I used that chance to reinforce the idea that slope is a number that indicates the direction of a line. I then asked the volunteers to walk in that "direction" with 'up' being forward and left/right being exactly that. I had backup volunteers stand at the original starting point and used a 2 meter stick to "connect the dots."

Today's goal: get students to make connections between things they already know about lines (parallel, perpendicular, etc) and what those concepts actually mean. That might be my single biggest surprise teaching math - even kids who have been successful in their math careers generally have little to no idea how to explain math concepts without using math vocab. In other words, they can't apply math to non-obviously-math scenarios.

I had 2 volunteers stand at their own starting points (taped on the floor). I then asked a random student from the class to make up a slope. Surprisingly, most responses came of the form "2, 6" (not 2 over 6), so I used that chance to reinforce the idea that slope is a number that indicates the direction of a line. I then asked the volunteers to walk in that "direction" with 'up' being forward and left/right being exactly that. I had backup volunteers stand at the original starting point and used a 2 meter stick to "connect the dots."

- Do the lines formed by these two points actually stop where the meter stick stops?
- So we know lines extend infinitely (written on board)
- Do these lines intersect?
- Conclusion is that if you walk in the same direction as someone else who started at a different point, you'll never cross their path
- Therefore, same slope --> never intersect and we call this parallel
- Converse must also be true, if lines have different slopes, they must intersect
- How many times will intersecting lines meet?
- This created some discussion. Some thought they might later on (with the infinite extension). I made a point to insist that lines are an imaginary construct - they don't bend around the Earth, they don't stop when the hit the floor, etc.
- Conclusion is that they only meet once
- What do you notice about the spacings created between the lines?
- Here I was trying hard to not talk about angles, especially avoiding words like acute & obtuse. I know they probably saw those words before, but we haven't discussed them as a class yet.
- Lead class to the idea that there are 4 spacings/angles, but really only 2 different ones
- Call these wide/thin or big/small
- Do intersecting lines *always* make a pair of big/small spacings?
- If no, what's the counterexample?
- Here I used Geometer's Sketchpad to create perpendicular lines (didn't use that word yet) and measure the spacings (kinda had to call them angles at this point).
- So it's possible to have 4 equal spacings. What must then be true about the slopes of the lines?
- Most kids would get the idea that the slopes are flipped. Had to point out that they're also negatives.
- Define this as perpendicular

That's where we stopped. I did hand out U1 WS2 as HW, but didn't have time to work through examples, so I'm expecting tomorrow to be more oriented around work and maybe whiteboarding than discussion.

## Friday, September 14, 2012

### Day 8: First Assessment

Unit 1 Quiz 1: slope and slope-intercept form.

I let students use notes and calculators - mainly because why not? I'm not asking recall type questions, so I don't see notes as an influence that masks what students truly understand. I also like the idea of encouraging students to pay attention and take notes in a class using SBG and not grading homework.

The quiz only took 20 minutes, so I tried to include bits of Frank Noschese's mindset lesson and how the brain can create new neural pathways through both physical activity and/or an enriched environment. I gave students a math perception survey to start, watched the video clip, and asked for basic feedback (on the back of the survey) before class ended. If I have time to look at the surveys this weekend, I might try to spend some time discussion what I noticed about their opinions on Monday.

I will certainly need to devote some time on Monday to explaining the results of the quiz since SBG is new to them. I also need to show them how to access their grades through ActiveGrade (I'm not using the school's online gradebook).

A whole week spent on slope-intercept form in a geometry class sure feels slow, but I'm planning on basing the entire course on graphing, so I'm hoping it pays off later. We'll see.

I let students use notes and calculators - mainly because why not? I'm not asking recall type questions, so I don't see notes as an influence that masks what students truly understand. I also like the idea of encouraging students to pay attention and take notes in a class using SBG and not grading homework.

The quiz only took 20 minutes, so I tried to include bits of Frank Noschese's mindset lesson and how the brain can create new neural pathways through both physical activity and/or an enriched environment. I gave students a math perception survey to start, watched the video clip, and asked for basic feedback (on the back of the survey) before class ended. If I have time to look at the surveys this weekend, I might try to spend some time discussion what I noticed about their opinions on Monday.

I will certainly need to devote some time on Monday to explaining the results of the quiz since SBG is new to them. I also need to show them how to access their grades through ActiveGrade (I'm not using the school's online gradebook).

A whole week spent on slope-intercept form in a geometry class sure feels slow, but I'm planning on basing the entire course on graphing, so I'm hoping it pays off later. We'll see.

## Thursday, September 13, 2012

### Day 7: Continuing the Discussion

We faced a variety of challenges trying to get through our first real modeling-style discussion. Essentially, they all boil down to respect.

2nd hour: Things went fairly well. A selective sample of questions were presented by groups and students asked insightful questions while I jotted down bits of what they were saying to highlight the key ideas.

5th hour: A struggle. 3 students had to be sent to the SRC (Student Responsibility Center) for continuously disruptive the discussion. Things got better after that, but in general the students are fighting the transition to becoming active learners.

6th hour: After the difficulties in 5th hour, I was a little frustrated. I noticed that when I stood silently in the center of the class, the students knew I wanted them to quiet down and generally did so. But as soon as I started talking again (even just to give instructions), conversations would immediately break out all over the room (35 students in 8 groups). I pointed this out to them and explained that I was going to remain silent for the rest of the discussion. I didn't really think this idea would work, but I figured it was worth a shot.

It was weird - for a second, they actually looked like they were going to pull it off. A few natural leaders took charge and would call out whichever group was next, the group would present, and they would move on. Sadly, no one was really interested in ensuring everyone understood the work and students were visibly (and audibly) frustrated at how everything was rushed at that i wasn't "teaching."

I let them finish and asked how the felt about what just happened. They hated it, with 'it' being the fact that everyone wouldn't quiet down and let any progress occur. I explained that if we switched back to a traditional classroom, nothing would change (I know, I've done it both ways). The difference is, *I* would get to be the focus of their disrespect instead of each other. The amount of learning doesn't really change, but they're happier because they're not responsible for the classroom environment.

For the last 15 minutes, I moderated a MUCH more respectful discussion of a few key problems and we called it a day.

I faced similar struggles when I adopted modeling in physics last year, and I was concerned that 10th graders just might not be mature enough to handle a student-led environment such as modeling requires. Now I think they *can* do it, but it's going to take some work. I'm not entirely sold on my 5th hour though - the big difference I see between "regular" and "honors" is behavior and maturity - not intelligence.

2nd hour: Things went fairly well. A selective sample of questions were presented by groups and students asked insightful questions while I jotted down bits of what they were saying to highlight the key ideas.

5th hour: A struggle. 3 students had to be sent to the SRC (Student Responsibility Center) for continuously disruptive the discussion. Things got better after that, but in general the students are fighting the transition to becoming active learners.

6th hour: After the difficulties in 5th hour, I was a little frustrated. I noticed that when I stood silently in the center of the class, the students knew I wanted them to quiet down and generally did so. But as soon as I started talking again (even just to give instructions), conversations would immediately break out all over the room (35 students in 8 groups). I pointed this out to them and explained that I was going to remain silent for the rest of the discussion. I didn't really think this idea would work, but I figured it was worth a shot.

It was weird - for a second, they actually looked like they were going to pull it off. A few natural leaders took charge and would call out whichever group was next, the group would present, and they would move on. Sadly, no one was really interested in ensuring everyone understood the work and students were visibly (and audibly) frustrated at how everything was rushed at that i wasn't "teaching."

I let them finish and asked how the felt about what just happened. They hated it, with 'it' being the fact that everyone wouldn't quiet down and let any progress occur. I explained that if we switched back to a traditional classroom, nothing would change (I know, I've done it both ways). The difference is, *I* would get to be the focus of their disrespect instead of each other. The amount of learning doesn't really change, but they're happier because they're not responsible for the classroom environment.

For the last 15 minutes, I moderated a MUCH more respectful discussion of a few key problems and we called it a day.

I faced similar struggles when I adopted modeling in physics last year, and I was concerned that 10th graders just might not be mature enough to handle a student-led environment such as modeling requires. Now I think they *can* do it, but it's going to take some work. I'm not entirely sold on my 5th hour though - the big difference I see between "regular" and "honors" is behavior and maturity - not intelligence.

## Wednesday, September 12, 2012

### Day 6: Whiteboard & Discuss U1 WS1

So close, and yet so far.

I have 3 geometry classes; 2nd hour, 5th hour, and 6th hour. Technically, 2nd and 6th are Honors classes, but I generally don't put too much stock in that label.

Today's task was centered around the discussion. I needed to remind students of SBG and how it related to homework (SB.1 I can come to class prepared) and I needed to lay out the rules for class discussion (mostly just variants of "be respectful."). Most students had completed their HW (phase 1 - check), and most got to task whiteboarding the questions I assigned without any issue (phase 2 - check). Anybody with experiencing modeling will know that phase 3 is the tricky one. And with 35 10th graders in the room, I was a little nervous.

2nd hour went great, and that might be a bad thing. I only say that because it got my hopes up only to be dashed by my remaining classes. Just too many kids thinking that whispering is OK and throwing the entire discussion off the rails.

We only got through a couple of problems today, so my new schedule is that we finish the discussion tomorrow and quiz on Friday (that will complete 2 standards of the 6 total in Unit 1). Part of me really wants to let the class determine how fast we go, even if it means taking 4 days on a simple slope worksheet that was supposed to be review. But I also don't want to give them a negative impression of the class on the 2nd week.

I have 3 geometry classes; 2nd hour, 5th hour, and 6th hour. Technically, 2nd and 6th are Honors classes, but I generally don't put too much stock in that label.

Today's task was centered around the discussion. I needed to remind students of SBG and how it related to homework (SB.1 I can come to class prepared) and I needed to lay out the rules for class discussion (mostly just variants of "be respectful."). Most students had completed their HW (phase 1 - check), and most got to task whiteboarding the questions I assigned without any issue (phase 2 - check). Anybody with experiencing modeling will know that phase 3 is the tricky one. And with 35 10th graders in the room, I was a little nervous.

2nd hour went great, and that might be a bad thing. I only say that because it got my hopes up only to be dashed by my remaining classes. Just too many kids thinking that whispering is OK and throwing the entire discussion off the rails.

We only got through a couple of problems today, so my new schedule is that we finish the discussion tomorrow and quiz on Friday (that will complete 2 standards of the 6 total in Unit 1). Part of me really wants to let the class determine how fast we go, even if it means taking 4 days on a simple slope worksheet that was supposed to be review. But I also don't want to give them a negative impression of the class on the 2nd week.

## Tuesday, September 11, 2012

### Day 5: Instruction & Practice

The goal for today was to connect yesterday's activity (creating lines of people and then describing them) to the notion that equations are just a way of describing lines with symbols instead of words. The first half of class was discussion (led by me, but I'm serious - it was a discussion and NOT a lecture), and the second half was practice on U1 WS1.

A couple of thoughts:

A couple of thoughts:

- My guess is the because this is a review unit, the students think it's beneath them, so they shouldn't have to listen. I really don't think the approach is to blame here, because I can't imagine lecturing being any more engaging than the discussions we've been having. But at the same time, when it came time to practice on the worksheet, most kids got stumped FAST.
- These kids really just want to be right. To the point where if there's a chance they're not right, they'll just leave the question blank. It seems like all I heard today was "I need your help - is this right?" I just kept asking them to show how they got their answer (which they hate). One girl caught on real quick - she's already labelled me as part of Team No-Answer. Awesome.
- I felt kinda weird about the discussion as it doesn't seem very modeling-esque. But I reassured myself that there really are some things you can't discover, and the intro unit is a good place for that (I'm thinking of linearizing graphs in physics). At least I didn't lecture in the sense that I did NOT say "this is slope intercept form, memorize it" (or anything along those lines).

Tomorrow is where the rubber will meet the road as I ask groups to whiteboard and present selections from the worksheet. Can they manage a respectful discussion? Are they ok with presenting answers they might not be 100% confident with? Will the understand the importance of leaning by making mistakes? Tune in tomorrow to find out!

## Monday, September 10, 2012

### Day 4: Why is slope so important?

I started class by having kids read the standards we were going to be working on this week (S1.1 & S1.6). I reminded them about the different grading scale and talked about how the unit would progress over the next couple of weeks.

Then I solicited answers to the question: "Where might you use slope outside of a math class?" I wrote anything anyone said on the board and their responses ranged from architecture to predicting trends for business.

I varied with exactly how I intro'd the challenge, but I was happiest with this method: Start by asking one group to stand up and form a line. When they've settled, ask someone from the rest of the class to describe that line. Continue, asking probing questions when appropriate until they class feels they've created a specific-enough description that the line could be recreated by an outsider.

The challenge (with a description already written on the board behind me) is for every group to make their own line and write down their own description (on a whiteboard) that is specific enough to be recreated by another group. Give the groups 5-10 mins to make their lines and walk around the room checking on progress, asking leading questions where necessary.

My classes are all above 32, so I have 7 or 8 groups in each class which can make things tricky. Thankfully I have a lab class (for physics), so I have plenty of room to spread out.

When everyone is done, I asked students to return to their seats and I grabbed a group's whiteboard at random and read it aloud to the class. I then called on a group at random and had them attempt to recreate the line in the center of the room. I first check with the class as a whole if the line was recreated accurately to what was given on the whiteboard. I then ask the group that created the line if the new line looks *exactly* like theirs did. We repeated this for 3 or 4 groups (no need to do every group if the point is coming across).

I then asked some students (at random) if they had any ideas why we did that. There was a stark contrast here between my two Honors classes and my one "regular" class. I could generally get kids to come around to the idea that being able to describe a line accurately is an important skill (and harder than it looks).

Finally, I try to get students to connect the descriptions used in our lines (N, S, E, W mostly) to descriptions of lines commonly seen in math class. The honors kids quickly jumped on the "slope as direction" connection, but the regular class had to be led there more directly.

In general, students seemed to have a basic understanding of slope before class, but few readily made the connection to something other than math class. I was fairly satisfied with how the day went - obviously there are things I will do differently next year, but not bad for a first try.

Tomorrow I hope to lead a discussion of where slope-intercept form comes from, show some examples and get them practicing on their own.

Then I solicited answers to the question: "Where might you use slope outside of a math class?" I wrote anything anyone said on the board and their responses ranged from architecture to predicting trends for business.

I varied with exactly how I intro'd the challenge, but I was happiest with this method: Start by asking one group to stand up and form a line. When they've settled, ask someone from the rest of the class to describe that line. Continue, asking probing questions when appropriate until they class feels they've created a specific-enough description that the line could be recreated by an outsider.

The challenge (with a description already written on the board behind me) is for every group to make their own line and write down their own description (on a whiteboard) that is specific enough to be recreated by another group. Give the groups 5-10 mins to make their lines and walk around the room checking on progress, asking leading questions where necessary.

My classes are all above 32, so I have 7 or 8 groups in each class which can make things tricky. Thankfully I have a lab class (for physics), so I have plenty of room to spread out.

When everyone is done, I asked students to return to their seats and I grabbed a group's whiteboard at random and read it aloud to the class. I then called on a group at random and had them attempt to recreate the line in the center of the room. I first check with the class as a whole if the line was recreated accurately to what was given on the whiteboard. I then ask the group that created the line if the new line looks *exactly* like theirs did. We repeated this for 3 or 4 groups (no need to do every group if the point is coming across).

I then asked some students (at random) if they had any ideas why we did that. There was a stark contrast here between my two Honors classes and my one "regular" class. I could generally get kids to come around to the idea that being able to describe a line accurately is an important skill (and harder than it looks).

Finally, I try to get students to connect the descriptions used in our lines (N, S, E, W mostly) to descriptions of lines commonly seen in math class. The honors kids quickly jumped on the "slope as direction" connection, but the regular class had to be led there more directly.

In general, students seemed to have a basic understanding of slope before class, but few readily made the connection to something other than math class. I was fairly satisfied with how the day went - obviously there are things I will do differently next year, but not bad for a first try.

Tomorrow I hope to lead a discussion of where slope-intercept form comes from, show some examples and get them practicing on their own.

## Sunday, September 9, 2012

### Updates

I updated the overviews for the first 4 units (after the sequencing change I already mentioned) as well as the standards. They're in Google Docs that allow commenting if you want to offer up some constructive criticism. Look back at the 'sequence' post for the links.

Tomorrow is the first day of the experiment - here's hoping I didn't waste my summer!

Tomorrow is the first day of the experiment - here's hoping I didn't waste my summer!

## Friday, September 7, 2012

### Day 3 - Bureaucracy

I wrote out a whole post describing what happened in class today and then I thought that nobody really cares to hear about why nothing got done, so I scrapped it.

TL; DR - administrative nonsense (aka: things that aren't geometry related) forced me to lose a class period today, possibly another next week, and definitely three more throughout the school year.

TL; DR - administrative nonsense (aka: things that aren't geometry related) forced me to lose a class period today, possibly another next week, and definitely three more throughout the school year.

## Thursday, September 6, 2012

### Day 2: Why we need to do things differently

Since yesterday was something of a 'fun' day, I needed to get through the class business today. After going through the syllabus and showing students the class website (www.mrfuller.net), I had two major goals for class: give a brief overview of standards based grading, and point out the flaws in the traditional model for school.

The kids seemed to appreciate how straightforward SBG is - they looked at the 6 standards for Unit 1 and were optimistic that this class wouldn't be too hard (Unit 1 is all about slope, which they should remember from Algebra). Students also liked the idea that they'll be able to focus their energy on specific things they've struggled with, as opposed to worrying about retaking an entire unit test.

As for the meat of the discussion, I stole the bulk of the ideas from Frank Noschese who reposted the ideas from Eric Brunsell (beg, borrow, and steal, right?).

I started by asking the class if they would classify themselves as a "good" student. I clarified that while "good" can mean a lot of things, I was looking for students who thought they knew how to succeed - whether or not they actually did. A vast majority of students self-identified as a "good" student, so I put them to the test and had them watch a video on plant reproduction (also linked in the page on Frank's website) while answering some basic questions about the topic. Most did OK after one viewing, but all wanted a 2nd chance to catch things they might have missed. We went over the questions as a class and everyone came to consensus on the answers.

Then I asked if the sequence we just went through - content delivery, confidence check, more delivery, then discussion & agreement - mirrored most students' experiences in school. They agreed for the most part, but some were quick to point out that not every class was like that (*phew*). But I reminded them that they labelled themselves as "good" students, so even if it's not the best way, they'd find a way to make it work, right?

I moved directly from that comment to showing the video on the retro encabulator. I love that video. I worked in automotive engineering before teaching and I still have no idea what that guy is talking about. I've watched the video a dozen times, and I still can't repeat his gibberish with proper placement of verbs and nouns. The kids are obviously all stymied and most can't make it through the 2 minute clip without voicing their frustration. This time I waited until after the video to hand out the questions and then I asked if they noticed what I did. We watch it again, and the kids are quick to point out that the questions aren't in order and that's not fair.

It all builds to a discussion of how silly the old model is and I try to probe for their own ideas on how to make it better. Most will come up with stuff along the lines of "learning by doing" and agree that I should not be unilaterally presenting content in any form (video, presentation, textbook). I'm really satisfied with how the day went and I hope the kids remember the point in a few weeks when they're struggling with the content and working collaboratively.

TL;DR Point out flaws in traditional teaching, get students to buy in on a different approach.

The kids seemed to appreciate how straightforward SBG is - they looked at the 6 standards for Unit 1 and were optimistic that this class wouldn't be too hard (Unit 1 is all about slope, which they should remember from Algebra). Students also liked the idea that they'll be able to focus their energy on specific things they've struggled with, as opposed to worrying about retaking an entire unit test.

As for the meat of the discussion, I stole the bulk of the ideas from Frank Noschese who reposted the ideas from Eric Brunsell (beg, borrow, and steal, right?).

I started by asking the class if they would classify themselves as a "good" student. I clarified that while "good" can mean a lot of things, I was looking for students who thought they knew how to succeed - whether or not they actually did. A vast majority of students self-identified as a "good" student, so I put them to the test and had them watch a video on plant reproduction (also linked in the page on Frank's website) while answering some basic questions about the topic. Most did OK after one viewing, but all wanted a 2nd chance to catch things they might have missed. We went over the questions as a class and everyone came to consensus on the answers.

Then I asked if the sequence we just went through - content delivery, confidence check, more delivery, then discussion & agreement - mirrored most students' experiences in school. They agreed for the most part, but some were quick to point out that not every class was like that (*phew*). But I reminded them that they labelled themselves as "good" students, so even if it's not the best way, they'd find a way to make it work, right?

I moved directly from that comment to showing the video on the retro encabulator. I love that video. I worked in automotive engineering before teaching and I still have no idea what that guy is talking about. I've watched the video a dozen times, and I still can't repeat his gibberish with proper placement of verbs and nouns. The kids are obviously all stymied and most can't make it through the 2 minute clip without voicing their frustration. This time I waited until after the video to hand out the questions and then I asked if they noticed what I did. We watch it again, and the kids are quick to point out that the questions aren't in order and that's not fair.

It all builds to a discussion of how silly the old model is and I try to probe for their own ideas on how to make it better. Most will come up with stuff along the lines of "learning by doing" and agree that I should not be unilaterally presenting content in any form (video, presentation, textbook). I'm really satisfied with how the day went and I hope the kids remember the point in a few weeks when they're struggling with the content and working collaboratively.

TL;DR Point out flaws in traditional teaching, get students to buy in on a different approach.

## Wednesday, September 5, 2012

### First Day

I really hate the idea of handing out a syllabus and going over class business on the first day. My #1 reason is because that's what every other teacher in the building does which means all of us start to run together in the minds of the students. #2 is probably more of an adaptation to the way my building is run. Student schedules are often not firmed up until the second week of school, let alone the first day, so why waste time going over something I'm going to have to repeat to a handful of new kids tomorrow?

So this year I tried something new. A coworker had forwarded an image of nested squares to the math dept staff as his plans for a generic first day activity. I wanted to connect it to my teaching philosophy and what goals with modeling for the class, so I adapted it to become a class long activity.

I started by passing out a copy of the image to every student and asking that they take ~5 mins to count the squares *by themselves.* That last part needed emphasis because on the first day with what was obviously a blow-off assignment, the kids wanted to see what their neighbor got and talk about it. When they were done, I informally polled the class to get a range of responses - generally from 16 to 36 if no one has seen the image before. I also asked students to rate how confident they were in their response.

Stage #2 involved giving each group (my desks are set for groups of 4) a laminated copy of the same image and a wet-erase marker. Repeat. This time I asked questions like "how much *more* confident are you?" and "what else could I have done to make this easier?" (access to different colored markers was the common answer to the second one).

Then we go through the image as a group and make sure we account for every square. I honestly didn't know the right answer when we started and I make sure the kids know that too. The concluding discussion revolved around the importance of the process vs. the correctness of the answer. I wanted the kids to buy in to the idea of working collaboratively and taking full advantage of the resources at their disposal. And if there is a "right" answer to be found, there shouldn't be an arbitrary end point by when it has to be given.

So this year I tried something new. A coworker had forwarded an image of nested squares to the math dept staff as his plans for a generic first day activity. I wanted to connect it to my teaching philosophy and what goals with modeling for the class, so I adapted it to become a class long activity.

I started by passing out a copy of the image to every student and asking that they take ~5 mins to count the squares *by themselves.* That last part needed emphasis because on the first day with what was obviously a blow-off assignment, the kids wanted to see what their neighbor got and talk about it. When they were done, I informally polled the class to get a range of responses - generally from 16 to 36 if no one has seen the image before. I also asked students to rate how confident they were in their response.

Stage #2 involved giving each group (my desks are set for groups of 4) a laminated copy of the same image and a wet-erase marker. Repeat. This time I asked questions like "how much *more* confident are you?" and "what else could I have done to make this easier?" (access to different colored markers was the common answer to the second one).

Then we go through the image as a group and make sure we account for every square. I honestly didn't know the right answer when we started and I make sure the kids know that too. The concluding discussion revolved around the importance of the process vs. the correctness of the answer. I wanted the kids to buy in to the idea of working collaboratively and taking full advantage of the resources at their disposal. And if there is a "right" answer to be found, there shouldn't be an arbitrary end point by when it has to be given.

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