As a country we talk about wanting the best people to be teachers, because if we put students first a great teacher makes a huge difference. Society says
that's what we want, the culture says that's what we want. But I just
received my contract for teaching next year. And there's a disconnect
between what we say we want and what we do.

In my former job in the
private sector, you would never think to sign a contract with blank
spaces. Yet my teaching contract for next year had a blank spot
for salary. And that blank spots' meaning cannot be lost on us and what it implies. (Also I don't blame the
school where I work for the contract I received. They are slave to state
funding, they have little choice but to give a contract that the state
dictates by their budget.)

It
implies that while we say we want the best teachers; we truly are unwilling to do the things that brings and keeps the best people in education. Unfortunately we really don't want the
best teachers, we want smart charitable people. The best typically will go where the rewards are.

In my case I cannot even be rewarded with a guarantee of what my next year salary will be, if I want a job I need to sign it. Due to how the state does school financing my school cannot even write in the amount that I made this year. How do we expect to
attract the smartest and the brightest people to make a real difference?

I
was successful in my former job, I was good at my former job. I wanted
to teach but it shouldn't have to be charitable. We should want the
brightest for education and should be willing to go get them.

I hear and read that teachers make the most
difference in a student's progress, yet they're the ones we abuse. We do not make teaching a
desirable position, and overall we don't respect the position much
either. I find myself more respected than other teachers. People will say "Oh, you're a teacher." and I reply"Yes, I teach math," and they go"Oh I couldn't do that."
That implies they could teach anything else but math, not everyone can teach. And to be good at it, and to keep the good people in it, the public sector must treat its best employees like the private sector.

The interesting
part is people talk of what 'has to happen in education.' But there really
isn't any drive to fix it. It takes great teachers in education to make
a difference, and we are not going to attract great teachers. Overall you get what you pay for, and with salaries and benefits going in free-fall compared to inflation simply means we will get mediocre teachers. (And the occasional few who
was simply want to teach no matter what the financial reward.)

I love
teaching. But every year, at about this time, I have to consider the pay and what I could
make in engineering, my former career. If the pay for teaching was simply a little
more, so I was not constantly struggling, and if the respect a little more, I'm sure I wouldn't make that
consideration. But those things are not there in education presently so every year I think about leaving teaching.

I'm at a loss for how to
change the culture and dedication to education of the United States; how we change how we treat
teachers. I'm also at a loss for how to put students first, meaning how to get great teachers. If you put students first, and I usually do, they need great teachers. That means compensation for the best, and a
contract with a blank spot for pay doesn't make the best want to stay.

## Tuesday, April 30, 2013

## Sunday, April 21, 2013

### AP Calculus - Crunch Time

So prepping seniors for AP Calculus is no easy feat. The second semester is here, all of them know their grades are no longer that important, and most therefore don't care so long as they pass (which is all true). They also start losing focus on the goal of passing the AP test, nothing really matters (I can hear Queen playing), but the AP does matter - it is college credit!

So every year I try to finish the Calculus AB curriculum by early March, leaving nearly 2 months of review. I continue with homework, but senior-irus keeps a large chuck from doing any real quality work, so we use the class time to hammer home the prep. But this year due to a variety of factors we did not get thru the curriculum until April 1, and that is leading to unprepared students for the first Wednesday in May.

I take pride in the fact that a student that has received a D or better in my AP Calc course has gotten a passing score on the AP the last 3 years. The way we do that is the prep time from March 1st, it is what solidifies the concepts and understanding. This year we simply have run out of time for the lazy stricken seniors, I find myself pushing down the path and not sure they will all make it this year.

AP problems are a beast of their own. Even though I include the free response type questions as soon as I can on my tests (usually around early December because of the base knowledge required), they simply need practice applying all their knowledge onto one problem. They also see a ton of multiple choice AP questions through-out the year - so the students are set on those. They cannot pass my course if they cannot do the AP multiple choice, and understand it. Yet if you get a D why would you think you should pass the AP?

But in previous years we were able to make it, so the lesson is to double up, do extra sessions, simply do whatever it takes to be done by March 1. Crunch time needs to be 8 weeks!

So every year I try to finish the Calculus AB curriculum by early March, leaving nearly 2 months of review. I continue with homework, but senior-irus keeps a large chuck from doing any real quality work, so we use the class time to hammer home the prep. But this year due to a variety of factors we did not get thru the curriculum until April 1, and that is leading to unprepared students for the first Wednesday in May.

I take pride in the fact that a student that has received a D or better in my AP Calc course has gotten a passing score on the AP the last 3 years. The way we do that is the prep time from March 1st, it is what solidifies the concepts and understanding. This year we simply have run out of time for the lazy stricken seniors, I find myself pushing down the path and not sure they will all make it this year.

AP problems are a beast of their own. Even though I include the free response type questions as soon as I can on my tests (usually around early December because of the base knowledge required), they simply need practice applying all their knowledge onto one problem. They also see a ton of multiple choice AP questions through-out the year - so the students are set on those. They cannot pass my course if they cannot do the AP multiple choice, and understand it. Yet if you get a D why would you think you should pass the AP?

But in previous years we were able to make it, so the lesson is to double up, do extra sessions, simply do whatever it takes to be done by March 1. Crunch time needs to be 8 weeks!

## Saturday, April 20, 2013

### Interest and Loans

During Algebra 1 (which is a combo of 8th & 9th graders) we work on an ongoing yearly analysis of loans, payment plans, etc. We use google docs as a landing page, with individual lessons linked to it; from those documents we create essays that address the questions in each of the lessons. Everything is about the interest we pay on loans and other things.

What I am reflecting on is a combo of where this project fits into the CCSS and my student's beliefs that stores, or vendors would not charge interest for a long payment plan. The lesson we just completed is about "Crazy Eddie" who sells a $2499 TV for only $66 per month (Lesson 7). The assignment is to determine, or give an estimate on the number of months and what interest Eddie charges.

Now you can tell I did not provide enough info, but my students are to make and defend their guesses in the essay. I do not grade for correctness, but just the essay format and the student's use of math as a base for their conjuctures.

Nearly all my students, except for a couple always guess the payments at 38 months. Their math is $2499/$66 per month = 37.9 months and they round to 38, a few even round down! And they think Crazy Eddie will only take $9 in total interest in 38 months, over 3 years! (38 months*$66/month = $2508; $2508-$2499 = $9 interest)

This lesson is "taken" from a Rent-to-Own situation. The actual plan is 5 years, or 60 months. The next lesson when they analyze the actual plan is really "eye-opening" for many students. It is funny the anger they get for Eddie, and the interest rate on the plan is less than some credit cards!

This is the things we should all teach. All of these students had done simple and compound interest, yet they had no real world feel for how interest really works. Yet as I plan my curriculum it would be hard to keep these lessons based upon the huge amount of standards we are now being expected to teach (now "a mile wide, and 6 inches deep!"). I am going to keep these money units and push a lot of the CCSS to PreCalculus, because the math and the understanding is just too important.

Because really understanding interest is way more important than Cramer's Rule, matrices, or proofs.

What I am reflecting on is a combo of where this project fits into the CCSS and my student's beliefs that stores, or vendors would not charge interest for a long payment plan. The lesson we just completed is about "Crazy Eddie" who sells a $2499 TV for only $66 per month (Lesson 7). The assignment is to determine, or give an estimate on the number of months and what interest Eddie charges.

Now you can tell I did not provide enough info, but my students are to make and defend their guesses in the essay. I do not grade for correctness, but just the essay format and the student's use of math as a base for their conjuctures.

Nearly all my students, except for a couple always guess the payments at 38 months. Their math is $2499/$66 per month = 37.9 months and they round to 38, a few even round down! And they think Crazy Eddie will only take $9 in total interest in 38 months, over 3 years! (38 months*$66/month = $2508; $2508-$2499 = $9 interest)

This lesson is "taken" from a Rent-to-Own situation. The actual plan is 5 years, or 60 months. The next lesson when they analyze the actual plan is really "eye-opening" for many students. It is funny the anger they get for Eddie, and the interest rate on the plan is less than some credit cards!

This is the things we should all teach. All of these students had done simple and compound interest, yet they had no real world feel for how interest really works. Yet as I plan my curriculum it would be hard to keep these lessons based upon the huge amount of standards we are now being expected to teach (now "a mile wide, and 6 inches deep!"). I am going to keep these money units and push a lot of the CCSS to PreCalculus, because the math and the understanding is just too important.

Because really understanding interest is way more important than Cramer's Rule, matrices, or proofs.

## Thursday, April 18, 2013

### Line Week Day 5!

Day 5 was a Monday. And we simply reinforced the concepts of slope and how to graph. Even though we focused hard for 5 straight class periods we will need to hit the concept of slope and how it works in real problems again this year.

At the end we can identify slopes and y-intercepts, can graph using slope-intercept method and table method, and just started to understand the idea of slope as a rate of change (with units leading the way!). Now I feel like students can do some problems at home for practice (solutions are always given) and make sure they can do the procedural side of "

The conceptual understanding is going to take more work and more practice/struggle -- perhaps Line Week Part 2!

At the end we can identify slopes and y-intercepts, can graph using slope-intercept method and table method, and just started to understand the idea of slope as a rate of change (with units leading the way!). Now I feel like students can do some problems at home for practice (solutions are always given) and make sure they can do the procedural side of "

*y = mx + b*"The conceptual understanding is going to take more work and more practice/struggle -- perhaps Line Week Part 2!

## Friday, April 5, 2013

### Line Week - Day 4

Day 4 of Line Week; today we practiced identifying slope and intercept from graphs! First a side note, I usually test each Friday - I consider this to have a couple of benefits - one it allows me to pull lots of review problems all year long not allowing any topic to lose mastery (cause if you don't use it you'll lose it), two it gives me needed chair time. When I teach I am up with the class, their doing, I am guiding, discussing, sometimes showing; Friday tests allow me to plan, grade and handle whatever is pressing (today it was ordering MS math team t-shirts).

So I broke with tradition a little and shortened Algebra's test so we could work on identifying slope and y-intercept as a class. We plotted a few lines, discussed slope and reinforced the last few days (then a "half-test"). Day 5 is Monday - wrap up day -- I like that it will happen after a weekend, it lets us review and discuss the concepts again.

The project over the next week is create two real world problems and graphs, one representing a positive slope situation and one with a negative slope. I would expect problems like "John had $20 in his wallet and did Frankie's paper route for $5 per day, how much money does John have after five days?" with a graph. It is a start (also all my projects are done until correct - so if it takes multiple revisions cause a student does have understanding they will work at it til they get an acceptable "product" - like a workplace). The real challenge is to take the next step, perhaps Line week 2, where we take data and decide if it is linear (something to add to Geometry?).

So not a bad week, next week we will practice and I will assign "line homework" next week. I never assign homework of the concept we are learning -- homework is practice of "known" things. So even during "Line Week" we did not graph lines outside of class. They practiced factoring....

Til Day 5.....

So I broke with tradition a little and shortened Algebra's test so we could work on identifying slope and y-intercept as a class. We plotted a few lines, discussed slope and reinforced the last few days (then a "half-test"). Day 5 is Monday - wrap up day -- I like that it will happen after a weekend, it lets us review and discuss the concepts again.

The project over the next week is create two real world problems and graphs, one representing a positive slope situation and one with a negative slope. I would expect problems like "John had $20 in his wallet and did Frankie's paper route for $5 per day, how much money does John have after five days?" with a graph. It is a start (also all my projects are done until correct - so if it takes multiple revisions cause a student does have understanding they will work at it til they get an acceptable "product" - like a workplace). The real challenge is to take the next step, perhaps Line week 2, where we take data and decide if it is linear (something to add to Geometry?).

So not a bad week, next week we will practice and I will assign "line homework" next week. I never assign homework of the concept we are learning -- homework is practice of "known" things. So even during "Line Week" we did not graph lines outside of class. They practiced factoring....

Til Day 5.....

## Thursday, April 4, 2013

### Line Week - Day 3 -- Identifying slope & y-intercept

So today was day 3 of "Line Week." (insert proper theme music here) We were in the computer lab again using our self-made excel sheets to graph different lines and look for relationships (see day 2 post). We tried a Jeopardy game where I graphed a line and we identified the slope &

We then discussed a graph about money and days! I graphed the line

I asked for units on

So

As always - when the really good learning started it seemed the class ended, but will pick up with Day 4 tomorrow and Day 5 on Monday! A weekend will allow for some good review of the previous week on Monday.....

*y*-intercept. It worked okay with me graphing on the computer and projecting for the class, but did not work well when the students broke into groups of 2 and 3 to do with themselves. We worked through it, but it is not something I will do again.We then discussed a graph about money and days! I graphed the line

*y*= 3*x*+ 12 in the first quadrant, with the*x*-axis being days and the*y*-axis being money. They quickly saw the y-intercept of $12 and the end total at day 7 of $33. I then asked how much money I was paid --- and the shout of $33 with quickly yelled! Then I got to say "Nope, why?" That was awesome! We worked our way thru the problem - starting with the slope of $3 per day, or the fraction $3/day. That led to the discussion that $12 was the amount of money I had prior to the seven days, leading to the answer of $21 for 7 days. This was a great entry into the*mx*and*b*having to be like terms to add discussion.I asked for units on

*m, x*and*b*--- without much effort the class was all able to explain the units of*m*-$/day,*x*- days and*b*- $. I then worked thru*mx*-- $/day times days -- which is $! The same as*b*! That then lead to the discussion of what is*y = mx + b*.*y*is the vertical point,*m*is RISE/RUN (from our day 1 work with the stairs),*x*is RUN and*b*is a RISE.So

*y*=*mx*+*b*is RISE = RISE/RUN*RUN + RISE, where the RUN cancels, so RISE = RISE + RISE! Like terms. This lead into a couple minutes of talking about how we should think of*m*. Again big ideas and fairly good returns.As always - when the really good learning started it seemed the class ended, but will pick up with Day 4 tomorrow and Day 5 on Monday! A weekend will allow for some good review of the previous week on Monday.....

## Wednesday, April 3, 2013

### Line Week -- Day 2 - Graphing slope and y-intercept in Excel

So today was day 2 of Line week and it went okay, but not as well as the first day. We spent our class period creating a spreadsheet in microsoft excel that had 2 lines where we could easily adjust the slope and y-intercept of each line. I was hoping we could do that in 20-25 minutes, it took about 30 minutes, which left only 15 minutes for plugging in different values (here is the file).

We started with shifting one curve over the other (using y-intercept), making one curve steeper (using slope), one student quickly discovered parallel lines, and so on. We were able to play around and some students started noticing how the y-intercept effect the "vertical position" of the line (yippie!). When I asked how they could guarantee the lines crossed in our viewing screen they figured out the idea of using positive slope in one equation and negative slope in the other. (Tomorrow we see if they figure out using the same y-intercept!)

The graph started to lead to good discussion and reinforced the slope lesson, but we were not able to finish with why

So it did not go as well as hoped, but we still created an excel spreadsheet that can now be used to solve 2 equations for 2 unknowns where the ordered pair are integers between -6 and 6! And we will continue tomorrow with line week - using our spreadsheet to find more relationships and make/test hypothesis. Then we will move to looking at plotted lines and figuring out formulas -- I am thinking a Jeopardy format - I plot the line on screen, they answer the equation in the form of a question - "What is y = 3x - 2?"

Overall another good day!

We started with shifting one curve over the other (using y-intercept), making one curve steeper (using slope), one student quickly discovered parallel lines, and so on. We were able to play around and some students started noticing how the y-intercept effect the "vertical position" of the line (yippie!). When I asked how they could guarantee the lines crossed in our viewing screen they figured out the idea of using positive slope in one equation and negative slope in the other. (Tomorrow we see if they figure out using the same y-intercept!)

The graph started to lead to good discussion and reinforced the slope lesson, but we were not able to finish with why

*mx*and*b*are like terms, which I hoped to do per my previous post. We will need to pick up tomorrow with placing units on our equations to help give it a context!So it did not go as well as hoped, but we still created an excel spreadsheet that can now be used to solve 2 equations for 2 unknowns where the ordered pair are integers between -6 and 6! And we will continue tomorrow with line week - using our spreadsheet to find more relationships and make/test hypothesis. Then we will move to looking at plotted lines and figuring out formulas -- I am thinking a Jeopardy format - I plot the line on screen, they answer the equation in the form of a question - "What is y = 3x - 2?"

Overall another good day!

## Tuesday, April 2, 2013

### Line Week! Day one - Slope!

So today was the first day of "line week." We started by breaking into teams and sending them out to staircases through-out the school to measure how 'steep' they are/were. I did this without any direct instruction on how to measure steepness, it was the first thing we did in class.

I only allowed about 15 minutes and each team had to post their solution prior to the end of the time. The answers were all over the board and we spent time discussing and revising but we concluded that rise and run were the critical components! That allowed us to move into lines and graphing stairs of a steepness ratio of 1 - which we then defined as slope.

Then we were able to graph stairs of 1:1 rise to run, 2:3 rise to run, and 3:1 rise to run, etc. Then I graphed slope of 1 and another line of slope -1 and we discussed if they were the same. We then made some analysis of the lines with the idea that the

Day one was a success.... (playing the theme from Jaws did not hurt either)

I only allowed about 15 minutes and each team had to post their solution prior to the end of the time. The answers were all over the board and we spent time discussing and revising but we concluded that rise and run were the critical components! That allowed us to move into lines and graphing stairs of a steepness ratio of 1 - which we then defined as slope.

Then we were able to graph stairs of 1:1 rise to run, 2:3 rise to run, and 3:1 rise to run, etc. Then I graphed slope of 1 and another line of slope -1 and we discussed if they were the same. We then made some analysis of the lines with the idea that the

*x*-axis was class periods and the*y*-axis being the money they had in their possession (to receive, positive slope or pay, negative slope). That worked really well! That ended the period and we are now moving into the computer lab to use units to tie slope to*y = mx + b*using excel. My goal is to have the students see that by multiplying*mx*you get the same units as*b*..... And Why that allows us to add (like terms!).Day one was a success.... (playing the theme from Jaws did not hurt either)

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