Day 10: Mathalicious and Making Connections

Today I started new lessons with my classes.  In Geometry, we began Domino Effect, which deals with prices of pizza based on the number of toppings and creating equations to determine price.  In Math 8, we started New-Tritional Info, which has students calculating the amount of basketball Lebron James has to play in order to burn off an extra value meal.  Both lessons, and the subsequent projects we will be doing, are products of the amazingly brilliant and creative people at Mathalicious.

These lessons, as well as the others on the Mathalicious site, are designed to add an authentic and real-world approach to learning mathematics and, from what I can tell, it's working.  The geometry kids did VERY well with theirs.  It was interesting to watch which kids struggle with which parts of the assignment and how I was able to redirect their thinking using pointed questions, many of which were suggested by the Mathalicious lesson planning guide.

It was clear that the students had seen the material before but that it had been a while.  Some of them needed a bit a of refresher, which I told them to get from their partner or small group.  Several students gave up early, claiming they had no idea what to do.  After some directed questions, it became obvious that they DID know what to do, but fell into one of two categories: 1) They didn't want to work or 2) They were having trouble with directions that were not explicit.  They wanted step-by-step Ikea-style directions to follow and when they weren't given those, they were uncomfortable and shut down.  Some poking and prodding got them back up again and back to work.

Overall, I was pleased and am looking forward to extending some of these in the next few days.  I hope to do this same lesson with the Math 8 kids near the end of the year, once they've talked about linear equations.

The Math 8 lesson did not go as well, but I don't think it had to do with the lesson design.  I think I vastly underestimated the skill level of my students as well as the way they think about math problems.  I need to find a class set of calculators, but more importantly, I need to train my students to answer a certain question before they complete a task:

Why am I doing this operation?

All too often, they say "We just multiply, right?" but can't tell me why they want to.  They don't know how to analyze a mathematical situation to determine the best course of action, or even a sensible course of action.

I don't blame them for this in any way.  We have trained them from elementary school that math comes in small, discrete packets.  We will provide them with one question and expect one answer.  "What do we do next?" is important, but so is "How do we set this up?" and we don't spend enough time on it.  On top of that, as soon as they see decimals or fractions, they shut down.  I don't want to modify the lesson to make the numbers "pretty" because then it loses some of the authenticity.  I even hate to pick an easier lesson because this one is designed for 6th graders.

Perhaps I simply need to have a more open discussion about how to find what is being asked for instead of relying on them to simply know.  I have plenty of time with double periods.  I can take the time to explain these things, but I REALLY don't want the class to turn into lecture.

I have faith that the more of these activities and projects I do, the more students will begin to understand what is expected of them.


In response to my query about good math practice and function over form, the brilliant and forward thinking Christopher Danielson suggested that I test my students' understand of the equal sign by having them answer the following question:

8 + 4 = [] + 5   What number goes in the []?

The idea being that students who have a less accurate understand of the equal sign would put an answer of 12 because the sum of 8 and 4 is 12.  These were the results:

It's not nearly as bad as expected, but clearly, we do need to have a discussion of the equal sign and how it does not mean "Put the answer here."

The second class did a bit closer to my expectations, which is unfortunate.  There are some interesting answers here, including ones that I think are clearly calculation errors instead of conceptual.

On the personal front, I had a student walk into my room today clearly in a funk.  She immediately put her head down and when I asked her repeatedly to pick it up, she got an attitude with me.  I set the class to a task and pulled her outside.

Me: "What's up with you today? You did great work for me last week and now you're giving me attitude."
S: "I don't want to be in this class."
Me: "I can understand that.  Have I done something to upset you?"
S: "No.  I just don't want to be in this class."
Me: "Well, unfortunately, there's nothing I can do about that and nothing you can do about it, right?"
S: "I guess."
Me: "So if there's nothing that either of us can do about it, then you giving me attitude is just making things tougher for you and for me, right?"
S: "I guess."
Me: "Alright then, I know everyone has bad days.  Hang out here for a few minutes, take a couple deep breaths and then come on back in ready to work."
S: "Ok."

AND SHE DID!!!  She did great work today!  I made sure to find her at the end of the day and thank her again for her great work.


P.S. Since attending TMC13, I've been thinking about every day things in terms of how I could use them in my math class.  When I saw my kids swinging, I immediately thought about Max Ray, the Drexel Math Forum and "I notice, I wonder."

I think there's a great lesson here about periodic motion and pendulums!

Weekend Thought: Notebooks

What is the point of a student notebook?

When I was in high school, my physics teacher required that we copy everything that was on the board.  I mean EVERYTHING.  He told us several times that if he made a stray mark, it should be in our books.  If it wasn't, we would lose points when it was collected.  At the time, I objected to this because I was lazy and didn't want to write stuff down.  Now that I'm a teacher, I object to it because I don't see the educational benefit of it.  If we were supposed to have EXACTLY what he put on the board, he should have given us a photocopy of his notes.

Even that would not have been terrible if room had been left to write notes to ourselves.  I think he did it partly as a power trip, and partly because someone told him that if students are keeping notebooks, they should be graded and the easiest way for that to happen is for everything to look the same.

Thinking back on this makes me cringe.

From what I can tell, well-intentioned notebooks exist for two reasons.

1) As a personal reference to be utilized when studying for a test or quiz
2) As a CYA measure for teachers to be able to say "Look! I did teach this concept!"

I think most teachers who require notebooks do so for the former reason.  From everything I've read about Interactive Notebooks, every change in what teachers require is implemented for the purpose of making the notebook a better reference guide for students.  If I'm wrong about this, I apologize to everyone who uses them.  Maybe a reason I don't use them is that I don't understand.  Regardless, with all the talk of INB, I've been spending a good amount of time thinking about my initial question.

What is the point of student notebook?  Or, more importantly, How can the notebook be a better educational tool for teachers and students?

I think that there are very few students who use their notebooks the way that teachers intend or expect them too.  I think too often, they write down class stuff, then never look at it again.

I have never "required" notebooks because I don't feel qualified to decide what is a good notebook and what isn't, let alone assign a grade based on that judgement.  I have always strongly encouraged students to have them and frequently say things like "You should probably write this down" or "this might be a good thing to have in your notebooks for when you study."

One of the things I remember from my graduate program is that we should be encouraging, as a method of studying and reinforcement of concepts, students to recopy their notes from the day.  We are told that people remember 10% of what they hear, 30% of what they write and 90% of what they teach to someone else (or whatever the real percentages are.)  By having them recopy their notes, I guess, we are helping them to remember more of what happened in class, I suppose.

On rare occasions, we focus on the "teaching others" part, we do activities like "get into pairs and explain your work to your partner" or sometimes "design a lesson around this topic."  These are excellent activities, but I think we can do more.

Since starting this blog, I've been thinking about reflective practice.  It's important enough that it's a required piece of a teacher portfolio.  Why aren't we making our students do this too?

I am going to change what I want my students to put in their notebooks.  Instead of having a list of things covered in class, I want my students to reflect on the class.  Instead of drills as homework, I would rather they go home and write a few paragraphs about what we did, what they learned, what they liked or didn't like, what they want to know more about and general thoughts about what we covered.

I want them to teach their notebooks about what we did in class.  If including examples helps them to do that, then they should include examples.

Pretty, but do they know what to study here?

The student notebook should be in the form of a reflective journal or blog.  If students want to make it web-based, typed into a word document, or handwritten, they can.  I want my homework assignment to be, eventually, "Teach your notebook what you learned today."

I don't think I can start there though.  I think it may be too open-ended.  I will need to work up to it, beginning with certain prompts.  For example:

Write at least 10 lines about what you learned today.
If you were to tell your friend what we did in class, what would you say?
In sentence form, write 3 things we talked about today, 2 things you found interesting, 1 thing that you think should have been done differently and how it should have been done.
Write at least 10 lines about how you, or someone, might use what we did today outside of a school setting.

The more I write about this and think about it, the more I love this idea.  I don't want my students to just be repositories of facts and formulae.  I want them to be able to synthesize new ideas and apply prior knowledge to new problems.  I think reflective practice and personal application would be a great way to encourage this.

I think it will be slow going at first, and possibly discouraging, with a huge learning curve for both me and the students.


EDIT:
To clarify, students should still be writing things down in class, such as examples and topics, but the point would be different.  They wouldn't be writing them down for the purpose of referencing while studying.  They should be writing them down so that they can write about them later.

Double Edit:
I know that there are teachers who do math journals.  I think my argument is that the math journal and the math notebook should be the same thing.

Day 9: I'm An Astronomy Major - I'm Taking Up Space

Geometry got me WAY off task today.  They asked if we could have "Physics Friday" since they know I am certified to teach physics.  We ended up talking about the scale of the universe and the new laser-based communications system that NASA is launching tomorrow.  It was a good discussion and they were actively engaged, even the students who typically have their heads down.

Discussions like this leave me conflicted.  On one hand, I know that they don't go to the math standards and I have a ton of stuff that I have to cover in not that much time.  On the other hand, which is the hand that always wins this debate, I'm an educator first and a math educator second.  If I can provide students with information that they are excited to receive, I'm going to do it.

Part of my job as an educator is, in my opinion, to expose to students to as many ideas and opportunities as possible, to show them the glory and beauty of the world.  Dr. Neil DeGrasse Tyson says that astronomy is the gateway drug to academics.  If you get interested in space, you have to learn math, chemistry, physics, biology, history, etc...  We are always looking for a "hook" to get kids interested in what we have to talk about.  What about the idea that we talk about what they are interested in?  We don't have to do lessons on XBoX or Playstation to get them interested in school.  They have varied interests and, more importantly, if they haven't been exposed to a myriad of topics, how do they even know what they are interested in?  There is a major at UNLV where students design and build Las Vegas stage shows and roller coasters.  THAT'S A JOB!!! The Ford Motor Company has someone on their payroll with the job title of "futurist" whose sole purpose at work is to think about the future of cars.  That job might as well be "Science Fiction Writer in Residence!"  If we don't tell our students about it, who will??

After our talk, we worked on line segments (yawn) and I started them on the locker problem.

We have 1000 lockers and 1000 students.  The first student opens all of the lockers.  The second student closes every other locker.  The 3rd student changes the state of every 3rd locker.  If they are open, he closes them. If they are closed, he opens them.  The 4th student does the same to every 4th locker, and so on.

Typically, this problem is accompanied by a question like "Which doors are open after all of the students are done?" or "Is locker number 298 open or closed?"

Instead, I took a page from Max Ray and the Math Forum at Drexel and asked "What do you wonder?"

I got some great answers.  Is there is a pattern?  What happens when they are all done?  How long would that take?

I got some not-so-great answers.  Why would they do that?  Don't they have anything better to do?

I have faith in Max that the more I do this, the more they will know the kinds of questions I'm looking for.


I liked the activity, but I don't think I gave them enough time.  They were working well, but you really have to do almost 25 iterations before you really see the pattern.  I told them to work on it over the weekend and I trust that 80% of them will obsess about it.  It's a great problem!

During the previous two years of teaching Math 8, I found myself getting insanely frustrated at the lack of skills and numeracy of my students.  I was infuriated that I had to teach subtraction to 8th graders.  It has nothing to do with how smart they are, but all to do with practice and how they approach problems.  I can't explain it but I found it depressing how low they were.  This year, the skills are at about the same level, but with double periods, I feel as though I have enough time to show them the patience they need and deserve.

We spent much of the time today doing practice problems with absolute values although we only did about 10 total.  After several conversations about formatting with other teachers, I decided that it was worth the time to slow down and emphasize the importance of having them write their steps on different lines.  I willingly and happily answered whatever questions they had, even if I felt they were a little low for the class, or if they could have come up with the answer if they had taken a few minutes to think about it.

Even typing that sentence, I realize I should have, instead, asked directed questions to get them to answer it themselves.  I'll keep it in mind for next week.

After that, we sliced pizza.

If I have a pizza with no cuts, how many slices do I have?  If I cut it once, how many slices?  If I cut it twice, how many can I have at most?  What about three times?

After we drew these on the board, I asked them to work in groups and figure out how many slices could be formed out of 4 cuts, if you don't care about the size of the slice.  What about 5 cuts?

It went well and they seemed to get into it, but I think it could be improved by maybe using a circular geoboard or some other physical manipulative.  If I had planned it further in advance...

In any event, I'm looking forward to a nice relaxing weekend, other than the 12 miles I have to run.  I'll be setting up the Mathalicious lessons that I plan to do next week.  I'm very excited about them, but I've been putting it off because it's a little intimidating.  I need to just jump in with both feet.

Also, I got AppleTV installed in my class, so now I need to come up with fun ways to use it.  I plan to have the kids play Wuzzit Trouble sometime soon.

I'm beat.  Time to go home, change into shorts, make some pizza and hugs my kids.  I hope they don't pee on me.

Day 8: An Unstable Chair

We started the guided notes today in geometry.  The students had an odd mixture of disappointment and relief.  I think the relief came from the fact that we were going to a format with which they are familiar.  Students have been conditioned to expect lecture and note-taking so when things go differently, they are often confused.

Students sitting in lecture remind me of people returning to family who are not nice.  There is discomfort and awkwardness, but there is a level of security because of how familiar the situation is.  You KNOW that your aunt Ethel is going to ask when you're finally going to find someone and settle down.  You KNOW that your uncle Jeff is going to be disappointed that you didn't bring home any hot friends.  Students know that they are expected to sit quietly, listen to the lecture and write down ...whatever.

I hope that by the end of this year, my students will have forgotten these expectations for lecture out of disuse.  I want the "sit and take notes" muscle to atrophy.

So, even with the guided notes packet, I tried to keep the conversation lively and make it an actual conversation.  I've been thinking very much about the idea that I should never say anything that a student can say.  I ask questions that direct students in specific ways and I'm not satisfied with answers until I get the one I want, or one like it.

We talked about points, line and planes and I had students go to the board to answer the questions in their note packets.  I ended with a critical thinking question:

What makes a chair wobble?
I happen to have a chair in my room that wobbles, so I put it on the desk and rocked it back and forth.
I received a ton of answers that were true, but weren't what I was going for.  "The legs are uneven." "The screws came out." "It's unstable!"

"So the legs are uneven.  Why does that make it wobble?"
"One leg is shorter."
"Yes, but why does that make it wobble?  Why does it matter than one leg is shorter, or longer?"

Finally, I got what I wanted.  "It means the feet of the chair are on different planes."

We talked a bit about this too and I asked about the two legs that don't leave the floor when I rock it.  One kid actually said "they are in both planes!"

Me: "Are there other points that are in both planes?"
S: "Not that we can see."
Me: "What do you mean?"
S: "Well, all of the points between those two would be also, right?"
Me: "What do you mean 'all the points'?"
S: "Like, if we drew a line between those two points, everything on that line."

So I ran a string between the two legs, as he suggested.
Me: "Like this?"
S: "Yeah! Everything on that line would be in both planes."
Me: "So what we can tell about where two planes meet?"
Class: "It's forms a line!!"

I was VERY pleased.

I also had my first real discipline issue in that class.  For the past 7 days, one of the students has been doing almost nothing.  He comes in, puts his head down, refuses to do most of the tasks and refuses to engage with me when I talk to him.  He sat through the whole class with his arms pulled into his sleeves.  Today, after asking him multiple times to take out a pencil and get to work and he refusing to do so, I took him into the hallway.  I explained to him that this was a high level academic class and his behavior was not acceptable.  He stared at me blankly.  I asked him what I could do to help him get back on track, that I wanted him to be successful and that I would help him however I could.  He stared at me blankly.

So I called his dad, who was very supportive.  I explained that I wasn't trying to get him punished, but wanted to make sure we were all on the same page with the expectations of behavior and academics.  I think it went well, but we'll have to wait to see if it produces any results.

Pre-algebra is falling back into the habits that I sadly expect of those students.  Today, about 70% did their homework, which is much better than last year, but not as good as last week (85%.)  I quickly did my lesson, which was dull, then had students work independently or in pairs for about 15 minutes and then put their answers up on the board.  They then got time to work on their homework, almost all of whom finished and got their answers checked.

This is really a great group of kids.  I often struggle to determine what is age-appropriate behavior.  How much of the acting out is because they don't know how to behave, or because they are 13.  In high school, I was able to treat them like adults, but here, they are on the cusp.  Some are over it and some won't be for a few years.  It's hard to be fair and treat everyone justly when they are at such different places.

Perhaps that will be the topic of next week's #MSMathChat.

Warning: The follow content is about content! Read at your own risk!

I've been thinking about procedures.  A few comments from Kate Nowak on Twitter today got me thinking about why we ask kids to do things in a certain way.  Sometimes it's because it's the only way to do it correctly, like Order of Operations, but sometimes it's because it's easier for us to give them steps and see if they can follow them.  But by the time they get to middle or high school, is there still educational value in that?  If they haven't learned it by then, maybe there's something else going on.

Also, I want to draw a distinction between not wanting to follow directions and not being able to.

I think there is a third reason for having do something procedurally.  This came up today when I asked my students to follow the steps I gave, not because I care how they solve a problem, but because I've been teaching long enough that I know where the common mistakes are and the steps help to avoid those.

I'm not opposed to making mistakes and there is great value in learning from them, but when the notation the students are using leads directly to the confusion, I think it's important to at least provide them with a road map until they can find their own path.  This is the example that has been coming up recently.

Evaluate 3b + c for b = 1, c = 4  (Number 1 in the picture)

Clearly the student knew what he was doing and got the right answer.  My concern is the string of equal signs.  As the problem gets more complicated, this type of notation will start to trip him up, and it did 5 problems later.  I don't want to impose my own procedural preferences on them, but I also don't want them forming habits that will hurt them later.

This is a very fine line...

Day 7: Success and Not So Much

The geometry warm-up today was the first real foray that we've done into points, lines and planes, which I should have started last week.  As usual, I got a little off-topic while talking about the concepts of dimension and how the students can't conceive of a creature that lives in 4 dimensions because we only exist in 3, etc.

The students did very well and were eager for more discussion, but I had to reign them (myself) back in so that I could get to our activity, which I LOVED!

Students were broken into pairs and asked the following:

How many distinct lines can be drawn using:

1 Point                                 2 Points

3 Points                               4 Points

5 Points                              6 Points

12 Points

I didn't give them any other directions and when they were confused, I asked directed questions.  I walked around the room, watching the strategies that different groups came up with.  Several pairs realized early on that there must be a pattern and tried to find that, instead of trying to draw lines between 12 dots.  I was even lucky enough to have a few pairs think back to what we had done previously and utilize that.

**sniff sniff**  I'm so proud of them!
There was a ton of great thinking going on.  Even the students who came up with wrong answers managed to develop theories on how to find further numbers in the pattern without drawing.

At the conclusion of the activity, I had students come up the board and draw what they had done.

Me: "For 3 dots, why did you put them in a triangle pattern instead of in a row?"
S: "When I put them in a row, some of the lines overlapped and it was hard to count them."
Me: "Did you find a way to draw the larger ones, like 5 and 6 points, so as to avoid overlap?"
S: "We made them around the outside of a shape, instead of a box with some points inside, like we had at first."

I emphasized to them that I was looking for them to be able to not only find the answer, but figure out how to do that as well.  Outside of school, they won't always be given step-by-step directions on how to complete a task.

In pre-algebra, I stole an order of operations activity from ray_emily with some modifications from the amazing Julie Reulbach.  Students were given laminated cards with operations and parentheses on them as well as one that read:

18     2     4     3

Students were then given a number, such as 8, and asked to arrange the operations so the resulting answer was 8.  (18/2-4+3).

It was a great activity, but not long enough.  The groups worked on it well, but I vastly overestimated the attention span.  The students who finished quickly were given more difficult numbers to reach and dove right in, but when they couldn't find the answer in 20 seconds, like they did with the first ones, they gave up.  At some point, I realized that the constant redirection to task was counterproductive.

I didn't give them a time limit because I didn't want to intimidate the students who were taking longer, but I can see that was a mistake.  Next time, there will be a time limit and I will ask someone to put it on the board and someone else from that group to explain the work.

Interestingly, the girls (who took longer for each problem) persisted while the boys (who finished quickly) pretended to work, but were talking about basketball.

In the second class, it went MUCH better.  I walked around the room and each time a group solved a problem, I gave them all stickers.  This spurred the other groups to find the answer as well.  "I WANT A STICKER!!!" "Then solve the problem."  "C'mon, y'all! Let's do this!"

Never underestimate the power of bribery, even with silly little star stickers.

When I do this again, I will add a sheet for them to record their work with the 18, 2, 4, 3 already written so they add the operations, with enough room for them to justify their answers.  I will also do a better job of separating problems into ones of easy, medium and hard to make sure that students do problems of increasing difficulty.  In theory, they will get the easy ones quickly and the difficulty will slowly build so they don't get discouraged.

Come to think of it, that's a good philosophy with ANY activity I do.


My guided note packets finally arrived for geometry.  One of my students saw them and the following conversation ensued:

S: "Does this mean we have to do real geometry now?"
Me: "Dear, we've been doing real geometry this whole time."
S: "I know, but it hasn't felt like it.  It's been fun and interesting."

This makes me very happy and very sad at the same time.

Day 6: Unprepared

I have always been a "wingin' it" type of teacher.  One of my huge strengths as a teacher has always been my ability to adapt my lessons on the fly based on the needs of my students.  Apparently, the fancy name for this "formative assessment" but I call it "teaching."

It is also one of my greatest flaws.  I rely on it too much.  Over the last few years, there have been many days where I've gotten up, come into work, sat down at my desk and only then started thinking about what I was going to do for the day.  I say "too many" because I feel like this is something to be ashamed of, but in reality, I can't think of a time when my lack of preparation has caused me any major problems.  It may have lead to more boring, less rich lessons, but I have always been able to get by.

This is the first year that I can recall actually stressing about prepping for my classes.  I spent some of the weekend thinking about what I wanted to do, but apparently not enough.  My lesson plans are not what they should be because I've never used my lesson plans before, except as a vague guide of what topics I wanted to cover.

In graduate school, we were required to write absurdly long and detailed plans that were supposed to read like a script.  They were to include what questions we wanted ask, as well as anticipate student questions and reactions.  I think this is an excellent idea in theory.  The problem for me was that writing a plan for a 45 minute class took me 2 hours.  It was too much and I found myself going WAY off-script as "teachable moments" happened.

As a result of this practice, as well as my own laziness and that I've never seen the importance of the various items in a required plan, I've fallen out of the habit of writing effective lesson plans.  That's assuming, of course, that I knew how to write them at all.

On top of that, I discovered last year that the more time I spent planning a lesson that I thought was killer, the less receptive the students were to it.  I think that could be because my expectations were higher, knowing how much effort I put into the planning.

All of this is to say that I, apparently, don't know how to effectively plan for my classes.  It has never been a problem, but now it is.

I am feeling the pressure of planning rich, deep, meaningful lesson coming from three different sources.

1)  My Students
I have been granted stewardship of the 8th grade geometry classes.  This is how I see my assignment this year.  I haven't been given this group of advanced, knowledge-hungry youth.  I am merely their custodian for the year.  I must do everything in my power to make sure that I don't squander that trust.  I can't be the teacher who kills their desire to learn by not providing them with the environment in which they can thrive.

2) My Colleagues
I don't mean the people in the building in which I teach, although, I do frequently compare myself to them for both positive and negative traits. I mean the educators I have met through Twitter and various blogging sites.  I have become highly active on Twitter in the last few months, using the medium exclusively for professional development purposes.  The resources and people that can be found there are invaluable and have changed the way I look at my profession.  This blog itself is a direct result of my interactions with them.  I feel as though this group will be there to help me, but also hold me accountable when I fall down.

3) Myself
The other two groups are exerting no pressure at all.  I'm just transferring all of my internal pressure to them in an effort not be filled with self-loathing.  I want to be good at my job.  I want to love my job again.  For the first time in a very long time, I feel like I can do both of these, but I'm clearly going to have to make some changes.

In preparing for Geometry today, I almost completely forgot to plan for my pre-algebra class.  They have workbooks with all of the required materials and word problems and grunt work, but I HAAAAAATE resorting to that.  It's what they expect and I want to shatter their expectations for math class.  I know I can do better.  I don't know how.

Preparing for something beyond the next day or two seems like such a daunting task.  I need to find a way to break it into smaller pieces that are more manageable.


With that said, today's geometry class went well, but felt very haphazard to me.  I didn't do a good job of connecting the various tasks in a meaningful way.  Part of the reason is that I changed my initial talk upon hearing the news that a London skyscraper is apparently a giant parabolic death ray!

Seriously! How could I NOT talk about that?

I gave them an activity to start them thinking about equi-distance and they did very well with it.  As with most of my ideas now, I got it from someone on the internet.  I need to develop it a little more, but I'm not sure how.  Must consult...

After that, we began working on a logic puzzle.  One of my goals this year is to improve the problem solving and critical thinking skills of my students.

But it still feels like I'm BSing...

I'm ashamed to say that most of pre-algebra was filler today (or felt that way).  I gave them some problems for homework over the long weekend and we went over them slowly today, working through whatever problems they wanted me to cover.  I need to send more kids to the board, putting the onus back on them and getting them to justify their answers and questions in a more coherent way.  This was almost the entire class.  They clearly needed the practice and clarification, but as in the norm with students, when I wasn't answering their specific question, they tuned out.  I gave them a sudoku at the end to try to trick them (and me) into thinking it was an interesting period.

My kids in 8th period were much more engaged in the same tasks.  I spent more time circulating through the room, redirecting students back on task and offering guiding suggestions.  I frequently picked a random problem off of the page that they had completed and asked them to walk me through it.  In these cases, kids picked up on their own mistakes and ushered me away so they could fix them.  A student who has spent the last 4 classes with his head down worked his butt off today, grinding away at problem after problem.  I made a special point to tell him how proud I was of his work.

I find it fascinating how an activity can work so well with one group of students and go over so poorly with another.  Positive reinforcement has never really been my M.O. but I could get used to it.

I REALLY need to find an interesting way to practice the order of operations.

I'm beginning to worry about how I'm going to hit the required content and still do interesting things.  I'm planning to start two lessons from Mathalicious next week.  The geometry classes will be exploring the non-linear nature of pizza pricing while the pre-algebra classes will be discussing burning off calories from an extra value meal.


If I want to keep these kids with me, I need to teach myself a better way to plan and prepare.  This isn't working for me this year.


I don't feel like I've adequately communicated my feelings in this post, but if I go back and read it again, I'll end up deleting the whole thing.

Weekend Thought: Finding Purpose

We put a ton of time and energy, especially in mathematics education, into trying to determine what skills and concepts we need to teach.

Common Core has helped with this by laying out the skills that students should have mastered by the end of each grade, but I feel it's missing something.  While (most) school districts now (somewhere) agree on what their students need to know, I never hear the discussion of why framed in a way that makes sense to me.

With that in mind, I propose that more so than Common Core Standards, or State-level graduation tests (on which Pennsylvania is working) we, as teachers, parents and life-long learners encourage something else.

I propose that all districts be required to publicly answer a specific question:

What is the purpose of education?

After that question, new policies and educational mandates would be required to answer "Does this goal/fad/mandate/policy align with the what we have stated  as the purpose of education?"


I ask this question because I honestly don't know.  Every time I think about it, I come up with a different answer, not all of which are mutually exclusive.  Here are some, a few of which I am not proud:

• To make students well-rounded citizens
• To prepare students for the workforce
• To prepare students to be leaders in their communities
• To provide students with the skills that the Department of Education sees are vital
• To help students learn to function independently as human beings
• To help students discover their purpose in life by exposing them to as many ideas as possible
• To protect students from the harsh realities of life for a little longer
• To provide a babysitting service until students turn 18

The reason I bring this up is that I often think that some policies that are initiated by administrators and required of teachers serve different purposes, which are often contradicting.

"I'm afraid I can't do that, Principal Jones."

Those of you who have read 2001 know that HAL wasn't murderous.  He was simply given contradicting orders and that lead to complete disaster.  This concept was sort of glossed over in the movie and instead was replaced with an acid-trip beyond the edge of the universe, where, apparently, you are an old man and a baby at the same time.  I think part of my disillusionment with public education has been exactly this problem (without the murder, of course).  All too often in my career, I have been given mandates for things that I see as counterproductive to the educational environment in my classroom.

So, because I don't have enough things going on this year, I will add one more.  I hope that my readers can help me with this.

What is the purpose of education?

Follow-up: Is it the role of each teacher to define it for themselves, or the role of the district to define it as the guiding principles of that district?

Please help. (Unless you are Stanley Kubrick)

Edit: To clarify, I mean K-12 education.  Not the abstract concept of education.