Two of Michigan's 7th grade Grade Level Content Expectations for math are:

A.PA. 07.09 Recognize inversely proportional relationships in contextual situations; know that quantities are inversely proportional if their product is constant.

A.RP.07.10 Know that the graph of y=k/x is not aline; know its shape; and know that it crosses neither the x nor the y-axis.

OK. I can teach that. We look at the length and widths of rectangles with fixed areas in the context of building a garden with a predetermined amount of mulch. We do a group activity where students are given a set amount of money to earn performing a service. For each of these, they create their tables and graphs, write their equations, and we analyze the situations in context of the problem.

But somehow, there always seems to be a disconnect, something missing, from the lessons. My students, at least half of them, do not understand the concepts of factors and multiples, and do not know their multiplication facts with automaticity. These are concepts they should have mastered in late elementary school, but still lack at the end of 7th grade.

How do we find the missing piece? Where is it? How do we get all the pieces of mathematics to fit together when students are simply moving on up the ladder of school without first mastering the concepts at each grade level. How do we get all these pieces together, organized, fitting together perfectly before they advance to the new math curriculum that expects all students to master through Algebra II?

Our school, along with others across the state, sees a train wreck when the bulk of the student population hits Algebra I as freshmen (The more math ready students took Algebra I as 8th graders). Suddenly, all those years of being sent along the continuum of math classes, without being ready for advancement, catches up with them. Here starts the catch-up effort, finally.

Wouldn't it make more sense to catch them earlier, provide some intense remediation when they first start to struggle? Not only would we provide students the opportunity to develop a strong numerical foundation, perhaps some of the math phobias we see could be overcome.

But then again, over 80% of this years 7th graders scored proficient on the almighty MEAP test. The state test seems to think they are doing OK. Oh, wait.. it is because the cut score is set so low that students with less than a 40% score are labeled as proficient. When the state says less than 40% is good enough, who am I to question? Maybe I need to rethink my grading scale. If we count 40% as proficient, that must equate to at least a B, so let's call 50% an A! From now on, scores of 40% and above will get A's, 30-40% get B's, 20-30% C's. Report cards will be amazing! Just think of all the kids on honor roll!

OOOOOOppppppsssss....... that won't solve anything will it? They will still get to Algebra I unprepared for the material, the train wreck will still happen, and kids will be struggling to graduate in 4 years.

Where do we implement change? How do we implement change?

There is much talk of how schools need to change from the sit and get method of teaching, to encouraging students to think for themselves. What a wonderful concept, in theory.

Too often, students come with the attitude of tell what I need to know, tell me how you want me to give it back to you, and I will reproduce your thoughts on paper, and BINGO, I win my 'A'. They are programmed to spew back facts and ideas fed to them without actually creating or investigating on their own.

When given a problem to solve, students stare blankly at the paper, afraid or unable to attempt to think for themselves. They want THE ANSWER. They don't like the thought that there might not be a right answer.

How have we programmed them this way or did they come to school with that mentality?

And now... how do we reprogram them to want to think for themselves?

I think one of the best ways to improve education and promote independent thinking is to do away with our current system of grading students. Students and parents are motivated by the almighty 'A' with little regard for what the 'A' actually means in terms of student achievement and learning progress. Other students seem so intimidated by grades they almost refuse to try, so certain they will never achieve that illusive 'A' they simply quit before they try, like taking the 0 for doing nothing is better than accepting a 'C' for working hard but not making the ultimate 'A' mark.

Teachers often feel pressure to give high grades so parents aren't complaining. Students also put their fair share of grade pressure on teachers. Participation in sports is often dependent on grades. But each teacher 'grades' their own way. Some give extra credit to boost scores. Some weight homework heavily, others rely on summative assessments for their primary source of reporting grades. Some give participation grades; others base grades solely on achieving mastery of the content. Some teacher allow retakes; others do not. Some average retake scores with the original; some let the higher score stand. Grades often mean nothing comparatively from course to course, teacher to teacher, school to school.

Without grades, school could actually be about learning, experiencing, and growing, instead of the letter that gets published on the report card. Students would not be intimidated by the threat of failure or not measuring up. Teachers could design lessons to spark enthusiasm and encourage risk taking instead of ones that are easily assessed on a 4 point scale. Students would move onto more difficult material when they were ready not when they sat their 9 months in a class, earned their percentage and were rotely moved along the conveyor belt of school. Learning would be fluid and flexible.

Would it work? Who knows.... but they way we are doing things now certainly isn't meeting the needs of all learners, or even preparing a vast percentage of students for college or life beyond high school. Perhaps it is time for something new!

With more and more cuts from the state, schools are being forced to make difficult choices in what/who to keep and what to let go from their budgets. It has gone way beyond cutting spending on classroom supplies and field trips, to districts eliminating transportation and cutting programs. How do you decide what to keep and what to give up? Is music more important than physical education? Is it more important to offer after-school tutoring or keep the library open?

These are decisions that should never have to be made in the first place. The wars in Iraq & Afghanistan have cost over $985,000,000,000 so far. The US alone has sent relief in the amount of $100 million to Haiti. The state of California spends over a billion dollars a year in medical care for illegal immigrants. Taxpayers foot the bill of smokers to the tune of $10 billion a year.

But schools are being forced to decide whether to put 35 kindergartners in a room or eliminate janitorial service. Our priorities in this country are out of whack. Until the general public realizes that without free quality public education, we as a society are doomed, and as a group step up and fund these institutions adequately, our country is going to become one of a larger divide between the have's and have not's.

We've forgotten that our children are out greatest resource. We've forgotten that our country was built on the principles of equal opportunities for all.

Just throwing more money at education is NOT the answer. But until schools are funded adequately, things will continue to deteriorate. Fewer college graduates will choose education as a career option, seeking more lucrative fields of employment. More people who can afford private options will seek those, further compromising the integrity of the public system. The downward spiral will become a self-fullfilling prophecy of failure and inadequacy.

What is the answer? I don't know for sure. But I have some ideas:

• Find ways to fix the system in place now for starters.


• Get rid of teachers and adminstrators who do not do their job.


• Eliminate wasteful practices and positions.


• Consolidate business operations.


• Remember the purpose of the school is to provide a quality educational experience for the students, not be an employment agency for adults.


• Work to support the whole child, providing services such as health care, counseling, and guidance.


• Provide support for parents, through parenting classes, adult education and opportunities to be a part of their child's education.


• Make sure students have and use the most current technology needed to make them competitive when they go to college or in the workforce, but stop spending on the latest and greatest tech toys, just to have them.


• Encourage teachers to learn and grow with and from each other instead of paying top dollars for 'experts' to come give 'sit and get' lectures. Provide time for embedded professional development where your best and brightest share and lead others.

And perhaps the most important place we can make improvements: change the paradigm in our society to value education. Expect excellence in students, teachers and parents. Demand excellence in students, teachers and parents. Let's work together to make systematic changes before it becomes too late.

Slope, y-intercept, slope, y-intercept. Over and over and over again until I think I must repeat those words in my sleep. Maybe THAT is the key to getting my kids to GET IT? They need math 3 times a day, every day, until those words dance in their dreams!

We learned slope early on, when we studied rate of change. Some got it, some didn't, despite spending about 2 weeks on it. But move on we must, and did.

Now that the time of the year for linear functions is upon us, we are revisiting slope, and now y-intercept, and the ever popular y=mx+b form. We've looked at the functions themselves, setting up function charts, solving them, learning about 'solutions'. We've picked out the slope and y-intercept from the equation itself. We've counted boxes on line after line, rise over run, rise over run. Go up, go over... which is x, and which is y. We've solved for slope from a table, using 2 points, calculating the difference in their y values, over the change in their x-values.

We've looked at multiple problems applying slope and y-intercept to real life situations from pledges for a walkathon, to different rates of phone companies, to today's problem (MY favorite) comparing buying yearbooks from 2 companies: Gorgeous George's :) and Outrageous Rathje's (my language arts sidekick). We've made BIG graphs on supersized graph paper. We've worked in small groups. We've worked in partners. We've worked in large groups. We've used the wireless chalkboard. We've used the document camera. We've done them alone. We've done them together.

and still....... there are those among them who look as if I am speaking Greek or Vulcan when I ask them to find the slope of a line drawn on the board, or suggest they start by putting a point on the given y-intercept.

and onward we move... towards inverse relationships, those dreaded y=k/x situations.

and I focus on the positives:
RL who answered every single question I asked in class today, even when I tried to shhhusssshhh him so someone else could have a chance. RL who is a rough character, from a rough family, but bless his sweet little algebraically blessed mind, he got every answer correct but one! He was THE one everyone wanted for a partner when it came time for partner work. He KNEW he knew how to do it all and so did everyone else. Then, I had to laugh when his partner couldn't read what RL had written because spaces between words, or even letters, is not a skill evident in his hen-scratched printed words. But all three of us knew the words written were right on target.

CH who is this tiny little guy who looks like he should be in maybe 2nd grade, and always struggles with everything we do in math. He yells out at someone up count from their y-intercept up for the slope, "NO!! IT'S A NEGATIVE SLOPE. GO BACKWARDS!! Make your line go DOWN!"

LF, the new girl with the jetblack spikey hair they call porcupine girl, who didn't want to go to the document camera, swearing she couldn't do it. But all of them rallied and encouraged her, walking her through, step by step, until her line was sketched perfectly, as she walked back to her seat with a huge smile of satisfaction across her face, beneath the jetblack eyeliner rimmed eyes sparkling her pride.

and I know..... tonight I will hear the same words over and over again, dancing like sugarplums in my head, rise over run, slope and y-intercept, rise over run, slope and y-intercept.

I wonder about the futures of some of my students, this year, more than ever. Some of them are destined for greatness; I can see them making a positive difference in the world someday, inventing, creating, imagining, teaching, leading. I see them reaching beyond the ordinary, finding cures, solutions, and innovations. These are the students with spark and imagination, curiousity and determination. They aren't necessarily my straight A kids, often not even the best behaved in my classes. But inside their minds, their personalities, and their willpower, I see the drive for success.

I worry about the others. The ones who sit, with that blank stare of disinterest, day after day, assignment after assignment, opportunity after opportunity. They can't be drawn into the conversation; they won't attempt anything challenging. They can't even be bothered to show up with a pencil, or their book. No doubt, some of these students will find their way, make their mark on the world eventually. But what about the others.... are they truly predestined for emptiness their entire lives?

It makes me wonder about intervention programs, early on. Can we really spot, at 7th grade, the students who will be 'failures' in life? If so, even with partial accuracy, would monies be better spent on intervening at this level than waiting for adulthood when interventions consist of incarceration, welfare handouts, or institutionalizing them?

What would interventions look like? Would they change the home environment? Would they change to school to look differently to fit their unique needs? What would that look like?

Is money better spent early on to find ways to create productive citizens? Would we rather spend money on education or prisons? Is the solution really that simple?

Stacking cups and stacking cups.... how high do they go??

The learning process of my students always amazes me when we tackle a problem. The intent of the lesson is often the least of what they learn in the doing of the assignment. Take today's Stacking Cup problem had my students measuring 5 different types of cups, creating a table of their data, then graphing the data, all ultimately to recommend the size packaging needed to ship these various cups. The intent of the lesson is to examine a constant rate of change, consider the meaning of a y-intercept, and how those concepts apply to a real-life situation.

Oh, but that was the least of the learning taking place!

First off, creating a table with so much information was difficult for students to organize. They want a template, a how-to, but I refused to give them one, so they struggle within their groups, trying to figure a logical way to organize.

Then the measuring itself. Final measurements needed to be in millimeters, but of course, the rulers measure in inches or centimeters. Seemingly an easy conversion becomes torture for some groups. Then the actual measuring of the cup heights. The ruler edge is not the zero mark. Do you lean the ruler against the cup? That isn't really the height, is it? Even once they start recording measurements, the inconsistencies cause problems. Why aren't the measurements increasing consistently?

Then, the creating of the graph. Whoa.... you would think some of them are building the Eiffel Tower! Backwards and upside down, and oh, can I borrow whiteout... and what do you mean not a bar graph?

It is fun to watch the process of learning, and even more fun to listen as they work among themselves trying to convince their partners of their way of thinking. I love problem based learning. I love the wheels turning in their heads, the smoke pouring from their ears, and the smell of brains wrinkling!

One guy did proclaim it boring, and even as I poohpoohed him, I began to fear for his safety in the hallway, as his classmates haranged him for his negativity :)

We finish tomorrow, sharing our graphs and talking about the actual slopes, y-intercepts and reasons for our linear relationships.

A good day in 7th grade :)

I did something today I am ashamed of, the very thing I always hated when my teachers did to my classes. I punished them all for the evils of some. Granted, it was a majority.... but I shouldn't have done it.

A couple of weeks ago, as part of a grant program, I received a new wireless chalkboard. The kids have been all geeked up about using it. As luck would have it, we are doing some graphing things that are well suited to using it. I promised today, the first day after spring break, they could finally get their hands on it to play.

Our Math Starter today was an introduction: Sketch 2 graphs, one showing your height from birth until now, another showing your hair length from birth until now. Pretty simple, basic and easily attainable by all students. I even gave a quick review of sketching a graph.

First hour was a riot, as they learned to use the wireless chalkboard, playing with the tools, laughing at each other's incompetence, discussing our graphs, and learning together the ins and outs of both the tech tool and the process of graphs. It was a wonderful conversation about their graphs, right, wrong, it didn't matter. We shared and laughed and learned.

Then, sixth hour... THAT hour of my day. Knowing this group struggles more with almost everything we do, I gave even more specific instructions on sketching graphs trying to get them started. Then, time to use the chalkboard to draw them, after they had each had time to draw their indivdual graphs in their notebooks. The first student who volunteered had no graph on paper and was unable to draw it. As I tried to find someone with the assignment done, this short 60 second assignment, anyone.... someone who could transfer their drawing to the wireless chalkboard, I could find no one with it done. After I had scanned the first half of the class and realized no one had even bothered to TRY, I quickly got annoyed. Here I have this cool, fun, interactive plan for the day, something THIS GROUP will enjoy, something that will engage them, something TECHIE to grab them, and they can't be bothered to sketch 2 little tiny graphs on paper first.

I took back the chalkboard and turned it off, telling them I didn't have time to share that tool with them. It takes SOOOO much longer with it, honestly, to draw graphs, I wonder about the true benefits of it anyway. But it is fun, engaging and lends itself to mistakes which makes their real mistakes in their graphs less threatening.

We continued the lesson,, simply drawing the graphs on the whiteboard, the usual boring way.

*SIGH* I wish I had more patience with them. I wish I could somehow let it go when they refuse to work. But it is overwhelming when no matter the assignment, this group can't be bothered to complete it. Short or long, fun or boring, the same few complete it. The same ones every day tune me out, no matter what I do. I can tell funny stories or dorky jokes; I can tease them; I can punish them; I can yell; I can whisper. Nothing changes anything. They are off on some other planet. I see easily how they landed in the 'low' group of our tracked math program.

Punishing them all is not the answer. I knew that, I know that... I am just at wit's end with them.

But tomorrow is another day. We are doing a lab, stacking cups, measuring them, trying to determine the packaging requirements to package them to ship them out. Will THAT hook them? I have no idea... but again, I will try.... wish me luck!

Thursday of spring break finds me with a long to-do list not done, including many school related items. I had this plan to be all planned and copied for most of the rest of the school year, but my Tuesday I set aside for schoolwork turned into a COPIER nightmare. I stopped counting on jam #62. I swear that machine has some personal vendetta against me!

We start our big graphing unit after break, taking what we know about coordinate graphs, writing and solving equations, slope and functions, and combining it all into linear equations, graphing calculators, and other fun stuff. It is always a fun unit for me. I love the logic of graphing, using that graph to predict and solve problems. I also love sharing the fun of graphing calculators with my students.

For most kids, it is easy stuff, fun stuff, stuff that falls into place. However, inevitably, I will have a few who still cannnot grasp the (x,y) coordinate process for some reason. For them, this is like torture because their graphs are always wrong, unpredictable, and make no sense. For other students, they will miss a day here and there, just enough to make what we are doing impossible to follow. Try as I will, there is simply no way to make up for the days missed with them, and they are hopelessly lost, with a Swiss cheese understanding of the unit.

But the school year is winding down, and I am becoming more reflective of what to do differently next year. I have some ideas for restructuring my math classes, especially my 'low' class. As those plans start to form in my mind, the reality strikes me, what will I be teaching next year. With declining enrollment, our looming budget crisis, and retirees in various positions, and other positions being cut, I wonder where the dust will settle and find me in the fall. I have been in this particular room and position, with a little variation, for a long time now. I love what I do and where I am, and am reluctant to leave. **sigh**