Line Week! Slope, slope, slope....

Slope & lines, lines & slope.  It is  truly one of the most important concepts in Algebra - if truly understood many things are easy, if simply memorized it leads to many forgetful problems.  So with that thought in mind I am setting up "Line Week" -- like "Shark Week" - except cooler and many more attacks resulting in gruesome death (students love the joke...).

So I made the joke(s) last week, and now I sit here Sunday morning trying to create the lesson that really results in students understanding of slope, intercepts, etc.  I teach 8-12th grade - so these students have seen (and forgotten) lines, they have been using x,y tables to plot points and create lines -- but with no real world understanding of slope etc.  {You may think what kind of person promises "line week" without a plan...  - well I do!  Lines are important and it is time for lines!}

I have spent the last 2 hours combing the internet for something (and if you pictured Mel Brooke's Space Balls combing the desert you're my kind of person) and have really not found anything amazing.  I have founded some fun songs - that I may use once they understand.  And some good worksheets, I may use those once they can do at home alone (in a month) for practice.  But nothing that really ties Rise over Run to y =mx + b....

My plan is to use a stair step example that I read about on I Want to Teach Forever, but then I want to tie slope and the slope-intercept equation.  It is units that will do it!  Perhaps it will be dollars per day for slope, thus using x as days - mx will become dollars...  b is dollars initial and thus with some practice the two will make sense.  That is the tie, seeing that mx and b are the same units (thus like terms).  Then zero slope is no money, and undefined slope is winning the lottery.... or being robbed.....

Hopefully there will be another post of something amazing, or at least acceptable...  Cause from combing the internet there seems to be very little that teaches the concept - just simply the procedure. 

Expectations...

Students meet expectations, period.  They want to know the minimum line, they will test you for it, but once they know where it is most will work to be just above it.  They may not want to do math, but they will -- they do just the minimum they need.  (Very few won't do...  those that can't/don't take some other pushing.)

The key is to hold high expectations and not to allow less than quality work and understanding to receive a passing grade.  Don't allow soft projects to replace mastery.  Don't let the nice student by, that is a disservice to their future - better to be the hard-ass today so the students succeed tomorrow -- in the real world, where multiple chances are rare.

But don't confuse school and the real world -- while multiple  chances are not the norm in the world, they should be in school.  It is the subtle difference between school and jobs.  School is the student's job but there is no immediate paycheck, or product/service to produce, I don't go out of business because a student did not do their work today or did not learn today.  In the world nearly every day counts, at school that is not the reality.  Just like I cannot fire a student, I could fire people in the world as a boss - but that is not a school's purpose.

A school's purpose is to educate a student.  Not to provide just the opportunity for the student to learn but to stand on their head and make sure that minimum standards are achieved.  It means multiple opportunities - it means follow thru.  Telling a student they don't have to do homework is not the solution, they need the skill --- yes in a workplace it would be too late, but school is not a workplace!  The school does not absolutely require every student to believe in the mission to be successful - most workplaces require employees working towards the business's mission.

I believe teachers have to have high expectations.  Our job is to then push, encourage and even beg our students to work hard to get over the line.  And I can hear some talking about teaching responsibility (or this does not teach it...) - but school does not teach responsibility!  Playing school does not make you a good employee, boss or leader.  That old phrase A students work for C Students comes to mind; but the key is that we make all our students have those basic math and problem solving skills.

Math Meet - a chance for all!

Today was the 5th annual Six Rivers Conference Math Meet!  It was exactly 5-3/4 years ago that I acted on the thought that our small school and the others in our athletic conference really needed an academic math event.  It has gone from me and other teachers begging students to being part to being an expected event!

It also gives a chance for students to do math in a fun and challenging environment.  But there is one caveat, the more, the merry is our motto.  Fill up a team then go ahead and throw a few more students on the bus, with proper expectations everyone can be part.  Juda had 56 students in the meet today -- out of a school of 92 students.  Each student had a reasonable expectation, which really centered with them just doing their best.

To those who say a student who can only get one correct should not be part - I say "posh."  It is an event, a problem solving day, a growth day - a day where math is really neat, really interesting.  And when done in the proper mood with students it becomes an event that your class room academics can build from and be better.  Math events should not only be gifted and talented events, though those students might excel, it should be event for anyone who can work the problems and learn from the experience.
 

And at least in this little corner of the world we have done it this way and have had success.

Results....

Starting 4 years ago I divided my class time into 3 distinct parts.  There was skill time, concept time and project time.  Concepts and projects are the most important so we spend about 70-80% on those during the week.  The skills which is simply quiz time take about 20% of the time; it is just previous mastered material put into a quiz without clustering or grouping.  Sometimes a few problems that are the same type are together but usually it is just one maybe two.  It makes the students' sharp with their skills and keeps the topics current.  It is about  50-55% of a student's grade in my course in High School - assuring material is mastered and stays mastered.  If you want to see the quizzes, check out the google doc.

It is this graph shown in the blog that makes me feel like this works.  By committing that previous skills are important, and making students continually accountable in an assessment, they retain the skills and concepts better.  And by maintaining some level of practice my students are more ready for new material and at the end of high school for post-secondary math.  These quizzes are graded as right or wrong, no partial credit (passing is 70% and up).    The idea is simply that what you use you do not lose....

Testing, calculators and numeracy...

Had an interesting question raised on one of the many communities I pay attention to, "Along with the practices calling for use of mathematical tools, do you think calculators should be allowed on the state testing?"

I feel we, as math teachers, must not get sucked into one answer about calculators and their use.  We must stop the pendulum between all or nothing, reform and traditional, there is a middle position!  That means some amount of non-calculator numeracy and the ability to use tools. (And if you think a TI-84 or 92 is a real world tool, you need to hang out in a production facility of some sort -- it is spreadsheets, databases, etc....)

I believe that numeracy is learned, any math instructor of any amount of time has seen something like this -- a student take 3 times 6  on their calculator, they miss the 6, hit 9 and fully accept the answer of 27 versus 18.  This is a by-product of instruction that only focuses on solutions and processes, it also demonstrates a huge numeracy deficiency.  I believe that numeracy is mostly learned with practice without a calculator, and when using a calculator a student must make an estimate to make sure they are getting a reasonable solution.

So what about the all mighty state tests...  If they are going to measure anything that approaches usable data, they would include no calculator through the grades where basic processes are learned, approximately 5th grade.  They would then include portions of the exam that allow any tool to solve problems, computer, calcualtor, etc for a portion of the test in 6th-10th grades.  As the grade level raises the longer the calculator/tool section, by 10th or 11th grade the non-calculator portion should be really short, about 15 minutes. 

In my room, 9th graders are not allowed calculators on tests/quizzes (tests are also designed so multiplying 15953.23*129.482 is not required).  10th graders and up do get to use calculators most of the time, with a small portion of quizzes being no calculator.  I do not use TI-84s until AP Calculus, all other classes use Microsoft excel for graphing and problem solving (a real world tool).

The real problem is we get caught in this discussion about calculators and other technology and miss the point that some amount of time needs to be on numeracy, processes and skills & more time on concepts, problem solving and math's interconnections.  I teach high school and I divide that time at about 30% skills, 50% concepts and 20% problem solving. 

At this ratio there are many topics I do not get to, yet my students are consistently testing into college math (not remedial), scoring well on the ACT and have worked through many large projects which they cannot see solutions to  --   that is our job.   Nowadays students are able to look up everything and calculators are an easily acceptable tool, thus we need to let students use them.  The real question is whether they will have the tenacity and understanding to find acceptable solutions to today's & tomorrow's problems.

Skills required.... Not quadratic formula....

So prior to teaching I was an engineer and manager for about a decade.  Then I started working on my masters in instruction to teach mathematics.  I was 33 years old when I started, was successful, and could no longer do the quadratic formula from memory, because .... wait for it.....   I did not need to.  But I could do algebra on demand, could find the quadratic formula on google to get roots, and could use the math I knew to dig in and solve problems.  The true reality of math required for being successful.

So as we start chasing the Common Core and its requirements we need to take pause and ask what is really needed.  Math has natural beauty, it ties together processes and our world - that is what students need to see.  They also need to be able to take large problems and rip through them looking for patterns and possibilities.  Meaning they need to be good at Algebra, graphing and problem solving.

Yet I fear these skills are going to be considered low level by teachers looking at the core (get them done in 9th grade -- know 'em, then never forget them, which we know doesn't work).  Most of the standards in High School are well above that, leading to my fear that the Core will scare teachers into showing everything, proceduralizing everything and developing a bunch of students who think math is just memorizing (an old school Biology course).

Worst yet, it will lead to a group of students who do not want to attack a math problem unless it fits into a little box they have seen...  I see it often with students who transfer to my school, students who won't start a problem unless they know the "procedure" to finish.  The problems we need to solve in our world are not this clean.

The Core will not produce problem solvers unless we look at our students and test them for true skills.  Yet it remains to be seen it we are going to test well, or measure end results well...    If we don't it will be another program with all the right thoughts and none of the right results.