Tyrant of OR

Tyrant of OR is an interesting article that was passed along to me, and has gotten me thinking quite a bit. It is the belief that we often feel we have to make a choice between things – that one thing wins and one thing loses. For example problem solving and computation but in reality often we don't have to make a choice. You can do both – it is little counter-intuitive but I like the idea.

At my school we wanted higher ACT scores and more students taking the test.   And the single answer has been rigor.  I have pushed rigor, which is not just more homework (for me it has been less).   And as I pushed rigor, I have also pushed the idea that all students can be college math ready.  So even though math grades did drop at my school, our ACT scores and percentage of students have both gone up.

And to get scores to increase we did not lean the pool of test takers, we increased the count -- challenged more students to see how ACT would rank their college readiness.  Pushing hard on students to take the test and do well.  We have seen our college math placement scores go up AND more taking it -- from 20ish to 22.5ish for score and less 50% to nearly 75% taking it.  Definitely not a tyrannt of OR  -- would those results be the expectation?

Would you expect students to take more math with increased rigor? More students to take the ACT? Cause they are, when I started only a handful of students would take math as a senior – now nearly all the students do. When I started not even half of the students took the ACT test for college placement. This year over ¾ of the graduating class took the test.

Why? Because high rigor raises student performance AND student expectations of themselves. The students know they can perform at high level and that college or secondary schooling are within reach. Not everyone has to, but the problem solving ability, ability to learn are skills that serve students well for a lifetime.

OR does not have to be choice, I am taking AND. 

Dr. Cathleen Becnel Richard is an Assistant Professor at Nicholls State University in Thibodaux, Louisiana. She earned her doctorate in 2010 from Northcentral University in E-Learning and Teaching Online. Her research interests include academic advising, distance learning, reflective learning, and service learning. - See more at: http://www.communityworksinstitute.org/cwjonline/articles/aarticles-text/bayou_tchgsustain.html#sthash.uZ3CFLf1.dpuf

The more the students do...

As teachers we all seem to agree that the more the students work the more learning that occurs.  Yet we seem to be prepared to lead them step-by-step through mathematical processes, we make them sit and listen to long periods of lecture, we read solutions to homework - we make them sedentary.

So I have been reflecting, planning and working hard to keep them doing math - utilizing the entire 44 minute class period.  Class time is our time for math, I couple that with smaller homework assignments and a constant barrage of "You have to study math" versus assigning problems to grade or check.  But making the class period a power packed period of doing math has been #1!  So no homework grading, lectures are broken into segments with students doing (trying to get to 6 minutes max of me talking).    The goal is to get most of the doing (which is learning) in the class period, where as an instructor I can guide them.

It means not being too helpful though, struggle is okay when guided - when I ride in on my white donkey (budget cuts) to save a student I am most often doing a disservice.  So I constantly remind myself to "be less helpful."

In the end - students need to work more, I need to guide more, "teach" less and I expect better student outcomes. yself to "be less helpful."

Progression of Homework

So I am still thinking about homework, how to do it (or should I), how much value does it have, what is the best thing for my students?

Where I started teaching just 8 years ago I ran a traditional class - or at least the class I was use to in High School (even though I was more than 15 years removed from it).  I did like many first time teachers - I taught  like I was taught (quite a bit). 

Class started with checking homework, I usually collected it too.  But we spend time grading it, answering questions and then answering more questions.  Then correcting what students did incorrectly the evening before, or copied in the hall.  And the whole time - 6 students really focused while 20 were zombies - eyes open and nothing going on.  Then I would be pressed to teach the lesson.

I quickly moved to just collecting and handling questions by doing a different problem with similar content so everyone could work it.  That quickly help, at least everyone was involved.  But I still had a ton of questions from homework and misconceptions to "clean up" from students trying to do their work and doing it incorrectly.  And why wouldn't I have to fix misconceptions?  I was assigning something  new, something that we had just been introduced too.

Then I started not assigning new concepts immediately, we would do new in class together for a number of days, and then my question time quickly decreased I would lead the problem as I walked the isles. 

And now over the span of years I have migrated where I supply solutions and just have students turn in their work occasionally.  That way a student who is struggling can have an extra day, find time for help in the class or study hall.  It opens up a ton of my time to help students during the hour. 

And there you see the progression, I no longer consider homework really important.  Otherwise I would be "on my students" to be done every day.  But homework is for the student, it is what he/she needs, thus I give some flexibility.  

The students know they are responsible  for the material in the text (I sure say it often enough) and their grade is based on their knowledge of that material.  I often joke that students "can learn through homework or through test and quizzes, I really don't care which way."  Note, in my class, grades are based upon summative recursive assessments on mastered material.  And since the quizzes are recursive, always focusing on mastered material students are continually "practicing" twice per week. 

Now is good time to mention that my goal is not their grades but the knowledge they leave my school with, are they college and career ready.  (They can be a pain with some students or parents sometimes - but when is last time a person was asked about their Algebra 2 grade when applying for a job?) 

I don't care how they learn it, students that play school do the work and earn a better grade typically.  But the student who really won't play school still typically gets the skills!  And a D in my class means they are ready for the next course.   (I find the D thing to be an epidemic - if a student gets a D and cannot do the work - how are they ready for college/career -- no wonder we have 30-40% of college students doing remedial math!)


And over the span of time the end results have gotten constantly better.  I have had better results on the ACT test, better results on the class assessments, better results from students who report back to me about how they are doing in their jobs or in their college math courses.  And that is because I feel I have increased the time a student does math!  I went from most students being zombies, who spent 20-30 minutes per day on math with homework, to an entire class doing math for 45 minutes, 5 days per week minimum.  Now the 6 students with questions just wander in before school or during homeroom for help.  My room is now a whirling dervish of math activity!   The homework is beyond that, and so if a student copies it (and that never happens) he or she is still doing 45 minutes of work per day.

Now I am pushing for less paper & pencil and more instant feedback practice - websites (Khan, IXL, textbook), spreadsheets, etc.  The hard part is changing me, I still find myself more comfortable collecting homework, than checking website reports -- and weird as that sounds it takes a lot more time to change me than to stay the same.   

I know practice is important and I will keep working for a balance between paper/pencil (a skill that must be maintained) and some sort of on-line portion (which I think gives students better feedback and increases the return on their practice time).

Most importantly - we will keep on trying to be better each day.

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....

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.

Results oriented

So what is my goal with my math students?  That is the question I am addressing, it is my "over-arching" question as I review the first half of the year and think about the remaining year & more importantly future years.  Am I trying to create little mathematicians/engineers (no), am I trying to create drones (no), I am trying to give them the problem solving skills they need to succeed in the world. I ask this "goal" question as I pull together ACT data from the last 2 tests and measure my students (thus myself).  The real challenge is tying the ACT to the CCSS to the skills really needed by my students.

The ACT is just a measurement made popular by colleges, but it does provide insight.  Making my students unafraid of problems with numbers that require thought and processing is my goal, the ACT does not measure that well at all.  But it does check the basic skills, it does indicate whether they are ready for college and/or career.  The skills/material we learn is just the tools we need for problem solving (now and later).  So as I enjoy my time off and lie around getting healthy (I was sick nearly all of December - 18 straight days of misery) I think about the CCSS (Common Core Standards), how it ties to the ACT and I wonder why there are so many standards in the CCSS.  An example may help....

I was talking with another local math teacher at a basketball game and she asked if I was still not teaching matrices in Algebra 2, and I am not.  The reason is if I put in big mathematical problems with processes there simply in not enough time to do it all.  I have no problem pushing matrices out of Algebra 2 into Pre-Calculus (I teach matrices in Pre-Calc in May - thus you see how little value I believe they have),  Some students need them for college but it is something that can easily be picked up at college and I use that Algebra 2 time for problem solving and being really good at the Algebra/Geometry.  Maybe in the future more Algebra will go from grade 8/9 to 7/8 then 6/7/8 & allow time for more topics, but right now there is no time for matrices.

I judge myself (and my students) if they are ready for college level math (not remedial) and/or career.  I judge myself (and my students) on whether they know the basics conceptually and understand that effort/studying is the key to math success (not math IQ).  But I learned one thing in my previous career you need measurements.

Data is the key to knowing where you are and where you are going, running by gut feel is the worst thing - so I track a few stats.  I track scores on the recursive quizzes I give, I track the ACT scores (it is what students need to do well on), and I track, what I believe may be most important, post HS data to really judge my students.  My post HS data is math placement and first math course success in college (that is the best part of a small school - tracking 20 out of 30 students is easy).  Funny thing is most schools that I have spoken with don't track post HS success -- but heck I view that as my true end-product.  I am unsure how the CCSS should be tracked, I am waiting (with baited breath) for the Smarter-Balanced exam and see the data it provides.

All the success, failure, tears, etc don't matter if I create a student who cannot handle the next challenge.  I continually chant that the students want me to be hard, so they struggle & learn with me, versus struggling later in college or career.  But how does this all this tie to the CCSS and its practices?  That is the question I cannot quite answer yet.

So as I pull together my ACT numbers I see many successes.  Our trend is great, our scores are good, but there are still students on the fringe and those are the ones that I will try and set up systems to help.  My favorite discovery  is my D students can do math -- and that is important key -- if they can pass they have the basic skills and thus can succeed - otherwise they should stay for more instruction (so my line in the sand seems correct for passing/repeating students).  The data lends to the idea that grades are timed-based thus not a great indication of ability.  A student who does poorly in my Algebra class does not escape it in Geometry, they continue to practice and do quizzes through-out Geometry on  Algebra topics.  That allows the student who need more time to get it, it also makes sure the rest remember it.   And it seems to work, my Juniors/Seniors do well compared to the rest of the country (where 5 years ago they were slightly below the rest of the country).

So I have found some success with recursive quizzes bi-weekly on previous topics that were taught conceptually.  I have found a gap in my measurements and the CCSS, which I am unsure on how to bridge.  I have found that while the CCSS spells out lots of good things, but it fails to point out the great, which as a small school teacher makes deconstructing them a priority with all my free time with 7 preps!   Yet I know this is a slow progression, just like in business, the CCSS cannot be achieved over-night, and I will continue to track data, ask the big questions, and push for 3-5% improvement per year -- which is results oriented!

Math Team -- Math Meet

So I am writing this post over 2 days. Currently it is the eve of the Tri-State Math Meet at UW-Platteville.  I am excited about taking my students on a "fun" off campus math experience.  This year I have 54 out of the 92 in the High School attending -- I am sure a couple will not make school for some reason but it is a great thing.  I have an excitement about math going.  (It also does not hurt that we have done well in the small school division (Division 4) for 4 straight years)

Some have asked if I am nervous about the meet, and I presume they mean winning it.  And I really don't worry about it.  I just want to make sure each individual student takes pride in what they do, how they do it and enjoys themselves.  My biggest worry is someone not having fun.  I also believe that we just keep doing our thing and the right thing happens, all runs end.  But making sure the students see math as something more than problems in a book is important (even though a math meet is not all that different - it is different).

So - when asked do you think you will win?  I reply that some students should do well and that I think we will place....  I believe it shows we have a strength, any day, any given test can give slightly different results - but I just want the students to feel good about their efforts and support each other and we do that  well.

My plan is to continue this post, tomorrow or Thursday discussing the day......

So it is Wednesday night and I just came home from the meet and we had a great day.  There was a bus and a van of students applying, thinking and doing math.  The day started and ended well with Juda placing 2nd overall in our division.   It is impressive that year in and year out these kids take the time to work at the math and the way they support one another is great.  I really enjoyed today and I am looking forward to our next meet in the spring.