Most Likely to Succeed

So here I sit late at night while sleep evades me.  Not because it normally does but because of a movie.  I read the book Most Likely to Succeed but the movie was far more powerful.  Still not as powerful as a brief few words by an administrator at NTC but powerful.

Never am I one to swing the pendulum too far to one side.  Let me explain.  I see most of the "new things" in education as advancements that have both good and bad to them.  Taking a look as some of the most recent best practices such as the flipped classroom and personalized learning leads to some very interesting conclusions.  First, neither is showing much for results.  Second, both are dependent on the right student culture.  Third and most important both are only as strong as the teacher in the classroom.  I like aspects of the flipped classroom just like I can see value in parts of personalized learning.  I just don't see sustained success in either one individually.

Today's student is a new breed.  Taking out the top 1/3 of the students that would succeed regardless of how they were instructed we are left with a mixed bag of students.  Most of which would rather sit at home playing video games than trying to dig into something new.  These students have a rather large issue coming at them.  For the first time in my almost 2 decades of teaching I believe the world they are entering has the potential to be vastly different than the one we were in.  I just don't think other teachers see this yet.  For the past several decades not much has changed.  Don't get me wrong, tons has but most people have a job, went on to school and became what they wanted to become.  Now, unemployment is sustaining at a high rate in part I believe because technology is replacing people at a much faster rate than in the past.  Furthermore, the climate of business almost promotes these changes.  Normal manual labor is still necessary and to a degree will always be there.  However, the jobs that are harder to find are the more skilled positions.  Computers are taking those jobs and keeping them.

Most math teachers have a certain pride in our level of expertise to teach math.  I must admit I really don't believe the students I produce become mathematicians.  I just want them to be thinkers.  Regardless nobody does the math we teach anymore.  To respond to the pundits out there, yet some do but play the math game.  Maybe 1 out of your entire building, not classroom, will go on to actually calculate/create using the math we teach.  Computers do all the work.  So why do we teach all of it?  Why even bother?

Speaking for one I am done teaching the stuff that really doesn't matter.  I am tired of preparing students to take an assessment that shows zero student success past the first year of college.  I want to prepare students to succeed in life.  My problem is where is the midpoint of all this transition. We can't just give up on all math.  Students/Families will require us to have certain cognitive understandings.  While at the same time I really want to see students thinking, creating, doing...  How do we determine where to begin?

Where is the balance between enough background skill and enough group interactive skills to ensure a child succeeds?  Then, even when we find it how do we communicate it?

Oh so many questions.  I think it is going to be a long night...

Making Retention Systematic

It has been said for many years. "I'm not sure last years teachers did such a great job. Students don't even know (fill in your major topic that students should remember from a previous year)." Teachers had very little way of fixing this without practically going to last years teachers and accusing them of poor instruction (Even though this is an extreme situation it is far from uncommon).

Maybe this doesn't have to be the case anymore. The Common Core State Standards have had many advantages in the classroom. The most prominent may be a basic set of expectations that all teachers at a specific grade level should see in their classrooms. This base-level has made it possible for sites such as http://jeffbaumes.github.io/standards/ to make retention more than just a lucky happening.  Not only does this site show clearly what standards your current instruction will lead to but easily identifies the "end" of a topic.  It also has the ability to identify those topics that make one think...why do we need this taught at this grade level?

After spending a while looking at the matrix, many of the standards I question happen to be Geometry standards.  For example, 5.G.4 asks students to classify two-dimensional figures.  Often, this is discussed in High School Geometry where inevitably we hear the words from teachers claiming students should know this "stuff" already.  Should they?  If we teach Geometry in 10th grade and the last time properties of 2-dimensional shapes is mentioned is in grade 5, a full half-decade earlier...should they remember?  The same argument could be made for angle measurement, another common topic in 10th grade Geometry.  Prior to Geometry the last time it was mentioned in the standards was in 4th grade.  Using a protractor is such a foreign tool to begin with.  Since it doesn't come up again until the 10th grade it makes sense that students struggle with what is perceived as a very basic task.  Instructionally this begs 2 questions, the first of which I would rather not tackle.

Why is this topic in the grade if it not important enough to expand on for 5-6 full years?

How can this help us form instruction to enhance retention?

This site makes it quite easy to see what leads into your current topic (provided you are teaching in K-8).  Take for example 7.G.2. This standard has no prior skills attached to it.  Therefore we know that all the vocabulary is new, all the concepts are new, and that we clearly need to attack this standard from step #1.  Taking a different perspective 6.EE.3 discusses the distributive property.  Any elementary teacher will tell you how often the distributive property is instructed, used, discussed from multiplication algorithms, to area models, and many more concepts.  The site confirms this.  In 6th grade the teachers role should be to access its previous uses and expand on them working their way into algebraic expressions.

In education, too often we get caught up on the goal.  Sometimes it makes more sense instructionally to look at learning from the students perspective and ask some important questions.

When was the last time this topic was discussed?

What was its context?

How can I expand on that context to tie it to the new standard?

It is those types of connections that make instruction effective.  So thank you Jeff Baumes and Jason Zimba for your work on the dependencies in mathematics.  Hopefully we can make effective use of your time.

A New Persepctive...Inquiry Based Learning

There are numerous studies that point to the need for instruction to be inquiry based.  Personally I cannot disagree.  What a student can figure out on their own versus being told will stick with them for years to come.  However I cannot help but think it is not just the inquiry process that enables the learning.  In fact, it may not have anything to do with it.  It is the changes in instruction forced by that process that matter the most.  In John Hattie's research about educational practices anything with an effect size greater than 0.7 is foolish not to incorporate into teaching and learning.  Anything

above a 0.5 is a medium effect size and still should be implemented.  Looking at Hattie's research things such as reciprocal teaching, self-verbalization/questioning, problem solving techniques, and cooperative learning all have effect sizes of 0.59 or greater.  These strategies are the same strategies that would be implemented with inquiry based learning.  Today we call this high quality discourse. 

As we delve further into an inquiry based model of instruction we find that there are limitations that need to be addressed.  Teaching students to think deeply is essential.  However, so is preparing them conceptually to proceed to the next grade level.  In writing this blog I don't want to debate the K-12 industrial system we call education.  The reality is almost every school in this great nation uses a grade level advancement system where one grade level has certain expectations or standards that need to be addressed.  The Common Core is built off this understanding.  Therefore, I'll put a non-negotiable out there that the Common Core State Standards need to be instructed and understood by all students at the appropriate grade level.  Inquiry instruction takes time.  A lot of it.  The great mathematicians of the past didn't discover this stuff we call mathematics in a 42 minute period.  

My question is how much time should we devote to discovering things that have already been discovered versus applying those things in a context that could be used today?

The reality is we don't have the time to discover every topic.  We have to decide which topics just need to be directly instructed and which can be found through an inquiry process.  By the way, direct instruction has an effect size of 0.59 according to Hattie which is the same as cooperative learning.  Once we admit that not everything can be discovered, or needs to be, it begs the question of what gets learned through an inquiry model?  What are the most important concepts for students to dig into as deeply as possible?  Once we have determined that, then determine what is the most engaging way I can instruct these topics enabling students to not only be able to complete the concept but more importantly, understand and apply it in a timely manner.

Inquiry is a form of instruction but the methodologies are what make it strong.  Using those same methods in a non-inquiry form of instruction will speed things up but also should enable students to continue to retain the knowledge.  The most important thing, until the industrialized version of education changes, is that students have an opportunity to engage, inquire, and retain the information necessary to move forward.  Where ever forward is.

What "this" means for Math Education???

It wasn't that long ago that Math was the subject that never changed.  We had our postulates, theorems, graphs, and our clear steps to solving equations.  The advent of the graphing calculator was about the biggest event in math education since, well, forever.  Sadly, even today some teachers still resist its use.

It seems now math is the subject in schools that doesn't stop changing.

The change may have coincided with the Common Core State Standards but that was not the push.  It started well before that but only is gaining traction in the last few years.  The change is causing educators to rethink how we teach, what we teach, the tools we use to teach and what students have the potential to do.  The change isn't just one thing but an onslaught of instructional opportunities.  An interesting piece of technology that came out a short while ago as improved to the point of being interesting is  Photo Math.

Photo Math     https://youtu.be/WvIoYUr1SWI

"Photo Math reads and solves mathematical problems by using the camera of your mobile device in real time. It makes math easy and simple by educating users how to solve math problems."  Not sure about the educating portion but it truly works.  Typed equations of almost any kind can be solved with all of their steps shown in a blink of an eye.  I tried it on a traditional Algebra 2 textbook.  It solved everything from multi-step equations to logarithms to systems of equations with 3 variables.  It solved it all.  So what does this mean for math education.  Are we to put our slide rulers away and just take a seat on the side?  Is our career in jeopardy?

The answer lies in math.  What is math truly about?  It's not about solving equations and multiplying correctly.  It is about patterns and logical reasoning.  This occurs outside everything everyone thinks is math.  It's about continuing the direction we are heading and making it stick.  Apps like Photo Math won't help solve an applied problem.  They won't help visually show why the best price point for a product is $8.57 according to a set of supply and demand equations.  They won't help analyze data or learn why higher mathematics is important to learn.

The easy solution is to ban the phone from the classroom or lock the iPad to only use a basic calculator upon entering the classroom.  The short sightedness of that is scary.  To ignore the opportunities to truly understand and enhance math through the plethora of available apps is to ignore an entire generation of students who are able to play and learn higher levels of mathematics than we dreamed possible before.  Not the math of algorithms.  The math of applications.

We live in a world where application is now easy.  Video, sound, photo are all made readily available by the same phone that makes a skill and drill problem useless.  We are entering a new playing field. It is time to take our skills-based DOK 1 and 2 style questions out of our summative assessments, place them as learning skills and formative assessments throughout a unit and focus on how to apply those same skills in a setting that means something to students.  People like Dan Meyer began the momentum several years ago and we started to listen.  Then others joined the game like Jo Boaler who decided to not just focus on tasks but on how we instruct and what we expect.  Now programs such as the Discovery Math TechBook change the way we offer instruction using a constructivist style learning with an emphasis on real applications.  We are finally seeing the combination of resources and quality instruction.

Discovery Education Math TechBook

For the first time in history technology and resources are catching up to classroom pedagogy.  It's up to us as teachers to make math instruction be what it was always meant to be.  A search for a better more efficient way to the find the solution to any problem life throws at them.