Sunday, March 26, 2017

Is Blended Learning the answer?

I've been thinking about the book Disrupting Class by Clayton Christensen.  In summary, for an educational model to be disruptive, it must meet the following criteria:

  1. It must be cheaper than traditional school.
  2. It must appeal to non consumers who will build a sustainable foundation.
  3. It must at first be sub par to traditional education for students already succeeding in that model. 
It will likely:
  1. Be simpler than a traditional school model.
  2. Not appeal to "successful" traditional school students AND teachers AND administrators.
I believe that some of the "non consumers" would include many kids in low-income schools and any kids, anywhere that are failing in traditional schools.  I believe this because the alternative to the disruptive model (Whatever that is) is almost the same as no class at all.   Why?  They are failing anyway.  Then for a disruptive model of education to thrive, it must appeal to said groups and meet their needs.

The blended learning schools I am seeing, reading about, and the one I work at are trying to appeal to students with whom many would consider successful at "playing school".  I believe this is the wrong direction.  We need to appeal to these non consumers that I am talking about and we need to succeed with them.  All we have to do is provide a better alternative than the one that they currently have and we will disrupt traditional schooling.  Innovations will come if we can do that.  In time, we will be able to provide a better product than what traditional schools already have.

Blended learning schools are very expensive.  I don't think it's sustainable.  It needs to be cheaper.  Part of the reason why it's so expensive is because these schools are purchasing learning software and hardware for every student.  It's very costly.  This is not a better alternative to traditional schooling.  This is worse!  It must be cheaper than traditional schooling.

I believe that what we really need is innovative teaching and learning, not more technology.  The technology will come with the disruption.  It always does.  We are too worried about that.  We want it to be there, but it just isn't there.  What we really need is to innovate how we teach and how we learn.  Innovating how we teach is simple, it will appeal to non consumers, it will be cheaper, and it will be sub par to traditionally educated students at first.   As we innovate, we will find ways in which technology can better serve us.  The technology that has been developed and is currently being developed is not innovative, nor is it disruptive.  It is a replica of the traditional model.  It will not survive if it doesn't change.  

Whatever ways in which we decide to innovate need to be simpler and cheaper than traditional models.  I think this can easily be done by focusing on curriculum and content.  Many traditional schools purchase computers and textbooks.  The blended learning schools I am speaking about are purchasing computers and digital curriculum.  It's the same thing!  In fact, I think it's more expensive because teacher to student ratios are far below traditional schools. 

We need to provide a cheaper option.  If we purchase computers and provide our own curriculum, we can still afford to lower teacher to student ratios.  

Computers are not a necessity at this point.  Computers will eventually provide much needed innovation in teaching and learning.  What I am saying is that the innovations need to mostly come without computers at first.  As the innovations in how we teach materialize, the computer will then be used to make the innovations more efficient, effective, and desirable than traditional schooling.  Use of the computer can't be forced.  It will happen because it's needed, but we haven't developed the need yet.

How will innovating how we teach in simple ways be sub par to traditionally educated students at first?  Because they have learned how to play the traditional game.  They won't want to try anything innovative because they don't need it.  They don't want it.  In their eyes, they are already succeeding.  So what does this mean for innovative education models, or those who so seek?  If we are drawing kids who normally succeed or excel in traditional schools, we are doing something wrong!  It must mean that we are offering or trying to offer a traditional education.   Why else would they take the risk?  They wouldn't.  That means they aren't taking a risk.  

When we opened our doors last year, we attracted many students whom I am describing as non consumers.  Many of them have left by now and are being replaced by students who very likely succeeded in traditional settings.  It worries me.  It must mean that we are in competition with traditional schools.  If so, we must be offering a sustaining innovation not a disruptive innovation.  Besides, we can't compete with traditional schools.  We are too expensive.  And if we are competing with traditional schools, what's the point?

Friday, March 24, 2017

Teaching Students to Become Thoughtful: Are we there yet?

As a teacher, I work very hard to help change beliefs about learning math and about education in general.  I'm not concerned so much about my students understanding every detail about algebra as I am that they are learning how to think.  Students will often become needlessly frustrated with specific topics or concepts or problems.  I think they can sense my angst and they automatically assume I am feeling what they are feeling.  But I am feeling that way because of how easy they have given up, because they are afraid of making mistakes and won't take risks, because they are overly concerned with their smart status, and many other things.

I don't care about the problem in the moment.  I'm looking ahead.  I'm thinking about how they are approaching the problem.  I'm thinking about the mathematics of the task while they are thinking about the performance of the task.  I'm thinking about all of the things that puzzle me and wondering why they aren't puzzled.

As the year progresses, the feedback I receive from students becomes more and more positive.  I feel like they are starting to get it.  I feel like they are starting to think like mathematicians.  I think this starts to change my approach a little bit because I start to believe that we are finally thinking alike.  As I start assuming we are on the same page, the negative feedback comes in.  Students are again focused on the performance of the task and the "right" way of doing things.

It's hard to gauge what's really happening though because I have to readjust how my gauge works.  Why?  Because that journey changed me.  Yes, it changed students too, but in the process of converting students, I converted myself on a deeper level.  Now I think differently.  Which makes it harder to gauge where they are at.  

As students change, the temptation is to change the focus in teaching.  But the very things that helped students change their way of thinking, and, subsequently, my thinking, are the very things that will help them keep changing their way of thinking.  "Are we there yet?!"  This is where I have gone wrong.  I have assumed that students would arrive at some end goal.  That journey is never over.  Learning to think is a task with no bounds.  It's the task of a lifetime.

Thursday, January 12, 2017

A 3-Tier Mastery Approach for Math at a Blended Learning School

Here are my latest thoughts on mastery design for my math courses.  Basically, students will work through 3 levels of mastery.  Students will repeat the 3-level mastery process for each concept, but the actual types of tasks--what they do, and what they produce--will allow for variety.  (At my blended-learning school, students may move at a faster pace if they desire.  This is not traditional lecture-led education.)

Level 1.  Students complete a task in which they explore ideas with an instructor.  Heavy instructor guidance.  The task will be such that it lends itself to guidance with an instructor. 

 Focus:  What scenario produced the concept I am trying to teach and how can I get my students to experience that intellectual need?  

Goal:  I understand this concept.

Level 2.  Students complete a task with a couple of check-in points near the beginning, middle and end with an instructor.  I don't think this should take much instructor time.  At this stage, the instructor checks to make sure they really got it from level 1 and continue to encourage deep thinking.   

Focus:  Mistakes: excepted, inspected, respected.  If we didn't make mistakes, we'd be done so why are we here?
Goal:  I can demonstrate my understanding of this concept.

Level 3.  Students complete a final task for that particular concept in which they work mostly independent with possible check-in points in the middle and/or at the end.  This task will conclude the learning for the topic and the student will produce something that demonstrates learning.  Students will keep this and compile with other similar tasks to create a portfolio of learning throughout the course.  

Focus:  What will students do to continue to develop, solidify, and demonstrate mastery of this topic?

Goal:  I can teach this concept.

With this 3-tier structure, I can keep them at level 1 until I feel they are ready to move to level 2 and then on to level 3.  One of the issues with traditional education is that students often arrive unprepared at what is supposed to be the concluding tasks for a topic.  Teachers then attempt to "review" the material until they are obliged to move on.  They don't need to review the material though.  They need to learn it.  They didn't get it the first time.

Thursday, March 10, 2016

Using Desmos to self-check

I have had many students use desmos to self-check their work.  One way in which they do this (and I stress that they do this AFTER they work out a mathematical thought) is to type each equation into desmos and check to see if the solution is the same each time.  For example:

I'm not overly fond of this method because I want students to be able to develop their own self-checking abilities and not rely on someone or something to judge their work; however, I can see some value in this method providing scaffolding as students gain confidence in their own abilities.

Another way in which students use desmos to self-check is by graphing complicated equations to see if they match.  For the same reasons, I see drawbacks, but some value in this as well.  I think there is value in helping them find connections between graphs and equations.  The example below shows how one student explored completing the square.

This led the student to wonder why the graphs didn't match.  Eventually they figured out that they need a coefficient of one on the quadratic term before they can complete the square. Link

How do you use desmos?

Monday, February 15, 2016

Desmos - Tech Tool Requirement for Every Math Teacher and Student

Throw away your graphing calculators!  Desmos offers a free graphing calculator that is very easy to use and they regularly add new features.  In terms of ease of use and features, there isn't another calculator that compares.

I discovered the graphing calculator shortly after it was launched in 2013.  I eagerly showed friends, family, and colleagues what could be done with it.  Here is the first graph I created with it (and 2 derivations):


Can you generate the graph I made?  Post in the comments if you can.

Desmos has a library of activities for teachers or you can create your own for your students here.  My personal favorite are the Marbleslides activities.  My students have explored these for hours of fun.

In subsequent posts I will highlight a few of the ways in which I use Desmos with my students.

Thursday, February 4, 2016

Tech Tool Criteria

Andrew Stadel poses the question: "What's your [tech tool] criteria?"

I am excited to see what the 21st century holds for the way in which teaching and learning will change.  It's hard to say what that might look like in 50 years from now, but I believe that replacing the thoughtful, empathetic, wise, intuitive teacher will be difficult, if not impossible to do.  What excites me is the ability of technology to:
  1. Automate non-thinking tasks/processes.
  2. Organize and inform teachers of student's thinking processes.
  3. Deliver, organize, and adapt learning opportunities in interesting ways.
  4. Utilize the teacher more effectively and efficiently.
The first 3 can basically be summarized by #4.  Utilizing the teacher more effectively and efficiently is the ultimate tech-tool guide for me.  What that looks like will vary by what is meant by "effectively" and "efficiently".  Teaching and learning philosophy form the crux of any tech-tool.

If you believe that students absorb information through rote practice, then the purpose of the technology becomes a tool to automate an endless supply of multiple choice, auto-graded problems.  This does indeed allow the teacher to be more effective and efficient--according to that theory of teaching and learning.

Contrast that with the adult learners I worked with this past week.  In particular, I worked with one woman in her 50's and one woman in her 20's on a similar topic--developing number sense through estimation.  It was fascinating to see how difficult it was for both of these women to push past old misunderstandings and create new understandings.  The brain is amazing.  Both of these women would begin to grasp the concept, but would almost immediately revert back to past misconceptions as they compared what they were now beginning to understand to what they previously thought was true.  They were perplexed, or, to put it in education lingo, they found themselves in disequilibrium.  The teacher is essential in this process of helping a student find disequilibrium.  Tech-Tool Requirement #1:  Help students find disequilibrium.

I have often thought that the best type of learning and teaching occurs in one-on-one situations.  But at the school district scale, this seems impossible.  However, the computer may make this a more likely scenario.  One of the challenges in teaching is finding the students who are in disequilibrium to help guide the delicate transition to understanding.  Tech-Tool Requirement #2: Help teachers find students in disequilibrium.

There is great value in the struggle to learn, but unproductive struggle is not desirable.

One of the most frustrating aspects of teaching is the desire to reach every student, but the lack of time and focused attention to do so.  Students enter the classroom with a broad range of skills, misconceptions, and experiences.  Tech-Tool Requirement #3: Help teachers address the individual needs of each student.

This could be done by organizing an effort to quickly display student thinking for the teacher to analyze--the most difficult thing to teach a computer to do and, therefore, the most important role of the teacher.  Are there several students with nearly the same misconception?  Imagine having access to that kind of information.  I think there is value in having such a diverse student-body, but the ability to target individual needs, thereby allowing the teacher to be more effective and efficient, is what I believe will be one of the most important roles in technology-assisted learning.

The potential ability of technology to automate non-thinking tasks/processes has enormous benefits in freeing up the teacher to focus on more important tasks.  As teaching and learning philosophies are improved and refined, perhaps some of the things teachers worry about will become irrelevant.  Paper and pencil, in my opinion, are not very intuitive and technology has the potential to provide more effective ways of communication between student and teacher.  What I mean by this can be described by the frustration I feel as I struggle to communicate ideas to another person and can't find simple, intuitive tools to get the job done.

I often find mathematics difficult to communicate through paper/pencil and especially tech-tools because they are too clunky, counter-intuitive, complicated and time consuming.  But I am excited to see what the future holds because I believe that the poor quality of many current tools is due to the foundation of philosophy.  Tech-Tool Requirement #4: Improve and simplify the process for displaying, discussing, and rethinking ideas.

I envision some kind of digital discussion/thinking/communication board that extends to infinity in all directions.  Though some tools currently have something similar to this, in my opinion what they lack is simplicity, ease of use, and intuitive design.  

What do you think?  What are your tech-tool requirements?

This is my response to Andrew Stadel's blog so be sure to check that out here: Divisible by 3 [Andrew Stadel]: Tech Tool Criteria