Monday, November 27, 2017

Empowering Students and Teachers - Freedom Within Limits (Part 2)

The structure of math class needs to be designed in such a way that students are given plenty of freedom to take charge of their learning within the limits of dependence on a facilitator.  What does that look like?  How do you design learning so that students believe that everything depends on them while at the same time believing that they need someone to facilitate their learning?

Task-oriented classrooms can provide an appropriate balance between freedom and limits.  When students are given a task, they are given the freedom to learn.  If that task is too easy, they won't need a teacher!  If the teacher tries to insert themselves into the conversation, students will feel that their progress is impeded by the intrusion.  Tasks that are just a little beyond their reach require students to rely on the instructor while at the same time conveying the responsibility that learning is their responsibility.  Students who are not accustomed to this type of learning may rely too much on the instructor out of habit.  However, with a little encouraging, students can quickly assume the role of responsible learner.

Tuesday, October 24, 2017

Empowering Students and Teachers -- Freedom Within Limits (Part 1)

Assessment drives instruction.  Well, so too, classroom structure drives instruction.  I believe this is why so many great ideas in education die.  Teachers give them up out of frustration.  The structure of learning time has to change in order for innovative educational ideals to survive.

This past semester, I set out to give my college students a world-class math education.  During the first couple of weeks I interspersed activities designed to teach and re-teach what an effective mathematics classroom should look like.  They got it.  They wanted it.  Then they got to work with what was prepared for them in the course.  It wasn't work that I had prepared though.  It was prepared by other instructors and handed to them through me.  It bombed.  I could tell that my students were frustrated that I was telling them one thing, and the work given to them was telling them another.  I was seen as an obstacle to completing their work and to their success because that's how they viewed success.

I realized that it wasn't that the ideas I had given them weren't good or desirable or effective, it was that the model was garbage.  This was the case in both classes I taught.  In one class, they read a textbook before class, took notes, then completed homework exercises on a computer during class.  Blah!  In the other class, they were supposed to function in groups by working through tasks prepared for them in a textbook.  In both cases, they had tasks given to them that they wanted to accomplish.  The moment they were given those tasks to complete, the role of the teacher changed.  Students were now empowered to take control of their own learning.  There was one monstrous problem though.  The teacher was removed from the equation!  In both instances, it became the individual's responsibility to learn, without much assistance.

I knew that what they were doing merely had the appearance of learning, but no substance.  That's why I set out to teach them more effective ways of learning math (though I would contest that they weren't really learning math in the first place).  The structure of the class did not allow for that though.  The structure defined my role as a teacher in both instances--wait until students ask you for help.  That's about the sum total of my role.  I can't do much else or they will get frustrated because they feel like I am impeding their success by preventing them from completing the task before them.  Bottom line, the structure of these classes gives students freedom, but no limits.

I have experienced much more success when I have been given control as the teacher to decide what my students will do.  In both instances above, I was expected to follow the structure of the class, although a vain attempt had been made to assure me that I could do whatever I wanted to within those limits!  But my freedom as a teacher was gone.

The problem with the tasks given to students in the second instance was that the task was too scripted.  The task was set up so that students had a smooth path to the goal.  The key to a successful task is a design that places students in a position that is just a little too difficult for them.  They can accomplish the task with the help of a teacher.  This ensures the teacher plays the role of facilitator, not observer.

Many educators and writers maintain that students need specific goals visible to them each day.  I prefer learning time constraints to agendas.  Students tend to rush to get to the end when they know there are a limited number of topics to explore.  On the other hand, when students know that learning is a never-ending journey, they tend to think deeper and not rush.  Time constraints allow for that, agendas don't.

I have described two typical classrooms where too much freedom is given: flipped classrooms, and group instruction driven through fill-in-the-blank textbook prompts.  The more traditional approach of simply lecture, homework, test, repeat doesn't even allow students the opportunity to take charge of their learning.  In this setting, any learning that occurs happens when the lecturer closes their mouth!

I am proposing that one way to empower students is by giving them freedom within the limits of smaller exploratory tasks, or tasks that are just beyond their reach.  When they finish, they are given another task.  When they finish that, another task is given.  This conveys the message that the limit is time not the number of topics.  There is an eternity of learning before them!  This gives the students freedom to work while at the same time giving the teacher the freedom they need to facilitate learning.  Both teachers and students are empowered in this model.

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.  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.  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

Wednesday, October 12, 2011

Lynn Scoresby, "Raising Moral Children".

Below is my very short summary of a 4 hour lecture on tape by Lynn Scoresby titled "Raising Moral Children".

A simple definition for morality/immorality that children can understand:  Morality is any act or intention that helps someone; Immorality is any act or intention that harms someone.  When teaching this definition to young children they will associate harm with physical harm, but as they develop, they will begin to see that harm can also include spiritual, mental, and emotional harm.

Don’t overemphasize rules or achievement, emphasize moral reasoning/judgment and agency
Kids that are heavily rule oriented might have difficulty not hurting someone because of the rules. Rules are necessary, but morality and agency are more important.  Sometimes it’s necessary to break rules in order to be moral. 

Moral Reasoning
Moral reasoning is the ability to interpret what helps or harms another.  
When your children ask why they should do something don't give them the easy answer, "Because I said so!"  Talk them through the moral reasoning you go through in your mind--meaning, delineate the reasons why obedience to such an action will harm or help another.  Tell them why there is a rule.

Empathy vs. Defensiveness

Empathy is the ability to understand others on an emotional level.  This is the ability to put one’s self in another’s place and make predictions of how they are feeling or how they would react in their situation.  To teach children to develop this trait, frequently talk with them about how they feel and how you feel.  It’s important that they distinguish good and bad emotions and build their emotional vocabulary.  When children are experiencing an emotion you need to help them recognize it and label it properly.  

Defensiveness is the opposite of moral reasoning.  Defensiveness means that you are unaware of your own feelings and that you shift responsibility of your acts away from you.  Those who are defensive make excuses, and blame or criticize others.  Being defensive prevents you from understanding others and prevents empathy and the development of moral reasoning. 

Moral Judgment
Moral judgment is the decision you make about whether or not to hurt or help.  

When a child explodes handle it with patience and quiet tones.  Then when they have calmed down you need to teach them to adapt their emotions.  Take them out of a situation and let them practice getting a hold of their emotions until they are ready to fit in. The adaptable human beings, adjusting from one situation to another emotionally, and the ones who regulate the intensity of their emotions are the ones who are moral. 

Help them learn to regulate the need to belong, the need for identity, the need to experiment, express anger, and the need for love and attention.       
Autonomy vs. Vulnerability


The two personality traits associated with moral judgment are autonomy and vulnerability.  Autonomy is taking personal responsibility for self and for actions.  Teach children a positive emotional style: joyful, cheerful, happy etc.  These children are more resistant to temptations and less likely to be vulnerable.  

The opposite of autonomy is vulnerability.  Children exposed to negative expressions are more vulnerable.  Teach them to be active, not passive.  Kids who are passive are much more vulnerable to temptations.   Limit passive activities and get them moving.  TV, video games, and sleeping are passive.  Get them up and moving or they will be vulnerable. 

Conversation Skills
The single most effective punishment is requiring your children to rehearse what was right and wrong about their actions.  Make conversation a punishment.   Keep talking about good moral reasoning and judgment until they get it right.  

Friday, October 7, 2011


I'm learning all sorts of fascinating ideas in my education class right now so this blog may just well be my venting area for a while.  What intrigues me about these theories are the similarities I find with gospel truths.  They are kind of like a preparatory gospel.  I like to think of the task of gathering truths (from wherever they may be) to the task the Prophet Joseph faced in the translation of ancient records and the bible.  It's going to require the Spirit, and, as Oliver Cowdery discovered, more than just asking.  It takes concentration, effort, and  diligence.  Of course you need a foundation of truth to build upon as found in the words of the Lord, but I merely wish to point out that there is great value in truth wherever you may find it.  I think you need both secular and spiritual knowledge to develop a well balanced character--which is the purpose of learning.  If your learning is too one-sided on either secular or spiritual, then you become quite, well, weird!  

Kohlberg's theory of moral development has six stages, but in class my teacher spoke of a simplistic version of this theory that I'll include here.  Talking about stages is perhaps the wrong word to even describe development because development is not a stage or event, it's a process.  The driving force behind Kohlberg's research was to discover the reasons or rationale people went through for doing things.  He wanted to know what motivated people to do things.  He narrowed it down to three main categories: Pre-conventional, Conventional, and Post-Conventional.

In pre-conventional, the motive for doing things is for personal reward or to avoid punishments.  Essentially, in this stage you do things for yourself.  A simple example would be a child obeying their parents to avoid punishment.  Similarly, a child obeying parents to receive a reward.  "What's in it for me?" is a giveaway for this line of reasoning.

Conventional reasoning is still focused on self, but in a round about way.  A person in this stage acts for the good of the group, family, or society.  They are concerned about the safety, happiness, or good of other people, but it in the end the benefits for being concerned about others is so that they will themselves be benefited.  For example, a person acting upon this motive would obey the commandment to not steal because they believe that chaos in society is prevented from obedience to laws such as this.  They are obeying to help society, but really the benefit comes to them in the end because there is a peaceful society that they can live in.  

Post-Conventional is the highest moral level and an individual in this level is not concerned with self.  Their actions and decisions reflect a sole concern for others without need for reward.  In the gospel, we call this charity.  When faced with a moral dilemma, this individual does not make a decision based upon whether or not they will be rewarded, or avoid punishment by their decision.  They also do not make their decision based upon what the law or the rule says.  They make their decision based upon the effect their decision will have upon the well-being of others.  It's not about them, it's about others.  Jesus is the prototype.  

Notice that in each of these stages the action can be the same.  What changes is the motive.  The connections with the gospel are quite apparent.  

Elder Oaks said something interesting about this:

"Each of us should apply that principle to our attitudes in attending church. Some say “I didn’t learn anything today” or “No one was friendly to me” or “I was offended” or “The Church is not filling my needs.” All those answers are self-centered, and all retard spiritual growth."

I recommend reading the whole talk:

This devotional is a must!  If you don't read the others, make sure you read this.

Another great talk from Elder Oaks about this subject: 

Tuesday, October 4, 2011

Maslow's Hierarchy

I used to be incredibly closed minded, but nowadays I'm starting to absorb the light from anyone and anywhere.

Maslow's Hierarchy of Needs has taken new meaning to me.  There are many philosophies out there to explain why and how we should do things.  It's best to approach each theory with scrutiny and realize that first and foremost it is, after all, just a theory.  When examining an aspect of your life it's wise to view it from several different theories, not just one, and derive the best meaning and value you can from each of them.

There are 5 basic stages of development to Maslow's theory: Physical Needs, Safety Needs, Love and Belonging Needs, Esteem Needs, and Self Actualization Needs.  According to the theory, you cannot move up the ladder of needs until that need has been met.

For most of us, the first two needs are pretty well taken care of.  There is, of course, some controversy over how much satisfaction do each of these needs require, but I think it's safe to say that most of us are not truly starving nor do we live in constant fear for our life.

I believe I have ascended the next three stages of development at different times in my life and I'm certain that whoever is reading this bore has too.

What I would like to point out is that upon personal reflection I realize that you can fall down the ladder at any time when one of the preceding needs is challenged.  For example, during my single life I climbed to the top of the needs ladder and reveled in the self actualization stage.  However, I became absorbed in my quest for a wife and the need for love and belonging was greatly challenged.  I could no longer focus on self mastery and achieving my potential because that need to love and belong was not met (according to the theory).

Here's some words to ponder about the meaning of each stage and where you are and what you can do to move up the ladder.  Perhaps the higher stages of development are only personal perspective?  Change your perspective and you move up the ladder?

Physical Needs - Food, Water, Shelter, Clothing etc.
Safety Needs - Protection, Security, Order, Law
Love and Belonging - Family, Affection, Relationships, Friendship, Feeling Appreciated
Esteem - Achievement, Status, Mastery, Respect, Self Esteem, Responsibility
Self Actualization - Personal Growth, Self Fulfillment, Realizing inner potential, Problem Solving, Acceptance of facts, Morality, Creativity, Lack of Prejudice