A Think-Piece: Does WHAT You Teach Match HOW You Teach It?

While it might seem a tad heretical to my colleagues in education, I’ve never been terribly fond of Bloom’s Taxonomy. As I watched students show their thinking in class, the demarcations sometimes felt a bit artificial and too fine-grained to me; I would have a difficult time telling the difference between “knowledge”, “comprehension”, and “application”, for example.

Recently, I’ve been reading Charlotte Danielson’s Enhancing Professional Practice: A Framework for Teaching, and I’m now thinking of a different taxonomy, inspired in part by the first chapter in the book.  Danielson does a nice job of describing constructivism, and in that explication, she hints towards a distinction between factual knowledge and conceptual knowledge, and suggests that each requires a different kind of teaching.

I can get on board with this.  Getting students to memorize facts is often just a function of time, and frequency of exposure.  Conceptual knowledge includes the relationship between those facts, and getting students to understand those relationships takes more deliberate practice in the classroom.

Further, I think we can elaborate on this idea of factual and conceptual.  As a teacher of physics and math, I would say that there is also procedural knowledge: how to apply a recipe or algorithm.  Math teachers love procedures.

Additionally, influenced by the great text How People Learn from the National Academy of Sciences,  (“Key Finding 2: To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application”) I think we can zoom out from simple concepts to a larger Conceptual Framework – the sort of knowledge that takes the relationship between smaller concepts, and organizes them into a larger set of relationships that ties the concepts together, that could help define the entire discipline or significant parts of it.

I’m not sure that this can apply to all disciplines, actually, but it really helps me think about teaching something like physics.  Here is how I might break this down within my discipline, and writing, according to some of my ELA teaching friends:

Physics Writing
Factual Gravitational acceleration is 9.8 m/s/s

The mass of a typical human head is around 3 kg

A force is a push or a pull

A noun is a person, place or thing.

Use question marks to indicate a question.

Conceptual Newton’s 2nd law:  an object accelerates more when there’s more force on it, and accelerates less when there is more mass.  As an equation: a = F/m. It is also written as F=ma Active voice is more powerful and more readable than passive voice.

An introduction to a piece of writing works best if it immediately connects to the reader.

Procedural If Force= 6 Newtons, and mass= 2 kg, then you can determine the acceleration: a = F/m = (6 N)/(2 kg) = 3 m/s/s Sentences should be written, such that they include a noun, a verb, and punctuation.
Conceptual Framework Systems can be described either by the forces acting on them (Newtonion mechanics), or by their energy (Lagrangian mechanics), or both. Persuasive writing usually involves an introduction, evidence, analysis, and a conclusion that are all connected

I think there is a fluid relationship between all of these kinds of knowledge, and particularly “facts” and “concepts”.   As we become more sophisticated in our knowledge of a thing, we start to move “concepts” of that thing into our internal reservoir of “facts”.   For example, while I recognize that Newton’s second law has several parts to it and internal relationships (making it a “concept”), I am so fluent in using and thinking about it that I often think of it as a single entity, as a building block for understanding more complex systems.  The same is true for our multiplication tables. We can understand 5 x 3 as a concept of adding three groups of five (or five groups of 3), but eventually 5 x 3 = 15 becomes reflexive, and it becomes a fact that we can recall very quickly. So in a way similar to how we move new ideas from working memory into longer-term memory, so can concepts become factual chunks for us.

And so it goes: we then turn groups of concepts into conceptual frameworks of increasing size and complexity.

We need to be wary.  People can learn and recall as “facts” things that just aren’t true.  And when they string together untruths, the resulting concept’s problems are multiplied.  An observation of the “flat earth” can yield all sorts of incorrect concepts about the nature of our planet and the way it moves, for example.  Part of teaching involves diagnosing misconceptions; we should gauge our students around not only their understanding of the relationships between the facts, but also the assumptions (what they consider facts) they make when discuss the relationships.

Taking a page from Danielson’s book, different kinds of knowledge suggest different kinds of acquisition.  Here are some ideas:

Knowledge type Notes, and means of acquisition
Factual Often doesn’t require the teacher – can be found from several sources.  Can be achieved through multiple exposures, like remembering someone’s name.  Often done with association: name with face; number with operation (3 x 5 = 15); lyrics with music, etc.

Frequently tested.

Conceptual Brings together facts and finds a relationship.  Sometimes the pattern IS the concept. Often requires some pattern-finding and analysis.   When people think of a concept, they very frequently share with others to check their own understanding (like what Vygotsky said)
Procedural Like factual, but includes a specific sequence.  Requires practice, and feedback. Often referred to as a “skill”.

Easily attained if there is only one recipe/algorithm, but for any kind of elaboration or permutation, or “if-then” decisions, it often requires a conceptual understanding of what created the basic algorithm.

This is often what is tested in math exams.

Conceptual Framework Usually found by patterns and relationships among concepts, so it requires exposure to many concepts.  Again – the relationship often IS the framework.

Teachers who don’t have a strong command of the subject they are teaching often don’t address this level of knowledge, because they don’t know it, and don’t know how to address it.

Again, different kinds of knowledge/acquisition suggest different approaches to instruction, and Danielson suggests that constructivism is an important approach to building concepts.  I agree.  Below are some examples and non-examples of constructivism.  They are in a table, because I love tables.

Concept Example of Constructivist teaching Non-Example of Constructivist teaching
Meter in poetry Teacher gives students two poems with the same meter and tells them “these have the same meter. Please read them aloud to each other”.   Teacher then gives them two different poems that are the same meter as each other, but different from the first two, and has the students do the same thing.

Finally, the teacher holds a class conversation about what they believe meter to be, based upon similarities and differences in the poems they read.  If necessary, provides corrections and clarity, and finally a definition.

Teacher might describe Iambic and Trochee meter to students with diagrams on the board, with students reading aloud.

The teacher then provides some examples of each to reinforce the idea of the kinds of meter previously introduced.

Slope = velocity on position vs time graph Teacher gives students three different position graphs of moving cars, moving at a constant speed.  The graphs have numbers on both axes. Teacher asks the students to rate the cars according to which is going fastest, without telling them how to do so.

Teacher also asks the students to find the slope of the lines of the three graphs, and asks them to compare the slopes to the speeds.

Different students share out their findings.  Teacher provides corrective feedback as necessary, and formalizes connection between slope and velocity.

Teacher draws a position vs time graph on the overhead, explaining the process the entire time, calculates the slope of the line, and then shows that the slope is the same as the velocity.  Students take notes. Teacher answers questions.

I’ll let the reader develop his/her own working definition of constructivism.  (See what I did there?)  What I’ve come to discover is that while some students can individually perform the tasks asked of them in a constructive lesson, several other students may find it very frustrating; they aren’t sure where to start.  Much more effective, I’ve found, are constructive lessons done with collaborative groups, where students bring several perspectives to bear in the pattern-finding or knowledge-building, and try ideas out on each other.  In essence, the students construct the concept together. (This is, by the way, how much of knowledge in the world outside of school is created, particularly in science. Data is observed, analyzed, and conclusions are made, then checked with colleagues.)

Eventually, the concept must be owned by each student, and that requires individual effort, and perhaps some practice.  So I’ve come to discover that the following seems to work:

  • Collaboration is best for concept development
  • Individual effort is best for concept mastery

I use this pair of ideas particularly when it comes to assessment, but also as I am designing my lessons, and considering – how far along the spectrum are the students in their concept formation?  Should my lesson be designed for more individual focus, or more group interaction?

The following table is not at all complete, but meant to provide examples of approaches well-suited to acquisition of different kinds of knowledge.

Knowledge type Possible Instructional Approaches or Techniques
Factual Any kind of repetitive process that provides multiple exposures to an idea.

Synchronous or asynchronous instruction.

Lecture followed by Reading

Reading on its own




Quizzing for mastery

Lab activities where students verify what is already known (e.g. “verify that the acceleration due to gravity is 9.8 m/s/s”)

Conceptual Constructivist, Student-centered teaching techniques that allow students to try new ideas on each other.  On a day to day basis, that might include

–       Socratic Seminar

–       Card Sorts

–       Fishbowl

–       Concept Attainment

–       Chalk talk

–       Interactive Lecture

–       Concept maps

On a unit basis, it might include problem based learning and project based learning (PBL).

Pattern-finding using data or sets of numbers, sets of facts, sets of concepts.

Quick writes

Lab activities where students use data to determine a relationship.

Procedural “I do/we do/you do”

Approaches that require student practice with a lot of just-in-time feedback.

Strategic use of non-examples (what did Johnny do wrong is his problem-solution)

Some lab activities, like titration, where the technique is target idea.

Conceptual Framework Pattern-finding using data or sets of numbers, sets of facts, sets of concepts.

Project Based Learning

Reflective writing after several units or projects that require connections between the units.

Ineffective classroom instruction is often the result of a mismatch of a teaching approach with the kind of knowledge that is desired as an outcome.  Among the primary perpetrators of this: “I do/we do/you do”. This is quite effective when you need to build skill in a procedure, like “completing the square” in algebra.  But if you want students to understand that acceleration is inversely proportional to mass, then a different technique (like a lab where students can discover that relationship) is much better suited than “I do / we do / you do”.

As a teacher, then, planning for your instruction should include a consideration of the type of knowledge you want to impart. You might have in your mind that you want to teach the parts of the cell in a biology course.   There are two parts to that, at least: (1) the factual names and functions of the various parts, e.g. the cell membrane acts as a barrier and filter, and mitochondria who provide energy for the cell, and then (2) the conceptual nature of how those parts interact, given the various roles of cells.   This might suggest that you could so some parts of an activity that include the factual acquisition (like with flashcards and quizzing for mastery), but then some interactive group work that might have a group create a concept map that connects all of the functions of a cell together.

I hope this is useful to someone.  By one recent measure, there 305 trillion, yes trillion, choices to be made about instruction, so planning the classroom environment and learning experience can be extraordinarily complex, leaving a teacher with choice paralysis.  By considering the type of knowledge, and considering a limited number of means of imparting or creating that knowledge, perhaps this framework could help a teacher become just a little more efficient and effective.

(post script: A follow-on to “How People Learn”, prosaically titled, “How People Learn II” has come out, and is free for a PDF download.  I plan on reading that here soon to see if I need to adjust this framework)



What To Do During Student Work Time


(This blog is mirrored on the New Tech Network web site)

At some point in your PBL lifetime, you will get to a point (and perhaps you already have), when you think you have achieved nirvana; the classroom is humming.  Students are working in groups on the project, they seem to be self-directed based upon what they need/want to know, and are enacting next steps that they generated, or next steps that you helped them generate.

This moment is to be relished, for sure.  But don’t sit down.  This is a golden opportunity for formative assessment, so that you can understand exactly how the classroom is humming, and where your student groups are going.  Too often, teachers will allow this opportunity to slip by, often by sitting down at their desk to attend to the million other tasks they have.

Here are a few options for teacher moves during that open “student work time”.  This list is not meant to be exhaustive, but a means of getting you started thinking about it.

Meet with groups on a rotating basis:

You can create a schedule of groups coming to see you, and apprise you of their progress thus far.  I’ve found it most helpful to create a table specifically for meetings, and they have to come to it: it makes the process just a little more formal, and important in their eyes.  The meeting can carry a grade, but doesn’t need to.  I often ask questions about (i)  progress toward the major task of the project   (ii) student understanding of the underlying concepts, and (ii) processes that the group is using to collaborate.   A checklist can help, especially if you fill out the checklist during the conversation, and give it to the students immediately after the meeting.  Here is a rubric that I’ve used with a fellow teacher for a project where every group created its own product in support of a Wildlife Refuge.   You can see that there is assessment for both team, and individual.

Observe the groups regarding their collaboration

As with all skills, the quality of collaboration improves with practice, and feedback.  Here is a form you can use to provide feedback for a group.  I prefer to use this without a grade.  It’s best to let all the groups know what you are doing, so that when you are standing in proximity to the group, they know what’s up.  If you don’t grade this, what do you grade?  A reflective summary from the group or from individuals might be an option.

Participate in conversations

Perhaps the work time for the groups requires them to make a decision, which could be informed by research, or an understanding of a concept.  This is a great time for you to act as that “guide on the side”, listen in on the conversation, and weigh in when you think it will help the group move forward.  If you choose to do this, make sure that you announce to the class that you might be joining the conversations.

Provide optional workshops

While some of the group is working, a group member might be having difficulty with a particular concept.  If you have seen a pattern in students across the class having a hard time with a concept, or even better, you have created a way for students to request workshops, then group work time might also be a time that you can offer a workshop to delve into some focused skill- or concept-building sessions with the student who need it.  HOWEVER, I share this strategy with some trepidation, because it can be tricky.  If you have provided some work time for groups, and you have suggested specific tasks for them to work on, or they are under a tight deadline, and you also offer a workshop, then you put groups in a position of making a difficult choice: should they all work on the task, or should they work on the task in the absence of a group member who is attending the workshop?   It might be better to save that workshop for a time when you’ve assigned individual work for the rest of the class.   Or, you can make sure that you call up entire groups up at once for workshops, so that everyone in the group is on the same page.

Develop the Rubric with the students

During some worktime, my teaching partner and I have held rubric-creating workshops.  All the other groups are working, and then you ask for input from a given group on the development of the rubric for your project.

In general…

From these examples, you might have seen some patterns emerge, but let me be overt.   There are a few guidelines to keep in mind when planning for group work time.  First, plan group work time always with the question:  what will I be doing at the same time?   If you don’t have a plan, then your time won’t be nearly as well spent.    Second, be sure that students know what to expect, both in terms of the tasks that they are meant to accomplish, and in terms of what you as the facilitator will be doing.  If they know that you will be participating in the conversations, they’ll welcome you.   If they know that they will need to meet with you about progress, they can plan their time around that meeting.   Expectation management is key to making work time useful, and students feeling (and being) in control of the work.

If you’ve got some moves that you really like to use during student work time, I’d love to hear about them.

Teaching Students How Not to Use Tech


Written in collaboration with Kris Williams

I am becoming convinced that a hugely important part of the work of tech-rich schools is equally about (1) how to use technology, and (2) how NOT to use technology.   

I am not  just talking about the avoidance of going to inappropriate web sites.  I am talking much more broadly about teaching kids to exercise restraint with any electronic attachment that carries the risk of becoming such a profound addiction.  And I speak from personal experience – I have spent no small amount of time on various websites (reddit could be my undoing) to the detriment of me doing things that are better for me.   Several of my students with smartphones had a seriously hard time leaving their texting, or Tumblr, or Twitter, or whatever, to engage in actual conversations and assignments in school.   The trick here is that we want them to have the technology to use – so we literally want them to be tempted – but we want them to be able to reject the temptation to spend all of their time (or even a significant amount of time) addicted to those parts of the technology that don’t really help them succeed in a project.

I’ve worked at 2 different New Tech schools, and because, by design, every student has access to a computer, we are uniquely positioned to help learners shun that temptation, and we can give them lots of practice.   The question that I have is this:  are we giving them the tools to really manage their relationship with their tech?   Are we developing an internal sense of self-regulation?  How do we teach this skill?

The idea of self-regulation is embodied nicely in New Tech’s Agency Rubric.  In fact, take a look at the “Actively Participate” domain of the rubric:  “Actively participates in the activity/discussion, team meeting, or independent time and has strategies for staying focused and resisting most distraction”  Sounds very much like a description of someone avoiding their phone, doesn’t it?

If we get our students to value what we value, if we get the culture in line so that students internalize both a disciplined approach to using technology and a desire to explore ideas productively, then teaching them becomes much more enjoyable and effective for everyone.    This is no surprise – we talk in the network about attending to culture first, but I think that we can be much more overt and detailed about what building culture means… and much of this comes down to:

  1. What kinds of relationships students have with each other – first we have to address the most fundamental level of respect and kindness, but then move to the idea of a professional relationship with colleagues, and what that means.
  2. The point of school is to learn and do, and in order for those to occur, you have to have a solid work ethic.  You have to buy into the value of being educated, beyond just getting a good job.  You have to buy into the notion that quality learning is NOT passive.  You cannot just sit and “take in”.
  3. The tool of the world is technology, but it can turn you into a passive learner if you let it, or into a learner that knows how to play Minecraft really well, but little else.   The technology has a huge potential to undermine so much of the culture in the school, so it has to be addressed head on.

I believe that we need to be more overt about the teaching of agency beyond just hitting students over the head with a grade.   We can’t just teach students how not to use technology just by saying, “Don’t use tech right now.”   We need to be explicit about the ways that we as professionals use technology so that it doesn’t hijack our lives and relationships and well-being.   We need to model good behavior with our own tech.  And we need to develop specific lessons that provide students those tools, and mechanisms that reinforce those values over time, so that students (and teachers, honestly) can come to internalize those values.

As an initial brainstorm, here some ideas for some activities or lessons that would move a school toward the goals of balanced and effective use of technology.

  • Consider having an intentional “No-tech Day”, including the use of computers. You can prepare the students for the eventuality, ensuring each student has a book of their choice to help take up time in the day when they don’t have access to their phones. It would be a good challenge for the faculty as well, who might be used to relying on computers for all of their lesson plans.  Consider incorporating a deliberate debrief of the day, and help students   (As a math teacher, I would say that you might want to exempt calculators from the no-tech rule)
  • Have the students track their phone use with an app like Moment, setting goals for spending more time being truly present at school and at home. (This is something almost everyone can benefit from, including teachers). Celebrate successes and the changes that were produced by meeting each goal.
  • Have each student develop a “lifeline” strategy to test out for keeping them from getting sucked into unproductive time online.  Consider having students name the strategy they are testing when developing group contracts or agreements.  For example, a student may say “My lifeline strategy is to give myself 3 minutes at the start of class and three minutes near the middle of class for off-task online time. I set a timer, and I shut off the tech or close that tab when the timer goes off.”  Have students share strategies that are working, or simply what they are learning from the experience, with others in the class.  This can also be an opportunity for you to share your own strategies for using your tech in a way that is helpful.  
  • Consider having students read and discuss this article.

These are just a few examples to get you thinking.  Please – share your own ideas or strategies for helping students use tech when it is best used.

Guest Blog: The Yellow Light Project


Today’s blog is from a colleague of mine, Heather Buskirk.  Heather teaches Physics and coaches teachers regarding Project Based Learning in upstate New York.  She and I have been collaborating on PBL training for the last several years, and as  you will see, she is a rather thoughtful practitioner.  You should consider her reflection at the end to be an invitation to brainstorm if you have any thoughts on her project for next year.

About a year ago, Kevin blogged a project idea about teaching kinematics through a automobile-themed project here.  Not one to pass on a great idea, I stole it and began designing a project around the question “What do you do at a yellow light?”  Since Kevin is not teaching physics these days though, he left figuring out all the details as an exercise for the reader.

First, a little context about my classroom.  I teach in a program for seniors called the Learning Project, which integrates conceptual physics, math, English language arts, government, and economics.  We meet daily for the first four periods (about three hours) and engage in wall-to-wall project based learning.  I serve at the science and math teacher and a colleague is responsible for the humanities courses.  Students spend the remainder of their school day taking classes back in our traditional high school or vocational technology center.  The students in the program cover the spectrum of achievement (from traditionally successful to struggling) but all share a desire for a different experience in their senior year.  

So while Kevin had given some inspiration about the physics in his blog, we had to find a way to bring in all our other courses as well.  We decided to have the students explore some structures of local government and the economics of auto insurance.  The project culminated with the students presenting to a panel including a representative of County Board of Supervisors Public Safety Committee, a local sheriff, and a local auto-insurance agent.  You can see our entry doc here.

We launched the project with a class discussion about how you should behave at a yellow light versus how people actually do.  The discussion was fairly rich and inspired great opportunities for some in the field data collection.  The sheriff gave us a list of the most problematic intersections near the school, which we then divided up and assigned to the student groups.  While formally, they had to just time the yellow lights and note speed limits for each approach to the intersection, by spending so much time at the intersections the students noted much more.  Every group returned with stories of watching in disbelief how many people blatantly ran the red light and several reported seeing close calls almost becoming accidents.  The field research fired the students up even more than I had anticipated and provided ample motivation to dig deeper into the physics of motion.

Our math course for the Learning Project is a senior elective called the Mathematics of Science, which allows ample opportunities for exploring the intersection of physics and math.  With this project, I wanted to review graphing functions (linear and quadratic) and do a bit with piecewise functions.  While my students come to me with math readiness varying from still struggling with Algebra to taking Calculus concurrently, I have no easy task when trying to support and challenge all of my learners.  I do find however that all of my students can benefit from a bit more practice with graphing.  In kinematics, the graphing can both serve as an access point for students who struggle with algebraic manipulations and as a entry into calculus.  In addition, all students were new to graphing and making sense of their own data and using online graphing tools.


We began by creating a storyboard for a car approaching and stopping at a yellow light.  From the storyboards, the students broke up the motion into pieces and then completed some quick investigations using toy cars and motion detectors to get the shapes of the motion graphs for each piece.  We then connected them to our kinematic equations and substituted in the real world values for reaction time, speed, and acceleration while braking.  

Student work - yellow light

This group’s analysis is broken into the reaction time for noticing the yellow light and applying the brake in purple, the time braking in green, and then the car at rest at the intersection.  With the final graph here the students figured out the car would travel nearly 30 meters before coming to rest given their data and assumptions.  Based on their analysis, these students then proposed the addition of signs at this distance from the intersection which would clue cars to stop if the light has turned yellow.  When the project was presented though, the analysis got a bit lost and jumbled.

In the end it turns out this project had a lot of pieces and they all did not fit together as seamlessly for my students as I had envisioned.  The tie in with Newton’s Laws was pretty forced and the students felt overwhelmed by the variety of panelists they had to address.  The analysis turned out to be pretty involved even with some fairly liberal assumptions (such as treating braking as a constant acceleration).  

So as I am turning my focus to the upcoming new year, I am seriously reconsidering my treatment of this project.  While the premise is strong, I think we need to focus the final product a bit more and tighten up the entry doc.  Also, now that I have a better idea of where the students will struggle through the analysis I can re-work my scaffolding plan.  Ultimately, I am wrestling with how can I give my students more agency and leadway in this project, without loosing the juicy physics?  Or alternatively, how can I get into some rigorous analysis without sliding to a super teacher centered approach?

Personalized PBL: Start With Senior Projects


For a while now, parts of our nation, and certainly the New Tech Network have been talking about “Quality education for all.”   It’s a good idea, but if you want to bring it to the place where the work really occurs, with the student, then we also ought to be talking about Quality Education for Each.    

This was the idea – quality education for all and each – that opened up the New Tech Annual Conference last week in Orlando.  Jim May pointed out something that I think is important to hold – that while the conference was themed with personalized learning, NTN is not saying that it has all the answers, or a recipe for the practice. Because we value great education for all and each, we are going to focus on this idea of personalized PBL so that we can learn together.  We haven’t figured it out yet, but we will.

To be sure, Project Based Learning represents a great platform for personalization.  Good PBL includes student voice and choice, so that students can be navigators and designers of their learning. Through the workshop model, facilitators can differentiate for varying student need.  Still, questions remain: sometimes teachers wonder how to deal with the practice that has all of their students working on the same project at the same time.

To address that concern, and as a scaffold for our collective learning, the New Tech Model already has some components that are perfect examples of personalized, project based learning, and one of them is near and dear to my heart:  The Senior Project.

As a teacher at NTH in Napa, and later at nex+Gen, I got to see the transformative power of senior projects.  In case you don’t do them at your school, here is how teachers at nex+Gen describe Senior Projects to community members:

One of the unique characteristics of nex+Gen is our requirement that Seniors engage in a year-long project of their own choosing.  The project can be about almost anything, but it has some specific requirements: it must have an academic component; a product of some sort must emerge from it; students must seek out and find an adult mentor for feedback and guidance; students must present their journey of learning at the end of the year.

Each project is individually done, and comes from the place of a student’s passion and/or interests. They negotiate with the facilitator the topic of the project to help ensure its weightiness, and then they embark on a learning journey that is truly driven by what they need to know.   Part of the process includes writing a research paper that informs their work.  At the end of the process, the senior present NOT to teachers, but to community members, and it is pass/fail.

Students rise to the occasion, and do extraordinary work when given the chance.  Here are some examples.  One student created, tested, recorded and illustrated tens of recipes to create her own Vegan Cookbook that is available on Amazon.  Another student connected with the local university to work on micro-pumps that are nano-machines used for medicine.  Several original albums have emerged from senior projects.  Another created and organized a fund-raising walk for Lupus Awareness.

As cool as those are, there are lot of other really good reasons to do senior project, and by proxy, to do personalized PBL:

It is developmentally appropriate.  As seniors get ready to move from the more structured high school experience into the wider world, Senior Project allows them to practice skills they will certainly need:  Asking adults for help; setting a budget and raising money if necessary; communicating with professionals in ways that keep the professionals from getting too frustrated.  The list goes on.

It helps your teachers become better at facilitating.  Because no teacher can be a content expert in all the topics of the senior project, it forces the teachers to help students learn how to learn, and how to focus on the Learning Outcomes.  

It reinvigorates learning for burnt out seniors.  One of my favorite quotations from a rather jaded senior about 4 weeks before the end of the school year: “I don’t really care about much other than my senior project.”  Take a moment to savor the fact that you just read about a senior caring about his learning more than just getting out of high school.   And this last year, at the end of the year, I asked my seniors:  should we make Senior Projects optional?  The resounding answer, in near unison:  “NO!”   As they justified that answer, they identified the Senior Project as some of the most difficult but powerful learning of their high school experience.

It underlines the idea of growth mindset.  Things will go wrong. Students will have to pivot and adapt. They learn that learning requires perseverance.

It has all the qualities of good PBL.  Deep connections to the community, cross-discipline, driven by need-to-knows, voice and choice, authentic audience, the works.

Even with all the benefits, there are, of course, challenges.  One of the biggest for the seniors is just coming up with a good project idea.  Handily, in advocating for personalized PBL, the keynote speaker at NTAC, Tom Vander Ark, (the author of Getting Smart Blog) provided a lovely scaffold!  He highlighted several of the big “megatrends” that students ought to be addressing.  Here’s a photo of his slide:

Tom V Megatrends

These would be perfect for seniors to use as an impetus for senior project ideas.  They are cross-disciplinary, rigorous, and they have an effect on the world.

To be sure, there are lots of other challenges with senior projects, but several schools in the network of NT schools have figured them out.  Reach out.  Find a school who has worked out some of the kinks.  Some good places to start:  Amy Reece at nex+Gen Academy, or Riley Johnson at New Tech High in Napa, or me.  And look for another blog, some time in the near future about specifics on starting senior projects.

Finally, if you are anything like nex+Gen, taking on Senior Projects will lead to very interesting conversations like, “How do we make our classes more like Senior Project?”.  And that, dear reader, is the beginning of a journey to personalized PBL.

Time Machine: Address to the Class of 2015


As we approach this year’s graduation, I wanted to offer the class of 2015 a reminder of the speech I gave a year ago.  If you are not of the class of 2015, then here is some context: at nex+Gen Academy, where I teach, students choose a faculty speaker each year to speak at the Senior Honors Assembly, which happens a day or two before the actual graduation ceremony. Last year, I was the faculty member selected to speak. The opening comes from the fact that I ask the students all year, “What is your class again?  2016?”  

Back to the class of 2015 – I would love to hear about your path to a substantive existence.


To the class of 2016….

Works every time. Every.single.time.   But in deference to you, I’ll start over.

To the class of 2015!

And to the rest of you: it turns out that the faculty speaker is selected by the students in the graduating class, so I am up here, I’m pretty sure, out the fortune of one student asking me one day, “Mr. Gant, if you were the graduation speaker, would you use different accents?” To which I said, of course.

That means, I’d better deliver.

<Scottish accent> I intend to do three things while up here. One, as a sort of retrospective, I’d like to describe you all as a class. Two, I would like to give you some advice.   And three, I’d like to do what I’ve done all year, and that is tell you what to do.

Perhaps I should have said that last part in a different accent: <Russian Accent>   Three, I will tell you what you will be doing. You will not have choice. And you will enjoy it.  <end Russian accent>

So: who are you?

The class of 2015 is one of contrasts and intensity.   Let me illustrate.

I’m going to use an SAT word, so I’ll define it first: indignation: strong displeasure caused by something that is unfair, or wrong, or offensive.

I saw the most indignation from this class from two things:

First, when you all watched the rather sophomoric rants of Lenar Whitney in her campaign speech calling global warming a hoax.

The other time when I saw the most indignation was when you discovered that I hadn’t seen the movie, The Sandlot. I thought that Ryan A. was going to either punch me, or leave the classroom and cry. Ray S., in fact, made me borrow it, and watch it.

You have similar responses to a global environmental catastrophe, and a movie about 11 year olds.


Next word: ebullience – cheerful; full of energy.

I saw the most ebullience from this class with two different events. The first was when I heard this phrase:   <very loudly>   YYEEEEAAAAAAHHHHH!

That…. was as a result of winning a game of kickball.

But the second was the feeling in the building after so many of you had finished presenting your senior projects, just awesomely killing it.


Of course, at nex+gen, where you speak a lot, I’ve seen presentations from students that were the result of 3 weeks of practice, and other so-called presentations that were the result of 3 seconds of preparation.

This last example of 2015’s contrasts is a little different, though.   It represents a choice, and it is a choice that’s not unique to you – it is a choice that all nexgen students have to make – you eventually come to a point when you ask yourself, “will I learn this material deeply enough to be truly educated, or will I just try to make my presentation sound good?”

In that moment, you face the dilemma of choosing between something of substance, or something made of meaningless words.

<English Accent> I mean, consider: Someone speaking in the most dynamic way to say something for which the esoterica does not reveal itself in the least, but yields to underlying, and simultaneous overlaying truths for which the truth testifies to the trueness of the content displayed in maximized efficiency in which, or for whosoever manifests the manifold perspective belying the obvious rationale precisely whence we offered the idea in the first place.  <end English accent>

Did any of you understand what I just said?   Me neither. I just strung a bunch of words together.

Even when I used big words, spoke confidently, and even used a British accent, there was still no connection with you, because there was no substance.

So here is the advice: as you get older, this choice between substance and making something look or sound nice is a dilemma that does not go away. You’re going to be confronted with this choice over and over, and how you resolve the dilemma will begin to define you.

As you go out into the world, where your voice must be heard, are you going to speak of substance, or are you just going to string together some words that don’t connect?  And what are you going to do? Are you going to do something of substance, or are you going to just string together some random actions that have no purpose?

In the world of Twitter limiting thoughts to 140 characters, or Instagram that doesn’t even require words, and the internet that doesn’t really require that you actually move in order to acquire something, you are going to be tempted into thinking that those things are the substance in the world, because they are pretty or flashy and easy and everywhere.

But here is a tip: being a person of substance is rarely flashy or easy.   It is hard work.   It requires that you think carefully about what you are doing and why you are doing it. It requires that you make connections with others. It brings you to the realization that your fortune and privilege obligate you to help others. It requires perseverance that build confidence that you can get real work done.


Finally, we move into third part of inspirational speech, where I tell you what to do, and you have no choice.   Remember, sitting for long periods of time is bad for you, so please, seniors, stand up.

(If necessary) No really, stand up. Come on…stand up!


Stand up, to withstand the temptation to go with only the easy and the flashy.

Stand up to start that long walk of perseverance.

Stand up, so that you can help others up, who might have difficulty lifting themselves.

Stand up, so that you can face your future with a smile, because you, you, have substance.


The faculty at nex+Gen gives our best to you all.

A Protocol for Crushing the Critical Thinking Questions


Heads up: I’m going to start by talking about science instruction, but this is a protocol that can apply to ANY class.

When I was a rookie science teacher, despite my inexperience, I still knew the kinds of questions that I wanted students to answer: they would require thinking, synthesis of ideas, and the application of those ideas.  This was what I called “critical thinking”.  An obvious place for questions like these was  in the follow up with lab experiences.  At the end of a Chem lab on flame tests, I might ask the question, “Which is the most important – the anion or the cation, to determine the flame color?  Provide evidence.”     At the end of an activity in bio that simulated gene insertion, I would ask, “Why are some people concerned about extra base pairs between the inserted gene, and the beginning of the bacterial DNA?”

I would get the following responses:  1% to 10% might answer the question.  Another 10% would come to me and ask for help.  The remaining 80-90% would leave it blank, knowing that they had done most of the lab, and they were content with the C or B grade they would receive.   With a lot of blank stares at me when I went over the work, I would end up answering the question myself.  As I heard myself answer the o-so-thoughtful question I had formulated, I imagined the slacker-thinkers smiling to themselves, quietly marking another victory in their quest for vapidity.

With some experience under my belt, I have come to understand that questions that require critical thought are one of the best uses of group discussion.  Not only that, interesting questions help students see the value of groups more than almost any other kind of group work.   Because the answers to complex questions frequently require some synthesis of data, knowledge, and even experience, then each group member has an opportunity to help formulate an answer – and students can use each other to develop an answer that might not have been as complete without the thoughts of others.

With that understanding, I formulated a protocol that works beautifully, so that I get 100% engagement, rather than 20%.

  1. Students in groups of 4
  2. Groups should provide letters to each person: A, B, C, D
  3. Present students with the question. When I did it recently, I was asking the question about extra base pairs in biology.
  4. Groups discuss their thinking about the answer, with a time constraint (I gave them 2.5 minutes). Person A writes the group’s answer.
  5. Assign Person C to take brief notes on the share-out from each group.
  6. Person B stands up, and reads the answer from his/her group. Person C in every other group is writing a synopsis of what person B from each group is saying.
  7. ALL groups report out.
  8. Groups use notes from person C to evaluate: which group had the best answer? Again, groups have limited time for discussion so that conversation is directed and efficient.
  9. A group can choose itself for the best answer, but if they do so, they have to choose a second place, and why they chose that group.
  10. Person D records group’s decision and reasoning, then stands up and reads the group’s rationale.
  11. You as the facilitator follow up: what were the arguments you liked? Did anyone not get an answer you were looking for?  This is a potential teachable moment.  You can reinforce some messages, alert students about misconceptions, or use the students answers to bootstrap to the next concept you need to address in the course.

I used this last week. In each class, about 2 – 4 groups would  come up with the point that I wanted them to understand: extra bases worry people because they could code for unexpected proteins.   The other groups identified that as their favorite answer.  There was a lot of, “Oh yeah huh!”   It gave me occasion to then say, “Pull out your notes, and let’s write both the question, and our class’s favorite answer.”

The group conversations ALSO alerted me to misconceptions, and how much base knowledge the students had, or didn’t have.

Since I work at a New Tech school, I could give my students a collaboration grade for the work.

Finally, the share-out provides a great assessment for my teaching.  If the kids can synthesize enough to adequately answer the question, I have probably done some reasonable teaching before the interaction.  If they cannot, then I need to examine what came before, to make sure that what I have been doing has been enough.

This protocol can be used in just about any course.  Here are some kinds of questions that might work:

“In the fairy tale of Snow White, is the apple a symbol?  If so, for what?  And does that have other implications for other symbols?”

“Is 2106 United States closer to the Roman Republic, or the Roman Empire?”  (this is a rather heavy question.  If you teach history, maybe you can give a better example.)

“Provide an English translation for this passage written in Spanish.”

Here are my “leave” questions that will so compel you that the comments section below will stretch into the horizon.  (Right?  Right?)

  • What questions from your own discipline would be appropriate for this protocol?
  • What tweaks might you make to this protocol?



Crucial Knowledge?


At what age should people know about antibiotic resistance?

This is the question that has occurred to me as a result of teaching about genetic engineering, and testing for plasmid uptake in a Freshman Biology course.  As a quick aside – don’t worry if you, gentle reader, have no idea what plasmid uptake is.  But to get my students to understand about it, they needed to know first that antibiotics kill bacteria.  On a hunch, I asked all my classes the other day:  “What do antibiotics do?”

Any guesses as to how many kids per class knew the answer?

Less than 1 kid per class.

I was surprised, because a huge part of every doctor visit I’ve had in the last 10-20 years, if it involved me coughing and feeling like hell, is the conversation about whether I had a viral or bacterial infection, and hell no they won’t give me antibiotics if my symptomology was consistent with a virus.   Of course, I brought up this experience  with the students (without the cursing, though it took some restraint) to help them understand what antibiotics do, and what they don’t do.

Upon reflection, I remembered that they are 14 years old, and they haven’t been to the doctor as much.  It occurred to me that this could be exactly the right time to help them understand the idea of antibiotic resistance, and the inadvertent genetic selection for the so-called “superbugs” as a result of over-prescribing antibiotics.   My students are now growing into a cognition that is rather adult-like, and logic works well with that level of cognition.   Understanding this issue requires some base-level knowledge about cells and evolutionary mechanisms.

And address the issue, I shall, but sort of by accident, and not because the state standards tell me to.  Here are the standards that might call for something like the idea of antibiotic resistance:

13. Explains how natural selection favors individuals who are better able to survive, reproduce, and leave offspring (NM – II.II.II.12)

14. Analyzes how evolution by natural selection and other mechanisms explains many phenomena including the fossil record of ancient life forms and similarities (both physical and molecular) among different species (NM – II.II.II.13).

24. Knows that specialized structures inside cells in most organisms carry out different functions, including (NM – II.II.III.2):

  • parts of a cell and their functions (e.g., nucleus, chromosomes, plasma,
  • and mitochondria),
  • storage of genetic material in DNA,
  • similarities and differences between plant and animal cells, and
  • prokaryotic and eukaryotic cells.


These standards deal with the underpinnings that allow someone to understand about the problems of over-prescription, but still, it seems to me that an educated citizen should know the difference between viral and antibiotic pathogens, so that when they get sick, they work WITH the doctors to ensure the right course of treatment.

So I can’t help but wonder: should there be additional standards for science courses that address the intersection between the underlying biology (or Chem or Physics or whatever) and its use in the world?  If the application is contingent upon specific technology, which will certainly change soon, then maybe not.  I don’t suggest any replacement of the underpinnings – I am saying that there are some ideas and applications that every citizen ought to know.  Their well-being, and agency in the world might depend upon it.

This instance makes me think of a couple of other examples, one of which isn’t even science:

Radioactivity:  Most people don’t understand that something cannot become radioactive if it is exposed to radiation.  This has real ramifications on irradiated food.

The Electoral College: I took government in high school, but I only really learned of the importance of the Electoral College during the Bush/Gore presidential election of 2000. Seems like it would be handy for someone know about that BEFORE they turn 18, right?

The Global Surface Temperature Record: A certain Senator from Texas is espousing that global surface temperatures have not risen since 1998, using satellite data for evidence.  Alas, this data doesn’t really tell us accurately about the surface – it measures the temperature of the “lower troposphere”, which includes a layer of air six miles thick.   People ought to know that a much more accurate record (that does show appreciable warming) comes from ground-based thermometers. You know, where the people live.

So I am curious: if you are an educator, what are the obvious holes in your current set of standards that might be at the application, rather than theory, level?  And even if you aren’t an educator, what should we ensure our students leave high school knowing that we are not yet teaching, or we are teaching spottily?

In asking this, I realize that I am opening the door to idiosyncrasies of individuals – there will be some of us who have our pet idea that not everyone else loves, but I suspect that there are some topics and ideas that a lot of us can agree with. And honestly, if you’d like to proffer your idiosyncratic topic, be my guest – I’m still curious.


When Project Rollout = “meh”

I should know better.

I started a project without running it by colleagues. It was such a good idea, I just KNEW the students would totally get into it. I had previous experience with Senior students who had utterly enveloped themselves in the subject: Genetically Modified Foods. This was a great chance to hit the ideas of how proteins are created in cells.

So here was the idea: I discovered that in 2013, a Senator to the NM Legislature introduced a bill requiring the labeling of genetically engineered food sold in New Mexico, similar to legislation that has passed in Vermont and Maine. It did not pass. Recently, this has been a contentious issue in the US Congress, with legislation introduced in the House trying to prevent states from passing labeling laws.

As I researched, I grew more and more excited. Look at all the issues coming up on both sides! Look how some people are using Biology (rogue proteins, yo) to make their case!   This will help the students understand protein synthesis deeply so that they could describe the biology around GMOs! It will help them take a stand (on either side of the issue), and have some agency in the world.

Thus emerged the task:

Write a letter to a NM legislator or a US Congressperson, stating your position regarding the labeling of GM foods, encouraging them to either support or block specific legislation. Your letter should demonstrate your understanding of the science behind genetically engineered food, and of the central dogma of molecular biology.

The project rollout plan was great.   “Bring some snack food for Monday. Your choice. Yes, soda is ok. Yes, Chile Cheese Fritos are ok, and in fact, PLEASE bring Chile Cheese Fritos. Yes, you can bring apples.” I kept the subject a bit secret – they just knew that a new project was coming down the pike, and it was staring with a party.

Bring the snack food, they did. We feasted on all sorts of genetically engineered corn snacks & corn-syrup-laden drinks and cookies. While we munched, I shared with them some facts about GMOs, the legislation that has surrounded them, then BAM: “You are eating genetically modified food.”

Their reaction?


Also: <blank stares>

If ever there was a nonplussed group of students, it was them.   Did I mention that these were freshmen? Turns out, I have discovered, that freshmen don’t care about the same stuff that seniors do. Maybe it is the lack of background knowledge. (Or maybe it WAS their knowledge? GMO food hasn’t been shown to be harmful, as it turns out) Maybe it is their youthful feeling of immortality. Whatever the case, pointing out the fact that the food they were eating wasn’t even labeled as GMOs did little to move them.   Sharing with them the project task proved to be an exercise in “Meh”.   Or so it appeared on their faces.

IN MY DEFENSE – I had adopted this 9th grade biology class that very week: the previous teacher had accepted a job elsewhere, and as the school coach who happened to be certified to teach science, I was the logical fill-in.   So in a Friday-to-Sunday period, I designed this project, and went into the class knowing some of the students, but not knowing them as a group.

So, with the tepid-at-best project roll out, I was back to the drawing board that night. What can save this? Do I need to start over? The next morning, I had a conversation with a colleague who had taught 9th grade bio before (thank you, @jennbeck24) and she was not surprised in the least at their reaction.   We spitballed, and came up with some alternatives.

On day two, I spoke with the class: “Give me a signal: Thumbs up if you are into this project idea, thumbs sideways if you are neutral, and thumbs down if you don’t like it.”

Mostly thumbs sideways. Some thumbs down. Only a couple thumbs up.

“Ok – let’s consider options – here they are.”

1) Write a letter to a NM legislator or a US Congressperson, stating your position regarding the labeling of GM foods, encouraging them to either support or block specific legislation.


2) Write a letter to or article for nex+Gen News, explaining why students should or should not be afraid of GMO foods


3) Write to APS, taking a position on whether it should or should not serve GMO food in cafeterias, and from vending machines


4) Your own option (must include writing) that demonstrates your understanding of the science behind genetically engineered food and protein synthesis, and has some use outside this classroom.


We discussed the options, and especially the 4th. I had each student announce which one they preferred.  Several had some really interesting ideas for option 4, especially those who had been not very interested in the project the previous day. Now a new poll – “What do you think of the project now?”

Mostly thumbs up, a few sideways. I’ll take it.



  1. If you have time (I didn’t), run critical friends on your project idea. Make sure the people with whom you run critical friends know something about the age group for the project.
  1. Pay attention to the kids’ response to the project. Had I just barreled ahead, this project could have been an awful slog. Right now, they are into it. The corollary here is that projects can and should be adjusted mid-stream, if necessary.
  1. Choice. Choice. Choice.   (I know this. I know this pretty well. Egad.)



Now that I am at the beginning of a project, I need to be planning the next project.  My intention is to gather a group of students to help design the next project, in a similar way to how I did with seniors in the past. It ought to be interesting, and I can’t help but wonder if it will be more like a focus group than like a brainstorming session, but I definitely want to make sure that I have students involved before project roll-out.



Completing the Square, Starting with Geometry

Contrary to my own experience learning to Complete the Square, which was an entirely algebraic affair, there is now a beautiful geometric analogy to the process.  This is done a lot online, and the videos seem to follow a bit of a formula: show the algebra first, and alongside, show the geometric analogy.  I quickly found three examples on youtube: One, Two, Three.   Seems like the instructors are starting with completing the square like they were taught, but then saying, “hey – here is also a visual way to understand this!”

With some freshmen, I took a slightly different approach.  Thinking that the geometry isn’t just a reasonable analogy, but that it could be a roadmap to the idea, I started with the geometry, then went to the algebra.    Sort of.

To be honest, I started the day invoking some algebra – this was for a geometry class where the students had already seen the equation for a circle, so I started with the algebra they had seen, and quickly took them to where they would get stuck.   Then I started the geometry.


Students quickly answered (3,5), and a radius of 36.  No!  6! 6! 6!

Slide02Students: Uhhh….

There was some casting about on their parts, but really not getting anything that they felt they could hold onto.  So we started into completing the square.


Me: How many squares?

Students: 2!

Me: Orange square is x on a side.  The leftover is 3 units long.  Capisce?


Students worked on this. I had groups verify with each other so that they came to a consensus, class-wide, about the area being (x+3)(x+3), or something equivalent.


Groups did this, checking with partners.  Now a moment of instant gratification – check your work!


High fives all around


5!  No!  25!   I check for understanding all around.


People are getting it.  49 came faster.

Me: you get the idea.  Now let’s do some analysis. (the blue equations are animated in after I prompt for simplifying the black)


In the next slide – students saw only the blue equation to begin with.  The black 25 and 49 come after they have stated what should be there.


Students could kind of remember the 25 and the 49, and did so much better by me going back to the previous slides.  Once they remembered, and we put those in, I reinforced the question: “How do you complete the square if you only have x2+10x ?  Or you only have x2 + 14x ?”    I encouraged them to discuss in partnerships.

And there it was. They created the rule: Take half of the coefficient of x, and square it. Add that to the expression.    Every single partnership.   To reinforce:


Me: Ok – does that work with the pictures?

We went back to the pictures.

One student: With our initial squares, we already have half of the x term.


Now to revisit the initial problem:Slide13.jpg

This took a while.  And no wonder: there are more skills involved.  Combine like terms. Complete the square(s).  Add them to BOTH sides of the equation.  Combine like terms again.   THEN convert to the form from which we can easily discern a center and radius.

What I didn’t anticipate was that last step – to reinforce the notion that x2 + 10x + 25 = (x+5)2

So the last part of the lesson was pretty didactic.

What stands out? The ease with which the students were able to navigate the slides with the visual geometric cues.  Completing the square proved to be really straightforward for them.  The following algebraic manipulation took the longest time.

So there is the next step, if I am to run this again: reduce the “cliff” that occurs at the last slide. More scaffolding to get to that final complicated equation.  I have a few thoughts, but would love to hear your ideas about how that might be a more gradual process that doesn’t require a bunch of me talking at the board, writing stuff down.


Ppt here: Completing the Square