Progress Through the Five Stages of Deep Learning

In this article, we expand our previous discussion of the five stages of deep learning. Specifically, we explore techniques you can use to accelerate your progress through each stage of your learning. Moving from stage 0 into stage 1 requires different type of practice routines than moving from stage 1 into stage 2, and so on. With each bit of progress, the learning skills you employ need to adapt to your growing level of expertise. Here, we explore what you can do to propel your transition from your current stage of learning into the next stages of your development.

Figure 1: The Five Stages of Deep Learning with Progress Labels

Discover (move from stage 0 to stage 1)

Recall from our five-stage model for deep learning that stage 0, known as unconscious inexperience, is the state in which you are completely unaware of the existence of your target knowledge. You enter stage 1 of learning, known as conscious inexperience, when you become aware of your own ignorance about a particular idea or skill. Let’s refer to the process of moving from stage 0 into stage 1 as the process of discovery. We say that we discover some knowledge when we become conscious of that object of study for the first time.

For many novices, the process of discovery is haphazard and seems to happen by chance. However, if you are training to be an expert, it is useful to create systems and relationships that accelerate your process of discovery in your field of interest. The strategy here is to actively search for new ideas as part of your daily practice. The goal of this search is not to decide on your next targets for deep learning. Instead, the major goal is to gain exposure to topics that are related to your desired expertise. This brings ideas onto your radar that might be useful in later explorations and skill development.

For example, a tennis player might subscribe to a monthly tennis magazine and read every article searching for new ideas. That same player might watch televised matches of top-ranked tennis stars as a way to hone her various shots. She might also work with a coach for multiple sessions each week to get exposed to new practice routines.

Another example of these type of discovery systems can be found in the world of academics. College professors and academic authors routinely read academic articles in their chosen field. These folks also attend academic conferences, sign up to teach classes they’ve never taught before, and read textbooks in adjacent fields from their expertise. All of these techniques are designed to propel discovery.

In order to accelerate your discovery process, develop routines in which you systematically expose the yourself to new ideas in topics related to your desired area of learning. Actively look to discover new facets of your ability that are currently outside your conscious awareness. Every time you do so, you create an option to engage in an improvement cycle and deepen your capacity to learn. Remember, the point of this is not to master the idea the first time you discover it. Instead, the intention is raise your awareness and expose yourself to ideas that might be helpful in the future.

Understand (move from stage 1 to stage 2)

In stage 1 of your learning, you are conscious of your inexperience with the target knowledge. You enter stage 2 when you’ve fully mastered the target of study for yourself. Let’s say that we build understanding when we move from stage 1 into stage 2. In other words, we say that we understand some knowledge or skill when we have conscious control over that knowledge. The process of building understanding does not mean we’re trying to memorize without thought. On the contrary, this type of understanding is built via intense focus and thoughtful practice. The end goal of our work to understand is to capture the target knowledge accurately and completely inside our body and mind.

Building understanding, or moving from stage 1 into stage 2, is by far the most challenging part of the learning process. This transition requires intense practice that includes many plan-act-reflect cycles. In other words, to really understand something, you engage in a iterative cycle of learning that involves a number of steps, including:

Step 1: Plan- Set a target for your learning.
Step 2: Act- Make an attempt to achieve your target.
Step 3A: Observe- Figure out the difference between your attempt and your target.
Step 3B: Reflect- Brainstorm corrective actions you can take to get you closer to your target.
Iterate: Repeat steps 1, 2, 3A, and 3B until you have control over your ability to achieve your target.

Figure 2: The Plan-Act-Reflect Cycle for Building Understanding

Recall that we defined learning as a process of activating brain cells, growing new connections between brains cells, and strengthening existing connections between brain cells. The goal of this work is to hard-wire the target knowledge or skill inside a network of cells that run throughout your brain and body.

When you build understanding, you biologically encode the target knowledge in a network of cells by activating those cells and growing new connections between those cells. That is what is happening as you progress from stage 1 into stage 2. But, each part of this process requires different learning skills. Below, we explore four different techniques you can use to build understanding via plan-act-reflect cycles as you work to transition from stage 1 into stage 2 of your learning process.

To plan, completely digest the target knowledge or skill

Begin your planning process by focusing on your target in it’s totality, from start to finish. Create a mental image of your object of study by concentrating on the whole thing so that you can see yourself re-constructing the knowledge or performing the skill on your own.

One of the challenges of building understanding is figuring out the different facets of the knowledge or skill you’re trying to learn. In your work to discover the knowledge for the first time (move from stage 0 into stage 1), you likely did not fully explore that object. Instead, you simply raised the target into your conscious awareness. But, if you’re going to understand your target at a deeper level, you need to push beyond cursory awareness and begin to perceive the entirety of your target knowledge. By viewing the object of your study as a complete entity, start to finish, you gather information about each aspect and begin to perceive subtleties that may have escaped your initial gaze. This process primes your mind to be able to emulate and reproduce the knowledge for yourself.

One example of this might be found in a young basket ball player’s desire to learn how to shoot a free throw. Before going out to shoot free-throws on their own, that player might watch another more advance player take multiple free-throw shots. During each viewing, the younger player might watch different parts of the shot to perceive what the more advanced shooter is doing with her legs, arms, head, hands, and body. With each observation, the younger player is building a mental image of the entire skill, trying to digest the skill completely before attempting on their own. This type of study is not for a weekend warrior who is simply out on the court to get some exercise. This is the type of study taken on by someone who is focused on improving their ability by studying more advanced players. It’s intense and takes lots of focus.

Another example is that of a college student sitting through a lecture and then going home to re-write a second draft of their lecture notes. The initial lecture is all about discovery: the teacher throws a lot of new material on the board that the student likely has never seen. By the end of the lecture, if the learner was engaged, well-rested, and attentive, that student has moved into stage 1 of conscious inexperience for the large collection of material that the professor spewed into the classroom. When that same student re-engages after class in an attempt to re-write their lecture notes, they begin to build a complete understanding of the knowledge covered in that day’s lecture. This is the process of taking intellectual responsibility for the knowledge presented in class for oneself. In truth, lectures are very poor tools for inspiring deep learning. In this example, I am not advocating that teachers should use lectures as a tool to help students learn. Instead, the point of this example is to highlight how the process of lecture re-writes fit into this model for learning. Assuming your teacher is using a lecture-based model of teaching, lecture re-writes can be very powerful tools to start the process of moving from stage 1 into stage 2.

To act, cut it up into smaller pieces

After you’ve gotten a big-picture view of the object of study and you can begin to imagine yourself re-creating that knowledge or skill for yourself, you move onto the next stage of the plan-act-reflect cycle. In this action phase of understanding, the goal is to divide the knowledge or skill into smaller components. This strategy allows you to focus on each ingredient of your target of study individually.

Most knowledge or skills that capture our attention are complex enough to be interesting and thus are composed of many different chunks of information. By breaking the entire target of study into pieces, you make it easier on your brain. Instead of having to hold lots of new information in your head at one time, you focus your mind on one chunk of information at a time. The goal is to master each chunk individually with your eye on the larger combination.

Let’s think back to our examples from above. The basketball player might break up the free-throw shot into pieces by focusing on each individual body part, one at a time. They might imitate the motion of the legs and hips first, trying to replicate the bending of the knees. Then, when they feel they’ve mastered that piece of the shot, the move onto the head arms, and shoulders, emulating the advanced players posture. Finally, they might focus their practice on the movement of the hands as the ball is released from their grip. With each chunk, the younger player is working to capture the different aspects of the move independently. In practicing each chunk, 100% of their focus is on the smaller piece. After they feel confident they’ve mastered the individual pieces, they begin to connect each of the chunks together into a larger group of coordinated movement.

We can think of the college student from the same lens. In the lecture re-write process, that student might break the entire lecture up into individual chunks of information. Perhaps the lecture begins with a set of definitions, followed by a theorem, then some examples, followed by a proof, with some more examples, and another theorem. The student might set in on creating their own notes of each individual idea, piece-by-piece. For each set of notes, the student is focused on taking full intellectual ownership over the ideas presented. This might mean they re-write some of the language used by the professor and then expand on the ideas by presenting their own interpretations of the material. This can also include making explicit connections to previous material unmentioned by the professor or imagining examples not written by the teacher. At the end of the re-write process, the student might ask how each component of the lecture is inter-related to the others, creating a mental image of the larger interconnections between component chunks in the current lecture. This might also include making explicit connections to previous lectures.

Thinking back to our definition of learning, this process of chunking the target of study into smaller pieces, focusing attention on each individual piece, and then re-combining into a larger whole is designed to build a fully functional neural network to encode the entire skill. When you break the skill into chunks and study each piece individually, you are building a collection of interconnected cells dedicated to that piece of the larger puzzle. By repeating that process for each chunk, you create special space inside your brain to encode each chunk individually. Then, when you combine these pieces together into the larger group, you build interconnections between these distinct circuits. This produces a network of cells and interconnections designed to capture the entire skill or knowledge, from start to finish, via mastery of the individual pieces and successful integration of those pieces into a larger whole.

To reflect, go slow: as slow as you can

Another technique you can use to build understanding is to go as slow as possible. The process of going slow enables you to form a detailed model of each individual piece. When going fast, you might miss some of the more subtle aspects of the skill or knowledge. At increased speed, your brain doesn’t have the chance to fully processed each piece of information in the rush to get through the entire task. But when you slow down, you force yourself to turn over every stone in your search for understanding. This gives a you a much fuller conception of the patterns and contours within the individual components of the target of study.

Beyond perceiving the subtle aspects involved in building understanding, there is another reason why going slow is helpful. Remember that the purpose of the “act” phase of the plan-act-reflect cycle is not the action itself. When you act, you empower yourself to compare your output to the target and to identify gaps in your performance.

That process of observation and reflection helps you identify your errors and make corrections before your next try. When you slow down, you heighten your ability to pay attention to errors and misunderstanding. You can leverage this extra attention to build more precise actions with each new attempt. The point is to create a complete and accurate version of your target, working as slow as possible.

In our example of the basket ball player, going slow might mean exaggerating each stage of the free-throw shot by elongating the time it takes to complete the entire motion. With each repetition, the player might use muscle control to spread out the motion and feel each chunk of the movement individually. The idea is to hone the individual parts and align the initial pieces of the motion more closely with the target. Perhaps this means that the player takes a minute to explore the entire motion before each attempt at a shot.

For the college student re-writing their lecture notes, slowing down might mean the student needs to confirm every bit of knowledge presented by the instructor for themselves. For each piece of knowledge, the student asks: do I understand this in full? If so, how can I document that understanding so that I capture this in my notes? If I don’t fully understand this, what questions come up for me? What am I struggling to grasp?

One of the parts of learning in college that is harder than athletics is that it takes a lot longer to complete plan-act-reflect cycles for intellectual knowledge than for athletic skills. Shooting a free throw takes maybe a few seconds if done quickly. Even for a very slow iteration, that process might last no more than a minute or two. But the individual chunks of a lecture re-write might take 5 – 15 minutes each. When thinking about the entire skill (capturing the entire lecture), that process might take 2 to 4 hours of work.

Not only does understanding component skills in college take more time than component skills in athletics, but it is often significantly harder for a college learner (versus an athlete) to assess whether or not their understanding is complete, accurate, and precise. In basket ball, a player can see almost instantly if their free throw shot is accurate and complete. They simply need to practice at full speed and look at what happens to the ball. But in college, the learner might need expert guidance to answer open questions as well as to identify possible errors in the way they process information. This is where the last technique for building understanding comes in.

As you plan-act-reflect, focus on making repetition easier

In all our work above, we focus our effort on helping you develop techniques to move from stage 1 into stage 2 by building your understanding. This last method keeps your eyes on moving into stage 3 of your learning. Specifically, after you move into stage 2 of conscious expertise, the next stage of learning is to write that expertise into your unconscious memory. To do so, we leverage strategic repetition. The idea is to strengthen your neural network by wrapping the interconnections between your brain cells with myelin sheaths.

When you build a neural network, you are creating a path for electrical signals to travel throughout your brain, activate the appropriate cells, and produce your desired results. By repeated that process in special ways over many practice sessions, your body begins to optimize the circuitry used to encode the knowledge or skill. That is the process of wrapping parts of your brain cell with myelin, which is like an electrical insulator that makes signal propagation faster and stronger. One of the biggest gifts you can give yourself during your process of building understanding is to create mechanisms that set you up to repeat your work more easily in the future. My TLC co-author, Henry Fan, calls this the process of creating a second brain. The idea is to capture your understanding in more permanent and organized storage locations so that you can refer back to your knowledge in future practice sessions.

For sports players who have access to a coach and advanced team mates, this technique is taken care of without much thinking on behalf of the player. If that player wants to recreate their knowledge, they simply ask a more advanced technician to repeat the task and to give individualized feedback on their performance and progress. However, college students are not so lucky. Once you’ve encoded a piece of knowledge in your brain, one crucial step is to make it easy for your future self to access that knowledge again. This is where the process of taking notes can be so critical. When you take notes to capture the depth of your understanding, you literally create a written log of the neural network you’ve constructed to build your knowledge. If you’re doing your note taking well, you can capture questions for asynchronous discussion and also create a custom map of your knowledge designed for your current and future consumption. This process can accelerate your ability to strengthening the connections between brain cells by making it easier to remember and repeat your target knowledge in the future.

Remember (move from stage 2 to stage 3)

When you reach the second phase of conscious expertise in your knowledge construction process, you’ve developed considerable competence with your target knowledge. In this phase of learning, you’ve created a robust network of neurons in your brain and made connections between those neurons with axons. The connections may still be weak (non-myelinated) but they exist to encode your target knowledge accurately and completely. You might not be able to recall the target knowledge easily or perform the target skill without thinking. It may take significant effort to produce the knowledge or demonstrate the skill. But at this stage of learning, you can do so routinely using self-control rather than luck.

In stage 3 of learning, you move onto unconscious expertise. In this stage, you don’t remember how much you know. You can easily recall almost any pertinent part of the knowledge or demonstrate the skill under various conditions. From the outside, your performance looks effortless, graceful, and maybe even super-human.

We refer to the process of moving from stage 2 into stage 3 as remembering which is the process of strengthening the neural pathways used to encode your target of study inside your body. We can also say that when you work to remember something, you are transitioning that knowledge from your short-term memory into long-term memory. Athletes and coaches say this happens when you build muscle memory: it’s as if your body knows what to do without the need for your brain to give directions. When you learn how to remember something, you go through a process of wrapping myelin sheaths around the brain cells that encode your target knowledge and thus make recall faster and stronger.

Suppose that you want to remember some piece of knowledge or a new skill. To do so, you can strengthen your existing neural network using repetition. A natural question that arises is: what type of learning strategies are effective for repetition? A related question is: what type of repetition strategies result in more shallow learning? Below, we explore some effective research-based strategies for using repetition to produce deep, durable learning. We also highlight some strategies that result in shallow learning. All of this work is based on the book Make It Stick: The Science of Successful Learning by Peter C. Brown et. al.

Focus on effective strategies for remembering

  1. Retrieval practice: recalling facts, concepts, or techniques from memory.

    The act of retrieving knowledge from memory has the effect of making that knowledge easier to recall again in the future. To be most effective, retrieval must be repeated again and again, in spaced out sessions, so that the act of recalling knowledge requires cognitive effort rather than becoming a drill in mindless recitation. The more cognitive effort required for retrieval, the greater your retention will be.  

  2. Distributed practice: space out practice sessions over many days, weeks, or months

    Practice is far more effective when it’s broken into separate periods of training that are spaced out. When learning something new, create learning habits in which you practice over many days, weeks, or even months. Ideally, you might create training periods that occur on a daily basis spanning many weeks.

  3. Interleaved practice: mix different ideas together as you do you retrieval practice, each time in a different order

    When studying a set of ideas, learning is much more effective if you interleave different ideas during your study. To do so, you want to work on multiple skills at the same time. Contrast this with block practicing during which you focus on only one skill at a time.

    When you engage in interleaved practice, be careful not to focus on component skills in discrete chunks. For example, don’t practice one definition for 30 minutes, then moving on one theorem for the next 30 minutes, and then finish by analyzing one example for the last 30 minutes. Instead, mix each component skill together during your practice. First test yourself on a definition, then solve the problem, and then state a theorem. Repeat this cycle in a different order. Mix in materials from previous classes and reshuffle each idea so that you never study the same material in the same order. Interleave your practice so that each time you retrieve an idea, you have to activate your memory and think critically about what you are doing.

  4. Varied practice: frequently change the tasks you are working on.

    During your learning sessions, change your tasks frequently so that you constantly confront novel instantiations of the knowledge you’re trying to build. Instead of solving a single problem or answering the same question multiple time, include many different problems that focus on the topic you want to learn. Try to choose diverse problems that test different aspects or applications of your target idea.

    A great example of this is described in a famous bean bag study in which a group of eight-year-old children practiced tossing beanbags into a bucket in gym class. Half of the kids practiced tossing bags into a bucket three feet away, never varying the distance of the bucket during their practice (not varied). The other half of the children practiced tossing their bags into buckets that were either two feet away or four feet away, where the distances changed during each practice session (varied practice). After twelve weeks, the kids were tested on tossing a bag into a bucket that was three-feet away.

    The top performers were those kids who engaged in varied practice on buckets that were either two or four feet away. This was true even though these students never practiced on a bucket that was three feet away. By having to vary the type of practice they did, they developed a more diverse set of muscle controls and proprioceptive skills.

    When you vary your practice, you develop skills and knowledge targeting different dimensions of the knowledge you are trying to build. This leads to a richer and stronger neural network and thus inspires deeper learning.

  5. Embrace difficulty: when learning is harder, it’s stronger and lasts longer.

    There is an inverse relationship between the ease of retrieval practice and the power of that practice to entrench your learning. The easier it is for you to retrieve your new ability, the less your retrieval practice will benefit your retention. Conversely, the more effort you have to expend to retrieve your desired knowledge or perform your new skill, the more the retrieval practice of will result in long-lasting learning.

Avoid shallow-learning strategies that lessen your ability to remember

  1. Avoid block practice

    Block practice is the rapid-fire repetition of a single skill or idea you are trying to burn into your memory. This is the conventional wisdom of “practice-practice-practice” on a single idea or skill until you’ve fully mastered that skill.  

    A great example of this would be to spend an hour focused on trying to learn a single definition from one of your courses. During that time you focus only on that idea. While blocked practice seems enticing as a strategy, it is actually a very inefficient method of committing an idea to memory. This is partly because blocked practice doesn’t sufficiently challenge your brain.  

    If you test yourself on an idea and then retest yourself two minutes later, you haven’t given yourself a chance to forget what you just studied. When you re-study that idea after only a small amount of time, you are not creating new neural new pathways or strengthening your long-term memory. Instead, you are mindlessly regurgitating the idea you just studied. Remember, the harder something is to do, the more likely it is that you are engaged in deep learning.

  2. Avoid rereading text

    Rereading text is the process of repeatedly reading your lecture notes, textbook, or homework solutions. This also includes the process of re-watching an online video or highlighting texts that you’ve already read. This method of study is unproductive from the standpoint of deep learning.

    When you reread a text, you are not actively testing yourself on the ideas from that resource. Instead, you are heavily relying on the author’s knowledge to guide your thinking without actively producing thoughts of your own. This is analogous to working out at the gym using a spotter. When you re-read text, you are effectively lightening the load by having the author carry most of the heavy weight. Don’t spend your precious time on this relatively mindless activity. Remember, deep learning is hard and should require active engagement.

  3. Avoid massed practice (i.e. avoid cramming)

    Massed practice is learning that occurs with no intervals or short intervals between successive bouts of learning. Such practice is designed to complete many hours of studying in one session. This might be followed by a short break and many more hours of studying on the same topic.

    A great example of massed practice is the strategy of cramming in which you wait to study until the days right before a major due date. Then you binge study and try to learn all the content at once. This strategy sometimes produces decent tests scores but does not result in durable learning. In fact, while you may be able to recall your learning in the few days after a massed practice session, these ideas are quickly forgotten and you need to relearn this knowledge if you want to use it in your future.

    This strategy is very inefficient. You aren’t spending enough time to encode the ideas in your brain, make mistakes, correct your mistakes, and then try again over many days. Massed practice results in shallow learning that makes it harder to remember the new knowledge you targeted far into your future.

  4. Avoid one-off problems

    One-off problems are problems that you solve once and never think about again. Many times when solving a one-off problem, you might write your solutions on scratch paper, fail to methodically track your work, or never create a system to capture the thought process that lead to your solution so that you can access your work at a later date. Instead, you care only about the answer to the problem. Once you get your answer, you move on and don’t look back.

    Many young math or engineering students view assigned homework problems from this paradigm. The thinking goes like this: I want to earn my college degree. To do so, I must complete this class. I want to succeed so I will try to get an A in this class. My professor says that my grade is based on graded homework and three exams. In order to get an A in this class, I will try to get an A on all my homework assignments and on my exams. To get an A on my homework, I have to get the right answer to all to the problems on my assignment. Because getting an A is what is important, I need to focus on getting the right answers to each of the problems. As long as I get the right answers, I am going to succeed on my homework. With this type of effort, I will most likely also succeed on my exams and in this course. If I just repeat this strategy every quarter, I will earn my degree and go on to have a very successful college career.

    From this perspective, it is easy to understand the feeling that a problem can be discarded after you’ve found the right answer. Following this logic, it makes sense to solve a problem once and never engage in retrieval practice or repetition. However, this is a less-than-useful strategy. Remember, just because you understand doesn’t mean you can recall or remember, especially under pressure. One-off problem solving is a classic example of a focus on transient understanding rather than durable learning. Sadly, many college teachers create policies that incentivize this type of short-term thinking instead of a focus on deep learning.

Sustain (move from stage 3 to stage 4)

The final stage of learning happens when we begin to share our expertise with less-advanced learners. This process is nuanced and deserves more attention than I can give in this current post. In future posts, we explore more about how to sustain your progress by searching out teaching and mentorship opportunities as part of your learning processes. Learning how to sustain your progress involves tapping into your intrinsic motivations, building highly effective learning teams who are invested in your success, and engaging in peer instruction as often as possible. We explore all these topics in future posts.

Community Challenge

1. In this post, we refine our five stage model for deep learning. Specifically, we explore techniques designed to help you progress from one stage to the next. Think about something you feel you’ve learned deeply. Think back to your learning process and make connections between what you experienced and the techniques discussed in this blog post. How do these techniques show up in your lived experience building expertise?

2. Think about your current major in college. Outside of taking classes, what other systems do you have to discover new information about your major and your desired career path? What new systems or relationships could you build to propel your discovery process and raise your awareness outside of taking classes?

3. Think about your current system for building understanding from lectures in your college classes. How do the techniques discussed in this post relate to your methods? What new ideas did you discover in this blog post? How might you refine your ability to build your understanding and how does that relate to the reading you’ve done here?

4. What is your favorite way to help you remember material from your college classes? Here, I don’t mean short-term memorization? I mean, what techniques do you use to make your memories sticky? What type of study skills do you use that help you remember something months or even years into the future?

5. Use your own words to describe each of the five most effective strategies suggested in this article. Try to recreate what you read from memory. Seriously. Put a timer on for 5 minutes and try to write as much as you can about the strategies that empower deep learning. When the time goes off, go back, read through that section of the article again and correct your mistakes. Then cover your work, and try to do that again.

6. In your own words, describe the four less-than-effective strategies suggested in this article. Leverage retrieval practice to test your memory and try to build your ability to remember each of these strategies.


12 thoughts on “Progress Through the Five Stages of Deep Learning

  1. Because you’ve published this without a paywall (although you earned all the flowers, and deserve the $$) , I’ve been able to chew on it for a long time!
    Thanks to your open access authorship… I know you know, this work “pays” off in human empowerment down the “line”. finite quarterly earnings << infinite community investments

    One idea I see valuable here, hidden before the Discovery Stage is a Recovery Stage where students are inspired (through story telling by their teachers & peers & communities they are in) then provided the guidance and opportunities to….

    1) reclaim what's been lost and stolen from their learning and curiosity
    2) craft various mindsets to affirm themselves and the people in their lives
    3) heal from grades
    4) read and draft their own fav problems list that hopefully span longer than the year ie.
    5) draft goals & horizons of focus from your taxonomy of significant learning
    6) understand and apply your various types of reading post!

    reminding myself, at this stage in my life, the most important teacher for me right now is myself!

    Liked by 1 person

  2. I love this comment Henry. The concept of recovery and healing is a central part of what I do in the class and I don’t think I’ve really articulated that as clearly as you are here.

    I love the idea of tracking questions as Forte does in that post. This is related to the book “The 7 Power of Questions” by Dorothy Leeds. In fact, in my classes now I teach students how to be very deliberate in writing, tracking, capturing, organizing, and revising their questions. This is related to the two minute rule that I discuss in the post below (see the content under Step 9):

    You’ve got a really fun idea in your writing here about doing that deliberately for different problems that map onto different levels of the horizons of focus model.

    As for your line: “reminding myself, at this stage in my life, the most important teacher for me right now is myself!”…

    YES! I have the meme in my syllabus: “Math cannot be taught. Math can only be learned.” The same is true for anything else you set your mind to. And you are a very sophisticated learner. You are your most powerful teacher that will ever exist in your life (assuming you have access to a good library of books and that you have the time to study them).

    Remember that this system is harmful… The entire infrastructure is designed to project a deficit lens on students. It’s designed to center privilege and to make it very hard for students from non-academic backgrounds (believe it or not, I group myself in this category for many reasons) to rise to the top. But, you are thriving despite the harmful design of this system. You are building transferable skills. You are figuring out how to learn in a system that is designed to manipulate your behavior and force you to comply to harmful policies. I see genius in you Henry. I know you’re going to accomplish anything you set your mind to. You are ready for whatever next steps you decide on.

    Ok… I’ll stop now. I hope we can connect over the phone sometime this week or next (Probably next week because I’m preparing for a talk this Friday).


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