Just Teach Them To Solve for X

A few people have asked me to keep posting to this blog instead of just consolidating.  So, I'm keeping this bad boy around, but I'll start posting these to my other blog as well. Incidentally, before writing this post (or looking at any comments on blogs), I created a video yesterday that is on my personal blog today dealing with this issue of metaphor. I want to assure you that none of this is ever meant to demean, disrespect or insult anyone - just provoke thought.   

Gertrude the Cognitive Acquisition of Newly Developed Youth Learning Achievement of National Data (CANDY LAND) Specialist approaches me in mid-lesson.

"Your schedule says 'math block' right now and I see your students sketching pictures."

"They're creating metaphors for the concept of 'x.'  So, they start with the picture and then describe the process using the metaphor."

"Why not just teach them to solve for x?"

"I want them to understand how variables work.  Most of them have no idea that 'x' isn't simply a magical number, but actually an independent variable.  If they can't understand how 'x' is used, how will they understand how it is used in life?"

"Look, I see kids drawing pictures of tools and bridges and revolutionary figures.  Why not just teach them to define and use 'x' instead?"

"Metaphors are how we as humans make sense out of the abstract.  It's the bridge between pure abstraction and the concrete, terrestrial reality we experience.  It's used by children and philosophers alike to grapple with a complex universe."

"I don't mind when you have the students replace the slates with paper, Tom.  That's fine with me.  I get it. They can go back and look at previous work."

"Yes, but you miss the full potential of paper when we simply duplicate how we used it with slates.  The genius of paper is how we can use it to construct knowledge rather simply copy processes."

"Your job is to teach them truth.  Cold, hard reliable truth.  Metaphors are messy and muddled and confusing - like a scavenger hunt through a swamp. It should be like clockwork.  Mechanical.  Bits and pieces as clear as day."  I find it odd that he uses two or three metaphors himself to make sense out of his own theory of knowledge.

"What if learning is messy?  What if confusion is the process that leads to clarity?  What if simply memorizing a computational practice does little help students understand how a variable works?"

"Are you arguing that we should make math more confusing?"

"The world's greatest teachers were often confusing.  They understood that truth involves metaphors."

"Like who?"

"Let's start with Locke, Rousseau, Plato, Erasmus, Jesus."

"You aren't Jesus, Tom."

"Good point."

"Look, it's just that metaphors are dangerous.  There's too much room for confusion."

"That's exactly why we need them.  Life is dangerous.  Learning is dangerous.  A bad metaphor can launch a war.  I want my students to know this.  I want them to see that language shapes our perceptions of reality."


  1. Wonderful!

    OK class! Deal with this! Intelligently! And don't be scared of the math. By the way, any idea what grade Mr. Spencer teaches?

  2. Pre-algebra!!!

    I am up to my neck in values of "x".

    Mr. Spencer, tell me more about your metaphor assignment. I have classes full of students who want to use "shortcuts" to solve equations, with no understanding of why it works, or when it might be used (heaven forbid) in real life.

  3. Mr. Spencer, I really enjoyed reading your post on your blog, but this was my favorite. Your metaphor assignment was so different, but it made a lot of sense. Variables are a hard concept for some students and you made a fun interesting way of understanding them. I love your blog!

    -Nicole Kelley (Student in Dr. Strange's EDM310 class)

  4. Anonymous9:25:00 AM

    Great post Mr. Spencer! You brought up a problem that I discourage me from learning the full potential of math in high school. I simply was not looking at the “X” as an independent variable just as something I needed to solve and couldn’t understand the BIG PICTURE perspective because my teachers never seen the big picture their selves. I wish my past math educators used metaphors in my math class because it would have spark curiosity which in turn would promote learning. Thank once again for this post!
    ~EDM 310 Christopher T. Reese

  5. Mr. Spencer, I love your blog posts! Like Nicole said above me, this was my favorite! The best part was when the person that was "downing" the assignment began using metaphors! I loved it. It was a very innovative way to teach variables!

    Hailey Rascoe(Dr.Strange's Edm310 Class)

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  7. Mr. Spencer,

    I am a student at the University of South Alabama in Dr. Strange's EDM 310 class. First of all, I really enjoyed this post and I feel as if you have it figured out. These things never occured to me until I got to college and I took biology. It is so hard to just memorize facts and steps when I don't know what it means. It is definitely important to know both. I believe doing so will prepare students for many different situations and help them to excel in college. You have really great ideas. I'm impressed with the way you were able to transcribe these ideas into words.. VERY cool!

  8. Hello, I am from Dr. Strange's EDM310 class. I am glad you posted this because it made me realized that there is more to metaphors than meets the eye. Dr. Strange said as teachers we need to "Bring our brains and turn it on." Metaphors take us out of our comfort zone and into different aspects of learning.

  9. I love this post! "Metaphors are dangerous!" Computers are dangerous which is exactly why students NEED to be taught the values as well as the dangers presented through them. I think its great that you can evoke your beliefs about computer education programs through the use of metaphors. Awesome!
    -Jameson Branch, EDM310

  10. This is a great post. I love that you can always find funny acronyms to get a point across. The value of "x" is constantly changing so why should we let it = the same when teaching. It is a great idea to let the students pick the value on each different problem. THis is really cool

  11. Hi Mr. Spencer! I am a student at the University of South Alabama in EDM310. I really enjoyed exploring your blog and this post happens to be one of my favorite! I feel like I can relate with the math. I think the metaphor assignment was a great idea. I am going to try and use and apply it. I'll keep stopping by your blog and checking it out!

  12. Hi I am a student in Dr. Strange's EDM 310 class. This is a great way to teach children!! Life in general is confusing so children need to be exposed at looking at everything in life from several different angles; so I believe that metaphors is an excellent thing to teach children.

  13. Hello,
    My name is Amelia Platt and I am one of Dr. Strange's EDM 310 students. I loved this post. It is so true in life we are taught some of the most useless information. When we teach a child a metaphor we are teaching them to look at the bigger picture and make them truly think. this IS SOMETHING Dr. Strange has us do a lot which is think. We do sometimes miss the point of what we are suppose to do, but with his guidance we make our way back and figure it out. Children need to learn metaphors so they will not be so lost in life. This is something I will take with me and apply to my teaching. It makes my kids and myself " Turn our brains on" and will keep me and the kids on our toes.

  14. Hi. My name is Brittany Schneider and I am also in Dr. Strange's EDM310 class at the University of South Alabama. This has been my favorite post by far. I love your use of metaphors and sarcasm in your posts. I also like your teaching style. You think outside of the box, as well as keeping your students interested without bribery and blame. I aspire to be a teacher without being angry, accusatory, and rigid. I believe there is a way to keep control of your class while keeping the students engaged without the use of total fear. Thank you for sharing.

  15. This was an excellent post! I love the view that you have on metaphors and encouraging students or people for that matter to think beyond the norm. Most people cling to structure because it is very easy and doesn't require much but as you said learning is RISKY and using metaphors or learning beyond the structure many classrooms offer is well.. messy! I couldn't agree more that we need to be challenged and we need to use our creativity rather than memorizing cold hard facts and then marking a,b,c, or d. Creativity allows freedom in learning and we should embrace it instead of run from it due to the fear of it's messiness!
    -Carrie Tucker, EDM310- University of South Alabama

  16. Hi Mr. Spencer! I really appreciate this post. It is an entertaining way of making the point that you can't just take things at face value. There is a message behind your post and like Dr. Strange says, we need to have our brains turned on to understand!

    -Haley Riviere (EDM 310)

  17. Mr. Spencer,

    Using metaphors to teach variables in math was disconcerting to me at first, but after reading the whole post, I can only hope that your students appreciate the approach that you are taking. The students that you reach will not only learn their subject, but will learn how to think on their own.

    Rachel Ward (EDM310)

  18. Mr. Spencer, thank you for challenging students to think outside of the box and to challenge all to learn and not just memorize. Learning is truly amazing and we have so many opportunities to think objectively and creatively. We are to understand what it means to educate and to be educated ourselves. Thanks for your thoughts!

  19. Hello! I am a student from Dr. Strange's EDM 310 class at the University of South Alabama. This is a great blog post. I think its fascinating the metaphors that are being used to show the students that the answer is not always what it seem. I have had to learn this the hard way. Thank you for sharing.

  20. Hi Mr. Spencer, my name is T.J. Vigneulle i am a student in Dr. Strange EDM310 class at the University of South Alabama. I really like how you kept saying x doesn't just have to be for math because we have problems we solve in everyday life. Keep encouraging your students to have open minds to everything.

  21. Mr. Spencer,

    My name is Brittany and I am in Dr. Strange's EDM 310 class. First of all I love reading your blog and have just recently found out you have two so I will be looking for your other one. By far, this has to be my favorite post. I love math and although we can use metaphors for many other aspects of teaching, I think starting with the subjects students tend to shy away from is a great place to start. I personally was taught in school that this was the way to do it because the teacher said so. I was never given a reason or explanation just a formula and a piece of paper. Although some things are hard or "dangerous" to explain, we as teachers should feel obligated to try and try our hardest. Simply not explaining and not making them think is more dangerous if you ask me. Thank you so much for all of you post.

  22. Hi Mr. Spencer,
    My name is Carlis Howze, and I am in Dr. Strange's EDM310 class. I loved reading this blog, and it made me think more into metaphors. I see that you said, "Your job is to teach them truth. Cold, hard reliable truth. Metaphors are messy and muddled and confusing." I agree with this point. I believe that metaphors shouldn't be used to a certain extent. They can be dangerous and if misused, can confuse an intelligent person. If used properly, metaphors can actually help a person understand a problem more clearly. Loved the blog though!

  23. Anonymous9:43:00 PM

    Mr. Spencer,
    My name is Ashley Goodwin and I am in Dr. Strange's EDM310 class. I really enjoy your blog posts, this being my favorite so far. I really like the fact that you address not only learning a formula, but also a life lesson. I think that is so important because students usually want a shortcut and teachers need to be there to teach them other ways and let them discover other ways of "problem solving".

  24. Good blog as always Mr. Spencer. I loved the way you describe the use of metaphors to the everyday workings of life. I agree that students learn from a more Grey approach to learning and not one that is set in concrete. Students need to be able to figure out how to get to a particular answer. This doesn't happen if they do not know how to go about doing that. I'm in Dr. Stranges EDM310 class at the University of South Alabama.

  25. I like this about the metaphors because to individual students metaphors make sense more than just telling them what "x" is. When you tell a student that an "x" is involved in math it is enough confusion in itself. Students that can provide a true metaphor for what "x" is can grasp the concept of how it is used.
    (Dr. Strange EDM 310)