I was told the other day from a fellow teacher that they enjoyed math a lot as a child because it was really objective. They recalled problems and questions that had exactly one right answer and enjoyed learning the rules to be able to find that answer.
My response went something like this:
I bet others liked History too as kids since the answers to questions were always right/wrong as well. You know, learn the names and dates, identify key events… There was no room for debate, the facts are the facts, there’s no room to refute the year Columbus landed or which country invaded which other country…
…and I bet many other people really liked writing essays as kids. As long as you can spell, remember punctuation, use the correct grammar and use the right hamburger style paragraph format there would be no red marks on your page. Spelling a word is either right or wrong, there’s no room to argue over if there is a topic sentence or not, or if we remembered a period at the end of the sentence. As long as you included each step, you did well.
…and I bet others really liked Geography too as kids. I mean all you had to know were the definitions of terms, and the capital cities… There was no way to argue a definition or a capital city. Remember these things and you’d do well.
…and I bet many people loved reading in school. All of the questions our teachers asked had answers right there on the page. If you didn’t remember what you read, you could reread if to find the exact answer. There was no debate about if you got the right answer or not, the answers were all there in black and white…
Come to think about it, most subjects were very objective… there was no ambiguity or reasoning or creativity or thinking…just get the right answers and get a good mark!
Now while my colleague stated she completely agreed with my point, she decided to argue back stating something like:
But in math, 2+2 will always equal 4. That’s math!
To which my response was:
…and to many History is about Columbus landing in 1492, not about arguing over the different perspectives or consequences of major events…
…and to many writing is all about the skills of spelling and grammar and structuring paragraphs, not about trying to convince, entertain, explain, or inform…
…and to many reading is about restating what happened or finding key information, instead of understanding character development/motivation or determining the writer’s bias or making inferences…
…and to many Geography is about naming capital cities, instead of looking for patterns of why our planet is the way it is…
At this time we were about to leave the conversation agreeing to disagree, but I thought I would add one last piece:
If we look at any good curriculum and any teacher passionate about their subject, their focus is probably on understanding why things are the way they are. They likely help their students develop by allowing them time to be creative & think critically. They likely focus on developing students to reason and make sense of things. They likely focus on using skills and knowledge as part of the process/product, without isolating them all the time.
While I think most elementary teachers are comfortable with the subjectivity of open questions in reading or writing or History or Geography where there is more than one possible answer, or more than one possible way of explaining an answer, I think many of us have a long way to go in math!
After leaving the conversation, I am now wondering why I believe this to be true? Really what I think this boils down to is our specific knowledge related to the subject. For mathematics, we call this Math Knowledge for Teaching. Take a look below. Which of these areas would you say you are strong in? Which ones do you think you need to continue to develop in (hopefully we can recognize we ALL need to continue to grow)?
The more we learn the mathematics, the deeper we understand the content, the more we understand how the mathematics develops over time, the more we understand which representations and models are the most appropriate at the right time…….. the more likely we will see math as more than a subject filled with distinct rules and procedures all meant to be seen as right or wrong…….. and instead come to see math as an interconnected rich subject filled with thinking and reasoning!
When we start to make these shifts, we come to allow our students to truly appreciate mathematics!
Thinking Mathematically 
Mark, thanks again for sharing your thoughts via your blog. I haven’t entered the realm of blogs–I admire those who have. I think this post points to the necessity to broaden definitions of what math is perceived to be. It’s so much more than 2+2=4. As with any subject area, yes there is product, but there is process as well. And for me, process is, at the very least, equally important to product if not more important (The truth is that I lean to process being more important because process broadens our definition of math) Thank you for sharing your conversation with your colleague. Sometimes, we do need to agree to disagree; but I’m encouraged by the potential of blogs like yours leading to deeper conversations.
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Hi Maria. Thanks for your response. Seems to me that math is more than just each individual isolated skill. Hopefully we have all experienced math as a richer subject them that. As for starting a blog, it is a great way to put into words the things that you believe. There’s something about sharing things publicly that helps with our own learning!Plus hopefully as the school year starts I will start sharing more actual experiences I’ve had with students doing math.
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My students were complaining about a pretty tough math writing assignment this year, so I posted this on my website. It somewhat goes along with what you’re saying.
You don’t go to science to do lab write ups. You go to learn how to estimate and predict future outcomes based on past outcomes using the rules of the world.
You don’t go to social studies to learn meaningless facts and dates. You go to learn how people act and decisions they make so that you don’t repeat the past.
You don’t go to math to learn how to solve for meaningless x variables. You go to learn how to think outside the box and solve real problems that don’t have solutions yet.
You don’t go to english class to learn how to only interpret the book that your teachers have chosen. You go to learn how to read unfamiliar texts and interpret and summarize them.
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I enjoy your analogies! I hope you don’t mind if I use some of them on back to school night. Great way to introduce my approach to the parents.
When I get comments about how math is objective and formulaic, (a closed-minded discipline), I sometimes reply that it is indeed logical, and I too love the naked logic that you find in math. Sometimes, I start to ask if there are infinitely many primes or not, and how would you possibly be able to tell anyway? I love sharing those big ideas, the juicy ones that just draw you in.
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Great idea Debbie.
I might aim to do some math that might prove your point with parents before you engage in some kind of theoretical debate. This way, parents can see that math can be creative, or beautiful…. This can either involve mental strategies to solve a math string, or seeing visual patterns in different ways or sorting atypical shapes with their choice of criteria… then making sure you connect all of their ideas together to learn the big ideas. Engaging in “doing math” means we are doing things that are non-algorithmic, non-linear. Parents need to feel what this means, see that they have learned a lot before they will accept your ideas as beneficial for their children.
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