Remember: 3 weeks ago, our Math specialist Sunil Singh started our new blog series “Expert talks” by sharing his view about Decision-Making mathematics for the new millennium.
It will also be the starting point of our brand new “Our expert answers” video series: Sunil will follow up with a chat where he’ll be developing his ideas and talk around your comments, so please feel free to get involved, and don’t be shy!
Common Core State Standards for Mathematics
To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.” These Standards are a substantial answer to that challenge.
The entire 90 page plus document of the Common Core has its entire philosophy for mathematical understanding reflected in the passage above. For far too long, students and teachers have been navigating the mathematical waters like a tourist cruise ship, trying to cover much territory with little time for deep exploration of neighbouring islands. As a result, much of the knowledge accumulated by students has been vague and cloudy–lacking sufficient memorability.
The only way to achieve an internalization of mathematics that has its inner workings tattooed to the mindset of children is not just one long visit to these wondrous habitats of numbers and patterns–but repeated encounters…
In other words, be a traveler not a tourist in the land of mathematics.
Repeated dives and digs of measurable and meaningful depth is not just the best way, it is the only way. Archeology is basically about recovery and discovery of interesting artifacts and learning more about our connected histories. The learning of mathematics then, is more akin to trying to be like Indiana Jones–having an insatiable appetite for knowledge that is, above all, deep and illuminating.. A cursory one time stopover at something, for example, as mathematically rich as Pascal’s triangle will do very little to internalize the mathematical experience as the exploration will be brief and shallow. It is only through patient submerging will students encounter connected roots to other mathematical ideas. And, I suppose that leads us to thinking about what kind of mathematical learner do we want now–and for the rapidly evolving future?
The best way to answer this is by understanding that we need students to be comfortable and excited about the Why questions in math? Previous curriculums focussed almost exclusively on unsatisfying What questions. These are only fragmented shards of mathematical investigation and history. Their level of disconnection is articulated by the general dissatisfaction and misunderstanding that students have left high school with over the last quarter century–at least.
Here are the qualities that the Common Core strives to nurture and inculcate for success in the Why Journey of Mathematics:
- Curiosity to begin and endlessly inquire
- Creativity to enjoy and play
- Patience to navigate the hard work of digging and scavenging
- Resilience to handle missteps, wrong turns and failure
If this is what we desire, what does the journey really look like? It’s definitely not straight, quick or smooth. This is the road less traveled. Currently, most of the mathematical pilgrims are relegated to sterile paths of memorization, trickery, and unhealthy acceleration. What will greet almost all of them in the end is a completely false portrayal of mathematics–which invariably means a false understanding of mathematics.
Every critical discovery in math has come from a journey that was filled with misunderstanding, mistakes, wrong turns, frustration, locked doors, dark alleys and mental exhaustion. Several centuries of such resilient-building experience are often required for solutions to problems. As such, our students need to be trained for a marathon; not a 100m sprint.
How does the Common Core correct this problem? How does it safely steer students–and teachers–into this rigorous,but utterly delightful, mathematical sojourn?
Well, it all starts with even a question like 32 – 17. No contrived narratives involving loss of fruit, cookies or coins. Simply the subtraction of two-digit numbers. The way that I “learned” to do these questions was subtraction involving borrowing. Don’t be fooled here. I never really learned what “borrowing” actually meant, I just learned of a method to subtract numbers without a calculator.
Whatever was happening between 32 and 17 was of no interest to me–because it was no interest to my teacher. Naturally, “15” is the answer here. And, students are expected to do dozens of these questions rather quickly to only complete the goal of acquiring an answer.
The Common Core wants to encourage students to look at this question with a new set of eyes.
To turn this question, first of all, into an addition problem–17 + ? = 32. There is an important landscape to see now if this question is posed as a “gap to be added” and there is, perhaps, a purposeful slowness to our emerging observations. The gap is now gaps.
17—+ ?—-20 ————–+ ?————— 30—- +?—–32
This is what is being encouraged to be explored–the critical multiples of 10 that anchor these gaps. Locating important base ten markers that make addition or subtraction easier. We can easily see that we need 3 to get to twenty, a 10 to get to thirty, and another 2 to get to our goal of thirty-two.
3 + 10 + 2 = 15
This solution is totally missed in the traditional algorithmic approach. And, what is the more important takeaway here is the initial understanding of how vital “happy”/”safe” numbers like multiples of 10 are in learning mathematics with creativity and playfulness.. The full dividends of this kind of deeper internalization/ownership will constantly be reaped as students progress through their learning of mathematics. These ideas and how they relate to the Why Journey of Mathematics will be explored in greater detail in my first webinar soon.
Math Specialist and Buzzmath expert
Next time: Portrait of a Young Artist: How To Release The Mathematical Genius In Everyone!