How we view the math curriculum influences how we plan for learning in our math classes.
If the curriculum is viewed as content to be covered, then it is understandable that there will be a desire to focus on the teaching of algorithms. I say this because speed of covering content becomes a major concern of a math program with this view of the curricululm. Of all the math skills available to the student, RECALL is deemed the most valuable. In this regard, math lessons tend to be chunked into discrete units and delivered successively.
I cannot speak for anyone else, but my early math teaching experience might have at one time reflected this mindset.
Under a content driven view of the curriculum, I used to:
- Refer to the math textbook when planning my lessons
- Do a diagnostic to diagnose what students know and more importantly don’t know.
- Find pages and numbers of homework that students could work on quietly after I did my lesson. Questions are essentially the same so students are engaged in practice of a similar type of problem.
- The next lesson would often be the ‘next page’ in the textbook. Followed by a note to be copied where I highlighted the steps and algorithm used to solve a specific problem.
- Assessment was essentially 2 or 3 quizzes marked out of 20 or 30, and then a unit test typically marked out of 50. A nice 3 week math unit.
If, however, the curriculum is viewed as contexts to explore, then attention is given to learning of math processes and concepts. In this view of the curriculum, exploration and development of concepts, not recall, is key. Of all the math skills available to a student: questioning, problem solving, proving, communicating and reflecting hold common ground and are all important. This ‘inquiry’ view of the curriculum then lead to math lessons that unfold and link from one unit to the next. Math is presented not so much as a group of discrete and separate units, but instead as a ‘whole’ where making connections from one math concept or context is encouraged and takes place.
Under this ‘inquiry’ view of the curriculum, what I try to do now is:
- Refer to my math curriculum document and develop an understanding of where my students, with respect to math learning, need to traverse.
- Instead of diagnosing math understanding, I attempt to create an environment where the students and I ACTIVATE math thinking. This is usually done using an overarching math inquiry question, a common context as it were, where students work with partners to share knowledge and engage with the problem using their intuitive math understanding.
- Questions for homework are developed from problems students had about the math task they worked on, while with partners. In this regard, the math homework questions students work on are not prefabricated.
- The next lesson often involves a problem that focuses on an area students showed difficulty with the other day. This is then usually followed by a math congress and a highlighting of what we have learned from our common context. On a BYOD note, I can get an immediate sense of ‘what students know’ the night before school because they post their homework electronically, on our learning management system (LMS).
- Assessment is more ‘small scale’ and frequent. Initially I don’t give levels or marks because it is all about activating knowledge and developing intuitive thinking about math. In my opinion, guess and check, and getting things wrong, is an important part of learning in this process and needs to be honoured.
It took me a fair bit of learning and work to get to this point, however. With a lot of help from math mentors. I am certain I still have more to learn. A reality of this whole process is that math inquiry requires solid planning and assessment because you are anticipating and guiding student responses to questions instead of, like what I used to do, anticipating when the unit will be completed.
How do you plan or prepare for math inquiry in your classroom?
How has your thinking about math and the learning of it changed over the years?