What if most activities in school asked students to “reach and defend a conclusion”?
- in Math, about quantitative or geometric relationships, about measurements of worldly phenomena, etc.
- in Music, about the effect of a melody line, about a particular mix of instruments, etc.
- in English, about effective use of language or metaphor, about storytelling techniques, etc.
- in Visual Arts, about the effective use of color or negative space, about how a work can be interpreted, etc.
- in History, about a set of events, about relationships between societies, etc.
- in Physical Education, about the effects of various activities on the human body, about the effectiveness of various strategies in a sport, etc.
- in Science about whether two measurements are related in some way, why they might be related, the consistency with which they seem related, about cause and effect, etc.
What might our schools look like under such an approach?
- The focus might shift from “reporting facts as presented by others” to using facts to support or refute a conclusion, to debate, to reason.
- Schools might feel more student-centered and less teacher-centered when students are regularly being asked to form and defend their own conclusions in every subject.
- The division lines between many subjects might blur. An activity for one subject can involve skills learned in many others – so much so that teachers would find it beneficial to focus on “integrated” activities most of the year.
- Students might work on fewer total activities in a school year, but each would have greater depth and involve multiple subjects and teachers.
- Skills, concepts, or facts can be introduced in many ways (traditional and/or progressive), leading up to a “reach and defend a conclusion” opportunity – where students integrate and demonstrate mastery by applying what they have learned in new contexts.
So, where do numeracy and mathematics fit into the above? Everywhere. Anything that can be quantified is potentially useful in either supporting or refuting a conclusion.
Younger students might use less complex quantitative justifications for their conclusions than older students, just as they are probably also using less complex reasoning and syntax in communicating their conclusions. That does not mean we have to base activities for younger students on simpler topics, only that we should probably assess what they produce using different rubrics. This opens up possibilities for activities that could be shared across grade levels as well as across subject areas.
I wonder if, under the above scenario, math teachers would no longer be asked “when I am going to need this?” Instead, many activities would probably generate questions like “How can I model data that looks like this?”, or “I can defend my first two statements, and it feels like I should be able to defend my third – I just can’t quite figure out how to get there.” This would become student-led learning, not just student-centered learning.
By asking students to use quantities to support or refute conclusions, we are asking them to “understand” in addition to “report”, or “calculate”, or “graph”, etc. The quantitative ideas, approaches, and tools we teach them would serve an immediate greater goal: they are being learned both to help them understand a situation better and to defend their conclusions about it more effectively.