That said, I think I can honestly say that my favorite part of the 3rd edition is also my favorite part of the 1st and 2nd editions. Investigations has always been and will always be about helping students make sense of mathematics.
But what does it mean to make sense of mathematics? Isn’t this the goal of every mathematics curriculum? I mean, who would have a goal of not making sense of mathematics?
In Investigations, making sense of mathematics is about having an idea of how to approach a problem and using what you know to figure out something you do not yet know. It’s about pursuing a solution pathway and knowing that sometimes you have to try another route. It’s about being able to visualize quantities, make a drawing, or build a model, as a way of representing a problem or situation. It’s about making choices about what tools to use and when to use them.
Making sense of mathematics is about looking for and identifying structures and relationships of quantities, shapes, and operations and using them as part of a solution. It’s about talking to yourself and talking to others, in order to explain your thinking. It’s about having an idea and being willing to put it out there for others to think about and react to.
Making sense of mathematics is about owning an idea, owning a choice, and owning a solution. It is about having “a live rapport with mathematics,” an old idea from mathematician David Hilbert, discussed in a new way in Tracy Zager’s NCSM session last spring.
Each new edition brings changes – a new look, a different sequence, some new content, a new Routine or Ten Minute Math, an old unit with a new focus or a set of new digital tools. All certainly nice, worthwhile, and important.
But my favorite part of Investigations 3 is what’s not new. In fact, it’s what’s old. It’s the set of goals and principles that, for more than 20 years, have guided our work and placed students and student thinking in the center of the work. It’s the drive to instill in students an expectation that mathematics ought to make sense.