*Investigations*?” My first inclination is to blurt out “That it’s finished!”, despite the fact that the development stage has been over for almost a year. While many aspects of the revision were engaging and rewarding, I’m sure that someday soon I will not cringe when I hear the word deadline!

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.*

### Karen Economopoulos

*Investigations*Center for Curriculum and Professional Development. Her work on

*Investigations*spans all three editions; she oversaw the development of K-2 for the 1st edition, and co-directed the development of the 2nd and 3rd editions. Karen works extensively with classroom teachers, administrators, and school districts in the area of curriculum reform. She is a former K-2 teacher with a special interest in supporting the range of learners in elementary classrooms.

#### Latest posts by Karen Economopoulos (see all)

- Counting is More than 1, 2, 3: Engaging Adults in K-2 Mathematics - August 8, 2018
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I found myself smiling often while reading your post. Thank you for the reminder of what Investigations and good math instruction has always been about and for saying it so well!

Thanks Stephanie! We have learned so much from you and others who work with pre-service and classroom teachers about how Investigations can support student thinking and also be used as a tool for professional learning.

Bravo Karen! This article is a must read for elementary math teachers. Your words elegantly sum our mission.

Mary

K-5 Math Specialist

I am always heartened when I think about the groups of people such as you and your colleagues who, for so many years, have been dedicated to math teaching and learning and that Investigations is one of the tools that supports the effort.

Reading this really put a big smile on my face!

I love how your writing makes clear how Investigations has always and continues to support the Standards for Mathematical Practices from the CCSS. Even before they were the SMPs, Investigations embraced and enacted the kinds of teaching, learning and thinking embodied in the SMPs. This piece reminds me that working in this way with students and teachers to learn mathematics has always been the heart and soul of the program.

Thanks for the good read!!

Yes! While the SMPs are the most recent label for how students ought to interact with mathematics, our long-held belief that all students have mathematical ideas has continually guided our work and influenced our decisions about how a curriculum can engage students in owning their math learning. We so appreciate our long-term, ongoing partnerships with teachers – like you! – who open up their classrooms and offer us feedback and opportunities to learn from them and their students.

I completely agree with the comments above and will add that the SMP support in I3 is one of my new favorite parts of the curriculum.

With every edition I have this feeling of someone “moving my cheese” as I get acclimated to a new layout. As I have been working this summer and school year with teachers, the SMP essays have really served as a practical way to see the practices alive in the work of the lessons. It’s one thing to study the standards and makes sense of them on your own, but it can be challenging to imagine or transfer this to what we are doing with the students. The essays alongside the SMP notes within the lessons and checklists are really supporting us as we digest each MP standard and then carefully observe students at work to see them come alive. While they may have always been there this tool is really illuminating them for teachers and students alike.

Thank you so much for this!

Kaneka, you have so aptly described one of the new features of INV3 and in this case, it IS what’s new about what’s always been old! A priority for the 3rd edition was, in part to illuminate the Standards for Mathematical Practice (SMPs) which we felt have always been a part of the fabric of Investigations. We also wanted to offer teachers more support in making sense of and recognizing opportunities for engaging students in the SMPs, within the content of the sessions, to help the SMPs “come alive.” We are so glad to hear that you and your teachers are finding those supports helpful!

So wonderful to read at the start of the school year! This post is quite wonderful in the way it celebrates the work that many have been doing for decades around the teaching and learning of mathematics, while also moving into the future. It creates a touchstone of sorts that we can read, remember and remind themselves that we want mathematics in our schools to engage children, foster deep thinking, and problem solving.

“Making sense of mathematics” may seem obvious, but quite often what it means and the myriad ways it is incorporated in our math classes can get lost in the day to day hectic lives of teachers, students and classrooms. While we are looking for materials, answering emails from parents, getting interrupted by fire alarms, solving recess issues, drying tears, encouraging excitement, reading this post allows us to stop and think about the purpose of teaching math with Investigations ? A student today said, “Math is about everything!” and when prompted the students in the class went on to explain that we can see math everywhere. When we think about how many, when we notice patterns, when we do some hard thinking, when we figure out steps we want to take based on something we tried yesterday, when we are building a building with blocks, and so much more.The threads that were woven into an outstanding curriculum 20 years ago are holding strong and allow us to teach and learn mathematics in a way that opens up the subject to all and deepens our understanding of what it means to make sense of mathematics.

Katrina, reading your comment made me think about just how busy and all-encompassing teachers’ lives are and how a tool like Investigations can hopefully support rather than complicate. I am reminded of the following comment from a 3rd grade teacher: “Now I don’t have to spend my evenings writing new multiplication word problems for my students because I trust that you, the authors, have done that. Instead, I can spend my time looking at how my students responded to the problems, and thinking about what they know or do not yet fully understand about multiplication.”

Karen, I agree with you 100%. I believe the Investigations curriculum has been and continues to be the best set of comprehensive elementary materials available. I believe this for precisely the same reasons you state. The main focus, purpose and strategies have stayed true to what we believe effective mathematics instruction and learning entail.

I sometimes show videos from my work in District 2, NYC, that are 20 years old, and audiences are so impressed at the student talk, the engaging tasks (mostly from Investigations) and the way teachers encourage multiple models and solutions and compare and contrast them. Isn’t that what we are advocating today? Effective teaching and rich mathematical tasks have the same general characteristics they have always had and we have gotten better at naming and practicing them as a profession.

Another thing I think we have in common is, we believe in children’s capacity to think and make meaning and persist without a lot of showing and telling. We believe in teachers’ willingness to rethink, relearn, dive deeper and we know they care deeply about their children’s learning. We have learned over the years that teachers learn alongside their students when using these materials and everyone seems to come to like math more and feel more confident. Though we want children to succeed on tests, we agree that the most important thing is that they learn to think, reason, problem solve and enjoy learning.

I congratulate you and the Investigations team and commend you for navigating the demands that were made on you while keeping your integrity in tact. Not an easy accomplishment.