Summer is great to spend time with family and friends, go on vacation, play, and recharge as educators. It’s also an important opportunity to purposefully reflect, learn, and think about continuous improvement with a new school year just around the corner. Here are some highlights from my summer reading, learning, and thinking:

- Many students view being good at math as the ability to “answer the teacher’s questions fast, right, and easily.” But when these students go on to higher mathematics and work as mathematicians, they quickly find the difference between true mathematical thinking and simply being able to follow directions. Math is not defined as following directions.
- We have to invest in our educators, not programs, to fix math instruction. Our own experiences as math learners heavily influence what we do as teachers.
- The math studied in school is “finished,” abstract, and known, which promotes obedience in teaching & learning mathematics. Mathematicians continuously play, create, wonder, ask questions, take risks, test conjectures, fail, try new things, make mistakes, seek connections, reason, and invent what is currently unknown; obedience is not doing mathematics.
- It is the classroom environment, language, and behaviors of the teacher that will instill the proper mathematician habits in students and cultivate a growth mindset for all.
- Students need opportunities to engage in descaffolded mathematical tasks that promote multiple entry points, multiple strategies, and risk taking (makeover tasks/problems from your textbook or search for new ones from sites like openmiddle.com, Illustrative Mathematics, or Dan Meyer’s 3-Act Tasks; routines such as Number Talks and “Which One Doesn’t Belong?” can serve the same purpose, too).
- Children have innate mathematician traits and natural curiosities before entering school; it’s our challenge not to derail into obedience and turn them off to math. How do we create curious teachers around mathematics as models for students and their curiosities?

**The innovator’s Mindset** by George Couros (@gcouros, #InnovatorsMindset)

- If we want students to become innovators and creative thinkers, we must first develop educators to do the same. Innovation is a mindset.
- An important reflection question Couros offers promotes empathy with our students by asking,
*“Would I want to be a learner in my own classroom?”*
- Connect and network with others via Twitter and blogs. There is so much great stuff being shared out there and so many great practitioners to learn from! Start a blog yourself to share your thinking and the great things happening in your classroom. Not only will blogging clarify your thoughts and improve your writing, but someone may stumble upon your ideas, too.
- Inspiring and empowering students requires reflection and examination of how we teach and design lessons – moving from compliant to engaged to empowered.
- Removing the traditional classroom labels of teacher & student in the classroom and replacing with
**“learners”** creates a culture everyone in the classroom is a learner (including the teacher).

It is refreshing that both of these books are written from actual classroom and school practitioners that share dynamic examples from their colleagues in classrooms. In addition, both authors stress the importance of reaching out and connecting with other educators and their open resources via Twitter, blogs, etc. There are so many resources available to us, and it’s about investing in **teachers****, not programs****,** to develop the facilitation of dynamic learning environments. (A shout-out to my colleague Zac Chase [@SVVSDLA, @MrChase] since this book reminded me of several ideas in Building School 2.0: How to Create the Schools We Need, written by him and Chris Lehman.)

I came across a couple of intriguing posts on teachthought.com (@TeachThought) over the summer, too:

How can these notions of constructivism, connectivism, the suggested 12 Principles of Modern Learning, and questions to drive inquiry to form a vision of math classrooms that go beyond checklists of standards, high-stakes assessments, and how we approach homework assignments? In other words, **how can we innovate math instruction and our math classrooms (that productively leverage the iPads and all resources available) for our students?**

**So what?**

I am now excited to start this upcoming school year with new perspective on the tools and resources we have been afforded by the support of our community and visionary leadership. We have an amazing opportunity in St. Vrain to transform teaching and learning with the iPads available to our students on a daily basis. Let’s not squander this opportunity to simply take our “traditional” teaching and learning paradigm and try to simply force-fit it into a 21st century learning model and continue the status quo. Let’s move beyond substitution in the SAMR model to true transformation.

And, math teachers, we have to stop using the excuse, “But math is different…those ideas just won’t work in the math classroom with all the content we have to teach.” Especially if our adopted instructional resources don’t force students to engage in inquiry where **they** are empowered to own their learning and create, it is that much more important we do it on our own and create those opportunities. We have the access to resources, we just need to make the time.

Those are some of my summer takeaways. What did you read, learn, and think about this summer?