- 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?

- 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
creates a culture everyone in the classroom is a learner (including the teacher).**“learners”**

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:

- The Difference Between Instructivism, Constructivism, And Connectivism
- 12 Principles Of Modern Learning
- 6 Questions Students Can Use To Guide Their Inquiry-Based Learning

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?**

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?

]]>*…There is no universally agreed upon definition of what constitutes STEM education. This complicates matters and allows each entity to define STEM education in its own way to fit its experiences, biases, and agendas—NCTM included. In some cases this leads to math or science classrooms where students build bridges or program robots, but fail to acquire a deep understanding of grade level (or beyond) math or science learning standards. *

*Could K–12 math classrooms fail to have students engaged and learning the mathematics content and practices necessary to advance in the curriculum, but have integrated some technology, engineering, coding activities, or connections to science and be called a “STEM Program”? If students are not equipped to pursue a post-secondary STEM major and career, is it really an effective K–12 STEM program? My answer is no. No number of fun activities or shiny technology will overcome this fatal shortcoming. *

STEM programming and opportunities for students to engage in engineering design challenges, using design thinking and productive uses of technology, certainly appeal to the Standards for Mathematical Practice & Colorado 21st Century Skills and Readiness Competencies in Mathematics, but math lessons should offer the same opportunities on a daily basis. It’s all about defined learning goals, intentionality in planning for instruction, and a desire to think beyond the textbook. Take LEGOs for example – students can use LEGOs in a very imaginative and innovative way to design, prototype, and problem solve (based on the open-ended task they are given); however, LEGOs can also be used to promote following directions and using prescriptive steps to achieve a predetermined result (did we all make the exact same spaceship?). Which one sounds like a STEM opportunity, and which one sounds like the typical math class? Unfortunately, most will answer this question the same way.

In St. Vrain, our team of STEM Coordinators crafted the STEM by Design document, which focuses on actions and attributes of a STEM program based on beliefs and vision. Most notably, this document is grounded on the notions of * integration in core content areas, direct connections to standards, and focus on Tier 1 instruction*. This work was funded through a four-year Race to the Top district grant, and like any good design challenge, it is a prototype that will keep evolving and improving.

- Who worked harder in my classroom, me or my students?
- What did I learn from my students this year?
- What new risks did I take?
- What opportunities did my students have to
concepts and content in authentic contexts, with or without the use of instructional technology?*investigate, communicate, collaborate, create, model, and explore* - What feedback do I want or need from my students to determine next steps?

Considering changes for next year? Here are some thoughts and additional questions:

*“It is unreasonable to ask a professional to change much more than 10 percent a year, but it is unprofessional to change by much less than 10 percent a year.” – Steve Leinwand*

*“A goal without a plan is just a wish.” – Antoine de Saint-Exupéry*

- What excites me?
- What don’t I know? What professional development or new professional connections do I need?
- What SMART Goal(s) will I set for myself next year? How will I hold myself accountable to the goals I set?
- What matters to me as an educator? What can I control?
- How will I push myself to take new instructional risks outside my comfort zone?

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*A survey last month of more than 2,500 parents found that they generally rank math and science as lower in importance and relevance to their children’s lives than reading. Moreover, 38 percent of parents, including half the fathers surveyed, agreed with the statement “Skills in math are mostly useful for those that have careers related to math, so average Americans do not have much need for math skills,” according to the survey by the Overdeck and Simons foundations.*

Another key quote from the article:

*“Nobody is proud to say, ‘I can barely read,’ but plenty of parents are proud to stand up and say, ‘I can barely do math, I didn’t grow up doing well in math, and my kid’s not doing well in math; that’s just the way it is,’ ” said Mike Steele, a math education professor at the University of Wisconsin-Milwaukee who was not associated with the study…”We need to shift the mindset that math is just some innate ability that has a genetic component, and you are either a math person or you are not, to a conception that everybody can do math with effort and support … and to understand why that’s important.”*

Our words matter. Changing our own beliefs and the language we use with children around mathematics is important if we want students to succeed in this area. Jo Boaler has created and published several resources around the notion of “Growth Mindset” in mathematics to support this change. Instead of saying, *“I’m not good at math,”* what if we begin to say, *“I’m not good at math… yet!”* It gives us as adults room to grow and learn new things, too. And perhaps that’s the best model we can be for our children and young learners.

**Houghton Mifflin Harcourt Algebra 1-Geometry-Algebra 2 (c)2015****Lial Trigonometry, 11th Ed.****Precalculus with Limits: A Graphing Approach, 7th Ed.***(Precalculus & Finite Math)***Stats: Modeling the World, 4th Ed.***(AP Statistics)***Elementary Statistics: Picturing the World, 6th Ed.***(non-AP Statistics)***Larson Calculus of a Single Variable, 10th Ed., AP Edition Updated****Fundamentals of Algebraic Modeling, 6th Ed.***(Intermediate Algebra)*

For **Algebra 1-Geometry-Algebra 2 **(A-G-A), each teacher will receive the following:

- Print Teacher’s Edition
- Classroom set of 15 print student editions

All teachers and students will have a digital license (web and app access) to access the full program, including PDFs and interactive features. The teacher license includes access to all ancillary teacher resources.

For the **“electives,”** (all courses above Algebra 2, including Intermediate Algebra), each teacher will receive the following:

- Print Teacher’s Edition & teacher resources
- Classroom set of 30 print student editions

Students will have access to an eText that can be downloaded onto the iPad mini for offline access.

]]>**HMH A-G-A Adoption Training**(**May 30 & 31**@ Longmont High School or**July 26 & 27**@ LSC Timberline Rooms; 8:00 AM – 4:00 PM; 1.0 credit)**Dance Math**(Friday, June 2; 9:00 AM – 5:30 PM; Sunset Middle School Gym; 0.5 credit)**– CANCELED!****Desmos.com**(Wednesday, June 7; 8:00 AM – 4:00 PM; LSC Timberline Rooms; 0.5 credit)**Developing Number Sense & Proportional Reasoning in Grades 6-8**(June 8 & 9; 8:00 AM – 4:00 PM; LSC Evergreen Room; 1.0 credit)**– CANCELED!****You: The Mathematician**(June 13-15; 8:00 AM – 4:00 PM [8 AM – 12 noon only on June 13]; LSC Evergreen Room; 1.5 credits)**IMP 1 & IMP 2 Training**(July 17-21; 8:00 AM – 4:00 PM; Silver Creek High School Room E206; 2.5 credits)

- 2016-2017: Review & evaluate candidate programs; determine one program for pilot
- 2017-2018: Pilot selected program in 1-2 classrooms per school
- 2018-2019: Implement selected program in all St. Vrain classrooms

Click here to see the adoption committee’s meeting notes and resources associated with this process.

]]>(1) **The role of student-driven questions.** Teacher questioning is important in facilitating classroom discourse and making important connections, yet we oftentimes leave *students* out of the question posing process. Fostering Student Questions: Strategies for Inquiry-Based Learning and Creating a Culture of Inquiry offer some ideas and protocols on how to develop a culture of student-driven inquiry based on questions, justification, and choice. Of course, good questions come from good tasks and learning experiences crafted by teachers. This is where the distinction between ** problems **and

(2) **Intentional Focus on the Standards for Mathematical Practice.** While all eight Standards for Mathematical Practice are important in terms of establishing habits of mind for emerging mathematicians K-12, particular emphasis should be made on two of them if we wish to transform our mathematics learning environments:

**SMP #1: Make sense of problems and persevere in solving them.****SMP #3: Construct viable arguments and critique the reasoning of others.**

If we make strides with these specific practices, our mathematics classrooms will feel and look very different. In addition, the role of student questions fits perfectly with these specific practices. But let’s not just limit these to the mathematics classroom, as these specific practices transcend all content areas and are good habits of mind for everyone within an organization. As a school department/faculty, when was the last time the team made sense of a school problem and persevered in finding a solution? When was the last time adult discourse occurred at a department/faculty meeting around critiquing reasoning and arguments (and not the people making those arguments)? When was the last time a meeting was driven by questions posed by the participants?

If we want students to carry the cognitive load and do the mathematical thinking in our classrooms, then we have to model these actions. As teachers, do we model posing questions around a problem? Do we model perseverance in solving problems, even when a solution strategy might lead to a dead end? Do we model complete mathematical arguments using proper academic vocabulary? If students never see their teachers perform these actions, it’s a tough ask to demand of them without some frame of reference.

Still not sure what this is all about or what the vision looks like? Mark Chubb (Instructional Coach in Niagara) offers some ideas in his blog post “Quick fixes and silver bullets…” that illustrates common practices that suppress mathematical thinking.

]]>- What are the concepts of Enactive – Iconic – Symbolic?
- How do these concepts relate to other educational theories?
- How can the concepts of Enactive – Iconic – Symbolic support the development of mathematical understanding by students?

There is also a document, Development of Number Sense & Computation in Grades K-5, that provides more detail with concept progressions across grades K-5 with specific representations and references from the Common Core State Standards.

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