Based on this vision of the St. Vrain Learning Technology Plan, how are we doing? Yes, we have the devices in our students’ hands (1:1 at secondary), ensuring access and equity. Yes, our new instructional materials adoptions are more digitally-based, packaged with dynamic content. Yes, we have Schoology as a learning management system for workflow, communication, and assessment. And yes, we have the Google apps suite available for staff and students. We have checked the boxes that earned us the distinction of a top 10 district for digital curriculum and integrated technology use in the country two years in a row. The question, however, is around how these devices and tools are being used: **Are our students digital consumers or digital creators?** (This can also be described as the digital use divide, as defined in the National Education Technology Plan.*)*

True, digital instructional materials in mathematics offer features and supports that no print textbook will ever provide. Seeing animations of concepts and relationships is much more likely to stick that arduously performing the same tasks with paper and pencil. Students getting instant feedback and help supports with digital assignments provide on-demand help and reteaching opportunities instead of having to wait until the next class period. But these value-added features still describe a student consumption-based model of approaching content; we’ve simply substituted print, static resources with digital, dynamic resources (remember the SAMR model?). So how do we move up to Modification and Redefinition and how might we support our students in transforming the school experience? The answer is not quite that simple in practice: *have them become self-directed content creators using the devices and suite of tools at their fingertips.*

Math educator Michael Fenton did an ignite talk in 2014, Technology and the Curious Mind, urging educators move away from **Indifference, Consumption, Competition, Isolation** to **Curiosity, Creativity, Collaboration, Conversation** with use of technology in the classroom. In 2015, Rick Wormeli published Moving Students from Passive Consumers to Active Creators, where he claims, “this is a call for more project-based learning, integrated learning, and inquiry-method across the curriculum. These three methods provide more opportunities for true student creation than simply listening and repeating content.” In era where a student can simply Google information just-in-time instead of relying on textbooks and teachers in classrooms, students need to engage in tasks where answers cannot simply be Googled (trivial facts) or solved by Photomath (procedural, rote exercises). Curious about project-based learning and have no idea where to start? It’s okay, anything new can be scary and lead to more questions than concrete answers, especially since most of us grew up in a traditional educational setting from elementary school through college (I sure did!). But since Google and Photomath are here to stay, the old paradigm of just-in-case education needs to be transformed using just-in-time technologies and resources. Let’s figure this out together, brainstorm, fail, succeed, and learn from each other, just like we expect from our students on a daily basis.

Resources:

]]>Promoting a growth mindset in our mathematics classrooms cannot stop at simply putting posters on the wall or responding with “yet” immediately after a student claims, “I don’t get it” or “I can’t do this.” It’s about changing our paradigms about teaching, learning, assessment, classroom culture, rituals, routines, language, and grading. Basically, embracing a true growth mindset around student learning in mathematics means abandoning the teacher-centered and compliance-based classroom paradigm most of us experienced as students in K-12 schooling and in college lecture courses. It’s a tall order that requires great reflection and examination of core beliefs. Here are some questions for self-assessment, reflection, and conversation to gauge if growth mindset is really being promoted:

- Who is doing the talking, the thinking, and the mathematics in your classroom: you or your students?
- How do adults perceive mathematics across the school? Do students interact with adults that claim they cannot do math or are not “math people?”
- When students are chosen to present in class, how are those students chosen? For right answers, correct processes, a mistake, or an interesting idea worth discussing?
- Is speed implicitly honored in your classroom?
- Do students demonstrate stamina in wrestling with in-class learning tasks or do they wait for the solution after minimal effort.
- How is praise given? For answers or for thinking and perseverance? Do you have students that identify themselves as “smart?” How does that label impact their behavior and academic habits? (See The Problem With Praise)
- Are students given the opportunity to experience productive struggle to find relationships, make connections, and use multiple representations, or are the opportunities based on replicating procedures and getting correct answers?
- How are mistakes handled in class? Are they viewed as opportunities for discourse or something to be “fixed” and admonished? How is feedback provided to students when mistakes are made or uncovered?
- Is feedback to students asset-based or deficit-based?
- Is student reflection part of the classroom, including opportunities for self-assessment and goal setting?
- Do assessment practices represent a static snapshot of understanding based on a pacing guide or are students able to demonstrate their learning at any time over the course of the year, building a body of evidence?
- Whose classroom is it? Is it teacher-centered with lots compliance-based rules, procedures, and routines or is it a student-centered, driven by their questions, ideas, and sense of empowerment?
- Are the questions posed to students answer-driven or ideas-driven?
- Elementary: Observe various flexible groups in your building and across a grade level. What do you notice? Describe the instruction and classroom culture in these classes. Are there implicit messages being sent to students?
- Secondary: Observe “honors” and “regular” classes in your building. What do you notice? Describe the instruction and classroom culture in these classes. Are there implicit messages being sent to students?
*What other questions should be added to this list?*

I’m not going to pretend to be an expert here or judge other who are giving growth mindset principles a try in their classrooms. As a high school teacher, I was more fixed mindset that I wish to admit, and my classroom was much more teacher-centered than I wanted it to be. The influences and practices of my K-12 teachers, my college professors, and even my cooperating teachers when I student taught formed a strong schema about how teaching mathematics was supposed to be. Fortunately, through some professional learning opportunities early in my career, I was able to recognize that *I was only teaching the students that learned like I do in my classroom and not all of the students in my classroom*. That recognition and acknowledgement alone was the first step in improving my practice as a young teacher. It was challenging to give up some traditional beliefs around assessment and grades, and I didn’t make all of the progress I could have. That’s why growth mindset is more than just a buzz term, posters on the wall, or catch phrases. To do it well and for it to actively live in our classrooms, we ** all** (teachers and students) have to challenge our schema and beliefs around mathematics, what it means to “do mathematics,” and the learning environments that best represent what mathematicians actually do.

*(Want more? Mark Chubb shared some similar thoughts and resources in a blog post last year.)*

These expectations of practice come from the presentation Secondary Mathematics Achievement by Design. For administrators, here are some guiding questions as you visit mathematics classrooms:

*What does “consistent use” of our instructional materials look like in your building?**What do you want to see more of in your math classrooms?**What does a sensible balance of print vs. digital resources look like?**Who is doing the talking, the thinking, and the mathematics in the classroom?*

- Growth Mindset in Mathematics card (for teachers – from Jo Boaler; youcubed.org)
- Positive Norms to Encourage in Math Class (for classrooms – from Jo Boaler; youcubed.org)
- See more growth mindset in mathematics resources at youcubed.org
- I grabbed this from a St. Vrain educator:

What’s missing here? What mathematical norms do you have in your classroom to create an inclusive, student-centered environment that promotes access, learning, and success for * all* students in mathematics? What norms would students create? What norms could come out of the question,

*(Want to learn more about promoting growth mindset in mathematics? Check out Jo Boaler’s book, Mathematical Mindsets)*

**NCTM Principles to Actions Book Study (online via Schoology)**(Begins September 11 and ends in January; 1.0 credit)*Participants must purchase the print book or eBook prior to September 11***Alternative Assessments in Secondary Math**(Saturdays – September 16, October 7, October 28, November 11; 8:00 AM – 12:00 noon each day; Silver Creek High School, Room E206; 1.0 credit)**Mathematical Tasks & Classroom Discourse**(Saturday, September 30; 8:00 AM – 4:00 PM; LSC Evergreen Room; 0.5 credit)

- 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.

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