- “Is this really what’s being taught now?”
- “What on earth would anyone learn it this way?”
- “How come you don’t teach the shortcut?”

Given the number of education reform efforts we’ve experienced over the last half-century, you’d think we’d be better at rolling out new standards. Why not start a new initiative in kindergarten and work its way up through our system each year? Wouldn’t that be less traumatic for our kids than changing an entire K-12 system concurrently in an arbitrary year?

Consider, for example, this problem that is circulating the InterWebs:

My friend was genuinely concerned about how this student must feel, being marked down for a correct calculation. Here was my reply:

What do you think? To what extent does me reply “hold water”?

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1. **Make it doable:** Attach meaningful standards to a multi-class experience. When a project can evolve over time, there are more opportunities for teamwork, reflection, and growth.

2. **Organize support:** Consider the students who will need the most scaffolding. What graphic organizers, reminders, calendars, or other structures will be likely to help them the most?

3. **Celebrate progress:** Students won’t need to look over their shoulders at what other groups are doing so much if we share good things we’re seeing happening along the way. Plus, who doesn’t like to be encouraged?

4. **Live humility:** Ask students, “What did you like about this? What would you change?” I find when I have thoroughly planned and fully engaged in real-time discussions with my kids, it’s easier for me to seek their feedback — and they give great ideas!

5. **Create an audience:** If there is no authentic audience for your project, just brag about your students to others and tell your students about it! If possible, give them a chance to share their own work outside the classroom.

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10. Context is king.

9. Manipulatives activate motor layers.

8. Number hunting is a symptom of comprehension.

7. Background knowledge is key to accessing tasks.

6. Students might approach topics in surprising ways.

5. Routine empowers creativity.

4. Portfolios celebrate growth.

3. Public notes provide academic bridging.

2. Valuable formative assessment matters.

- Depth of knowledge brings math practices.

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While changing curtains has a 1-in-2 chance of getting you the grand prize, keeping the old curtain had merely a 1-in-3 chance because it was chosen when three curtains were still available. The fact that we now know one of the choices that would’ve been a “loss” doesn’t impact the probability.

This problem took me awhile to comprehend when I first saw it. The same thing happened when I posed this problem to a mix of 7th and 8th graders. “But it’s a 50-50 chance either way!” they protested. Only after collecting data simulating the experience over 50 times did they start to come around to the idea, and even then it was usually, “Well, that’s probably right but I still don’t believe it.”

Cognitive dissonance may also describe the larger view our society hold of mathematics these days. According to this great interview with mathematician and computer programmer Keith Devlin, the use of pencil-and-paper algorithms is largely grounded in a 19th-century world. It took me a minute to catch that this didn’t even mean the 1900’s, but rather the 1800’s!

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Yes, simple can be beautiful. Mathematicians talk about the beauty of numbers. Albert Einstein talked about an idea’s *internal symmetry*. Maybe the Common Core State Standards for Mathematics could use a little simplicity right now, since so many parents and teachers seem to be confused by their rollout. So here we go. Why are we using these standards?

1. We want a more mathematically literate workforce.

2. We want more kids to do well at the university level.

3. We want a society of problem solvers.

Is that too simple? Perhaps, but it’s intended to be a starting point. A “reset button,” if you will. For anyone to start making more sense out of evolving approaches to mathematics, check out this article from The Hechinger Report.

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Dan Meyer’s work shows how to turn textbook problems or everyday situations into guided explorations that capture the spirit of mathematics.

We Use Math introduces the work of many professionals who rely on mathematics in their work. (BYU Dept. of Math, 2010)

The Mathematics of Love applies a mathematical perspective to patterns in relationships…and arms races. (Dr. Hannah Fry, 2014)

What is Calculus Used For? discusses ethically difficult scenarios in the field of human health that use mathematical modeling. (Jeff Heys, 2012)

What Is Math About? details how mathematics is fundamentally about something deeper than numbers and logic. (Masao Morita, 2012)

Mathematics and Sex explains evolutionary roots of our brains. (Dr. Cleo Cresswell, 2014)

As a side note, I enjoyed meeting Mike Byster in the Chicago area years ago. He’s got great strategies for teaching kids to feel competent with calculations that sound difficult to most of us.

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- Students need to learn things and then use them.
- We need to take advantage of brain research to start teaching in ways that kids learn.
- Get rid of testing because it’s totally driving curriculum.

Since that time, we have begun to implement the first two ideas. The third may have gone backwards as evidenced by this article about testing and another report suggests similar conclusions. Perhaps one question worth considering is whether more testing leads to more learning. A key might be in how we utilize testing.

**Summative Approach** Judge schools and school districts. Reward the best, punish the worst, and publicize results in the newspaper. Evaluate principals and teachers.

**Formative Approach** Assess schools and school districts. Publicize current strengths and action plans for weaknesses in the newspaper. Support students and staff in learning more.

This is sure to become a hot topic if it isn’t already. What’s your opinion?

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- How do educators communicate that which is still being understood? It’s not an easy task. Some districts are experiencing a gap between their previously adopted curriculum and newly mandated, more rigorous standards that balance conceptual development, skill acquisition, and application of ideas. (Rigor is not defined as “being more difficult.”)
- Many of us have seen details taken out of context. A common post on Facebook has shown subtraction by addition. Many people don’t realize these tasks help kids “decompose” numbers
*prior*to learning a traditional, efficient algorithm in elementary school, and that the idea of number strings is helpful in learning middle school mathematics. - There is a percentage of students who were highly successful without new standards. It can be hard to see why change is worthwhile. As a side note, check out this Duke University study demonstrating the danger of pushing kids into advanced math before they’re ready for it.
- There’s always backlash to change, especially with a lack of ownership in the change. The bigger the change, the bigger the backlash. For many teachers, change feels like the only constant there is in education…and it can be exhausting.

A very interesting article in U.S. News & World Report brings multiple perspectives to light!

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**The Partnership** What a caring parent! It was great to build this relationship from the ground up, in a get-to-know-you fashion. This is a strong foundation for the rest of the year. I’m striving to do this with a greater number of families.

**The Outline** Here are the conference questions I used. Keep in mind that asking them verbatim off the page is not the goal of the conversation. In fact, I didn’t ask the seventh question so I can only vouch for the first six. They worked wonders!

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This reminds me of my student who calls out “I don’t get it” and starts distracting others from learning rather than digging into a task. That student usually cannot repeat or paraphrase directions back to me.

“You have great potential to complete this task, *if *you work hard.” This is the message I so often need to come back to using. If you haven’t read Carol Dweck’s book yet, this recent article from The Atlantic does a great job using research to illustrate her central theme.

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