Deconstructed math

Common Core’s advent has inspired math teacher Jessica Hiltabidel to find ways to instigate thinking and encourage “productive struggle” she writes in Educational Leadership.

Pre-Core, Maryland middle-school teachers would guide students through a word problem, such as:

To receive a discount at the Half-a-Dozen Flags Amusement Park, a group of visitors must purchase a minimum of $600 worth of full-day and half-day tickets. Twenty-six tourists in a group purchased full-day tickets at $15 each. Write and solve an inequality to calculate how many more tourists in this group would need to each buy a $9.50 half-day ticket so this group qualifies for the discount.

The “inquiry-based instruction that undergirds the Common Core State Standards” calls for “open-ended questions,” Hiltabidel writes.

One textbook question read, “To go to Disney World costs $50 for each adult ticket and $30 for each child’s tickets. X tickets are bought of each. If the total spent is more than $800, how many tickets were bought?”

She “deconstructed” the problem to read: “You’re taking a trip to Disney World. How many tickets do you buy?”

Students were told to solve the problem any way they wanted as long as they could explain the process.

Some students . . . bought enough tickets for their family and friends. Others bought enough tickets for the Baltimore Ravens football team or all members of their favorite boy band.

After students had presented their ideas and we discussed them as a class, I asked, “How much money would you spend to take all these people to Disney World?”

This time, students were energized and focused on the process of discovery. One group used the Internet to figure out the actual cost of a ticket. . . . By the time we were finished, all my students could identify what key information they would need to solve a word problem like this and what simple operations they could use.

Then she showed them the textbook question. They used “the structure they’d discovered” to “see this complicated question” as a set of steps: Multiply the cost of an adult ticket by how many adults went; multiply the cost of a child ticket by how many children went; add the total, and make sure the sum is larger than $800.

I don’t understand the textbook question. Were an equal number (X) of adult and child tickets purchased? Or is it just an unknown number of both? Is the question asking for the minimum number of tickets purchased that would total more than $800? If it’s not, then there are an infinite number of answers.

Her “reconstructed” question doesn’t involve math. And I’m not sure speculating on who you’d like to invite to Disney World leads to an understanding that you need to multiply the number of adults and kids by the cost of their tickets, add the sum and then . . . What if the total is less than $800?

Am I missing something?

Where’s Abe Lincoln?

LincolnThe new College, Career and Civic Life Framework for Social Studies State Standards, released on Constitution Day, is “avowedly, even proudly, devoid of all content,” writes Checker Finn on Education Gadfly. What it’s got instead is “inquiry.”

Nowhere in its 108 pages will you find Abraham Lincoln, the Declaration of Independence, Martin Luther King (or Martin Luther), a map of the United States, or the concept of supply and demand. You won’t find anything that you might think children should actually learn about history, geography, civics or economics.

Instead, you will find an “Inquiry Arc,” defined as “as set of interlocking and mutually supportive ideas that frame the ways students learn social studies content.”

Turn to table 23 on page 49. This has to do with “causation and argumentation” and purports to be part of the inquiry arc as applied to history, in particular to “dimension 2,” dubbed “causation and argumentation.”

By the end of grade 2, “individually and with others,” students will “generate possible reasons for an event or developments in the past.” (That event might be World War I, or it might be the day grandma dropped the turkey on the floor.)

By the end of grade 5, they will “explain probable causes and effects of events and developments.” (Let me tell you what happened after Susie smacked Jamie.)

By the end of grade 8, they will “explain multiple causes and effects of events and developments in the past.” (Actually, she said she hit him for two reasons.)

And by the end of high school, they will “analyze multiple and complex causes and effects of events in the past.” Now we’ve moved from “explain” to “analyze,” and we’ve added “complex.” But, as throughout the entire document, there is no content whatsoever. No actual history.

“Many state standards in social studies are overwhelmed with lists of dates, places and names to memorize – information students quickly forget,” said Susan Griffin, executive director of the National Council of Social Studies. The new framework will stress . . . wait for it . . . critical thinking.

More than half of students scored “below basic” on the National Assessment of Educational Progress exam in civics, notes AEI’s Rick Hess. “Most college graduates can’t identify famous phrases from the Gettysburg Address or cite the protections of the Bill of Rights.”

If our “national experts” can’t bring themselves to come out and just say “Kids should know when the Civil War was” it’s not clear that “an inquiry arc of interlocking and mutually reinforcing elements” will help kids find out.

He wonders: “Just what it is that students are going to think critically about.”

Social studies follies

There are no Common Core social studies standards, nor even a framework for standards, but there is a “vision” of a “framework for inquiry,” reports Ed Week.

Welcome to the social studies follies, writes Checker Finn on Education Gadfly. The “vision” of a College, Career and Civic Life (C3) Framework will “focus on the disciplinary and multidisciplinary concepts and practices that make up the process of investigation, analysis, and explanation.” The document goes on:

It will include descriptions of the structure and tools of the disciplines (civics, economics, geography, and history) as well as the habits of mind common in those disciplines. The C3 Framework will also include an inquiry arc—a set of interlocking and mutually supportive ideas that frame the ways students learn social studies content. This framing and background for standards development to be covered in C3 all point to the states’ collective interest in students using the disciplines of civics, economics, geography, and history as they develop questions and plan investigations; apply disciplinary concepts and tools; gather, evaluate, and use evidence; and work collaboratively and communicate their conclusions.

The C3 Framework will focus primarily on inquiry and concepts, and will guide — not prescribe — the content necessary for a rigorous social studies program. CCSSO recognizes the critical importance of content to the disciplines within social studies and supports individual state leadership in selecting the appropriate and relevant content.

Nowhere is there a mention of “knowledge,” complains Finn.  “When was World War I, why was it fought, who won, and what were the consequences?” Dunno.

Of course, “content” is mentioned, but Finn isn’t impressed. “This could turn out to be simply awful.”

American students don’t know much about civics and aren’t prepared for citizenship, writes Rick Hess, who’s co-edited a new book, Making Civics Count, with David Campbell, political scientist at Notre Dame and authority on civic engagement and Meira Levinson, education philosopher at Harvard and author of No Citizen Left Behind. In a 2006 survey of college students, “more than half of seniors did not know that the Bill of Rights prohibits the establishment of an official national religion.”

What works? The sage on the stage

Unless they’re experts, students learn more when teachers fully explain the material, write Richard E. Clark, Paul A. Kirschner and John Sweller in the new American Educator.

Discovery learning, problem-based learning, inquiry learning, constructivist learning — whatever the label, teaching that only partially guides students, and expects them to discover information on their own, is not effective or efficient. Decades of research clearly demonstrates that when teaching new information or skills, step-by-step instruction with full explanations works best.

Minimally guided instruction (“the guide on the side”) takes a great deal more time than explicit instruction (“the sage on the stage”). The  brightest and best-prepared students may “discover” what they’re supposed to, but the less-skilled students will fall even farther behind, the authors write.  “Minimally guided instruction can increase the achievement gap.”

In a second story, Principles of Instruction, Barak Rosenshine discusses “highly effective instructional practices, such as teaching new material in small amounts, modeling, asking lots of questions, providing feedback, and making time for practice and review.”

Common Core rap

Common Core Essential Standards change how we teach, rap a group of STEM teachers in Charlotte, North Carolina.

The teachers don’t seem all that happy to be “reassigned to the pep squad,” notes Missouri Education Watchdog, which speculates it’s a professional development must-do.

Here’s the lyrics:

Chorus: Focus on student engagement
Practices communication
Relevant data, yes
Common Core Essential Standards change how we teach

No longer can a teacher be the sage on the stage
Common Core Essential Standards change how we teach
Become the guide on the side the students to engage
Common Core Essential Standards change how we teach
The other verses contain these points:

No list of algorithms to memorize
Graphing calculators and real world ties

A variety of problems, problem solving strategies
Complex texts and technologies

Hands-on inquiry with questions to promote
Analysis of data, not answers by rote

Clear and concise, rubrics (whole)* guide
students will improve the quality of work with pride

* hard to understand in the video

So, up until now, teachers haven’t tried to engage students, pose real-world problems or use relevant data? But once the new standards go into effect, they will.

In the comments, Barry Garelick notes that the new Common Core math standards, which the teachers see as cutting edge, have been criticized for being too traditional.