Truth in American Education

Fighting to stop the Common Core State Standards, their Assessments and Student Data Mining.

  • Home
  • About Us
    • TAE Advocates
    • Network Participants
    • Related Websites
  • Common Core State Standards
    • National Education Standards
    • Gates Foundation & NCEE Influence
    • State Costs for Adopting and Implementing the Common Core State Standards
    • National Curriculum
    • Common Core State Standards Content
      • Standard Algorithms in the Common Core State Standards
    • Myths Versus Facts
    • States Fighting Back Map
    • Closing the Door on Innovation
    • CCSSI Development Teams
  • Common Core Assessments
    • Opt Out Info
  • Race To The Top
    • District-Level Race to the Top–Race to the Top IV
  • Resources
    • Legislative Bills Against CCSS
    • Pioneer Institute White Papers
    • Model Resolutions
    • Parents’ & Educators’ Executive Order
    • CC = Conditions + Coercion + Conflict of Interest
  • Audio & Video
  • Privacy Issues and State Longitudinal Data Systems
    • Statewide Longitudinal Data Systems
  • ESEA/NCLB
    • Statements and Proposed Plans
    • Every Child Achieves Act July 2015
    • Student Success Act
    • Every Child Ready for College or Career Act
    • No Child Left Behind Waivers
    • ESEA Blueprint, Briefing Book, and Position Paper
  • Home School/Private School
  • Action Center
    • Parent and Community Action Plan
    • Stop CCSSI ToolKit
    • Sign Up or Contact TAE

Instructional shifts, Formative Assessments, and Taking Matters into My Own Hands

June 24, 2020 By Barry Garelick

Editor’s Note:  This is Chapter 16 in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California.  He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices.  He is also the author of three books on math education.  Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Please read at your own risk.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10,  Chapter 11, Chapter 12, Chapter 13 and Chapter 14 and Chapter 15.

Chapter 16 Instructional shifts, Formative Assessments, and Taking Matters into My Own Hands

Whenever the word “shifts” appears in an article about education, it is highly likely that what you’re reading is blather, claptrap, drivel, garbage and idiocy. (Sorry for all the adjectives; I was trying to avoid saying the word “crap”.) Even more so, if the article talks about formative and summative assessments. While formative assessment is a valid concept, its meaning may vary depending on who you talk to or what article you happen to read.

For example, formative assessment may be defined as evaluating how someone is learning material while summative assessments evaluate how much someone has learned.  So says one expert. Another says summative assessments can be used formatively, by using the results to guide approaches in subsequent courses.

These hermaphroditic definitions have provided me much cover in my quest to appear aligned with whatever shiny new thing happens to be in vogue.  My first parole officer, Ellen, got me started down the path of formative assessment. Although she had no shortage of suggestions for things I would never consider doing, there was one that I thought I’d try. “Have you ever let students use their notes for a quiz or test?”

I liked the idea and during my first year at Cypress, I allowed my classes to use notes for quizzes, but not tests. I felt that this would reinforce the idea of the value of notes. The problem was that some students’ organizational skills were lacking—resulting in this typical conversation:

Student: How do you do this problem?

Me: Look in your notes.

Student: I can’t find it.

Me: (Drawing a diagram on a mini-white board.) How would you find the time each of the cars are driving?

Student: I don’t know.

Me: (Writing “Distance = Rate x Time” underneath the diagram)

Student: Oh!

Such incidents led me to provide help to students in a direct manner rather than the “read my mind” approach that entails asking vague questions that serve to frustrate rather than elucidate. Sometimes I would partially work out the equation for a particular problem. Other times I would use an example of a similar problem. Expanding from a worked example to solve similar problems demands critical thought, and does exactly what math reformers pretend that unguided discovery does.

I continued this approach with my Math 7 class during my second year at Cypress. I was intent on bolstering the confidence of my students who had suffered the previous year and were convinced they could not do math. I was making headway with them using JUMP, and I could see that getting decent test scores had positive results.  But as we got into more complex topics, they were having difficulty and asking for help.

I knew that there was a potential that such approach could quickly blossom into grade inflation and an artificial sense of achievement. So I justified my giving them help by telling myself that their difficulties helped guide my instruction. But I knew there were limits.

“It’s hard for me to not give help when I see they’re on the wrong track,” I told Diane during one of our sessions.

“Yes!” she said. “They have to learn from mistakes.” 

Fearing a foray into Jo Boaler’s money-making “mistakes make your brain grow” motif, I rapidly changed the subject and tried out a new idea. “I’ve been thinking of giving students a choice when they ask how to do a problem, or whether it’s correct.  If I answer, it will cost them points deducted from their score. I need to wean them from this dependence on my help.”

“Brilliant!” she said, took a sip of coffee and said again “That’s brilliant!”. And so I tried it. For the most part it worked. Jimmy asked if a problem were correct and I said it would cost 5 points for me to answer. “Never mind,” he said. For those students clearly lost I would not deduct points. Over time it became a judgment call—do they really need help or hand-holding?

I continued this technique and have used it at St. Stevens. It has evolved so that I will offer help as needed, but at a certain point in the school year, I will announce my policy of deducting points for certain questions.

If there are many questions in the course of a test or quiz, I find myself falling back on one of the many definitions of formative assessments, telling myself I’m using the results to guide future instruction.

My algebra class at St. Stevens was a case in point. The class was a mix of students, most of whom were able to stay afloat and do well on tests and quizzes. But there were others who perhaps should not have been placed in the algebra class who struggled and were falling behind. I would offer hints and help for those who were clearly lost. Some students would ask for help, some would not. And for those that did, they would also attempt problems on their own.

And then there was Lucy.  Despite the one victory in which she was motivated enough to find a method for factoring more complex trinomials, she once again settled into her usual mode of angrily putting down answers that she thought made a kind of sense. In fact, I found that she had forgotten how to factor trinomials. She rarely asked for help during tests. I gave it to her anyway.

In keeping with summative sometimes being formative, I advised her parents that it would be best if she repeated algebra 1 in ninth grade. Lucy and her parents were receptive to this. There was one other student for whom I made the same recommendation and it was accepted, no question. Both went on to get A’s in algebra their freshmen year.

My interpretation of formative and summative assessments may not be what others think it is. Also, well-intentioned learning scientists may view me as not providing students with enough “retrieval practice”, “interleaving” and “spaced repetition”. I’ll let you look those terms up on your own. (I assure you I do all those things.) In the end, it all boils down to what used to be called “teaching”.

Filed Under: Education Reform

About Barry Garelick

Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in the Atlantic, Nonpartisan Education Review, Education Next, Education News and AMS Notices. He is also the author of three books on math education.

  • Email
  • Facebook
  • Phone
  • Twitter

States Fighting Back

https://app.box.com/s/10nl1409mkaf00zzzuyf

CCSS Opt-Out Form

  • Click here to download the CCSS Opt-Out Form

Campbell’s Law

"The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor."

- Donald Campbell

Copyright © 2021 Truth in American Education · Developed & Hosted by 4:15 Communications, LLC.