Editor’s note: This is the thirteenth chapter 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. Also, to my devoted readers, I decided to name the first school I taught at as Cypress School rather than “my previous school” to reduce confusion and irritation with the author.” The previous chapters can be found here:Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5Chapter 6Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11 and Chapter 12
Ch 13 Faulty Assumptions, the Best of Intentions, and a Croaking Frog
In planning my future classes during the summer before the upcoming school year I proceed from an undying faith in my expectations of how things will be. During the actual school year, I then deal with the reality. In the end, it is always astounding to me how some intuitions turn out surprisingly well.
My Math 7 class at Cypress my second year was the non-accelerated version. I had taught accelerated Math 7 the year before, but was now faced with a challenging group of students who I knew were disheartened about math and likely dreading the next year. While planning my lessons during the summer using the JUMP Math teacher’s manual, I had a vision that the students would upon succeeding and getting good grades on tests and quizzes, eventually discover that the math was actually interesting and that they could manage it.
The reality was slightly different as I was finding out and as I’ve written about in preceding chapters. I knew that something was happening. Just not in the manner I had envisioned.
The next year when I started at St. Stevens, I found that my Math 8 class was similar in some respects to the Math 7 class. I had assumed during my planning for it that the ability level would be high, thinking that was the norm for private schools. I therefore sought to overcome what I called the vast wasteland of disparate topics and dearth of algebra that is typical for Math 8. I thought that I might introduce more algebra than is usually included, drawing upon the simpler problems and approach in another book authored by Dolciani called “Basic Algebra”. I selected some topics that I thought would provide a basic grounding in algebraic concepts that would help them when they took the regular algebra 1 class in 9th grade. These topics included multiplying polynomials, factoring, algebraic fractions and various word problems.
As it turned out, my Math 8 class struggled with the various topics we had covered. I realized that my plan for trying to squeeze in the basic algebra might not work, despite my having worked out lesson plans for the same. On top of that, the two girls with whom I had been doing intervention work were on a separate track. I had them work on homework for other classes during the Math 8 class, and worked with them two days per week during their first period on bringing them up to speed on very elementary equations, percents, decimals and fractions—and insisting they learn their multiplication facts.
In the case of my Math 8 class, I realized that however mistaken I thought my initial expectations were I would have to go through with my original plan. This realization came after a bout of rainstorms that left puddles throughout the campus, waterlogged green areas, and a tree frog next to my Batcave classroom. I don’t know for sure that it was a tree frog, but it was definitely a frog—and it croaked. Its croak was distinctive and almost as loud as the crows that used the palm tree next door as their resting place.
One day, as the class was starting to work on the homework I had assigned, the croak of the tree frog filled the room. This provided a distraction that the eight students quickly took advantage of.
“Can we look for the frog?” they asked. “Jared is really good at catching them.” Jared had an albino snake at home, and was known for being proficient at catching lizards which also populated the school campus at times.
“Let’s do it,” I said, despite the admonition of educrats these days that all teaching must be done with “intention”—that is, nothing left to chance. I decided that if anyone asked about my intentions, I would say I meant for that to happen. Alternatively, I’ve toyed with the idea of talking about God’s intentions, but have decided not to go there.
The class ran out, looking around for a misplaced frog. Jared scaled up a hill on the other side of the narrow outside corridor that led to the classroom. They looked in vain for a frog that croaked when least expected and somehow made it sound like it was coming from the narrow corridor—where it was not. Most of the time, however, it knew when to keep its mouth shut.
It was during the futile five-minute search for the frog I decided that I had no choice but to go ahead with my original plan to teach the basic algebra.
My reasoning had more to do with the remaining months of school than anything else. The textbook the school used for Math 8 was one of those which had one day devoted to a “discovery” type activity, and the next day a “direct instruction” type lesson. Book publishers tout this as a balanced approach, usually on their front covers. I tend to skip the discovery type lessons and teach the traditional style lessons, supplementing heavily from older textbooks. There wasn’t much left of the book, leaving me with a lot of time to fill until end of school.
The next day, I announced my plan to the class. “We will be learning some more algebra,” I said. “In fact, it is the same algebra you will learn when you take algebra next year.” They became strangely quiet.
“This will have an advantage,” I continued. “When you take algebra next year, some of the concepts will be familiar to you.” The croak of the tree frog then filled the room.
“It’s back,” I said. “Let’s try this one more time.”
I opened the door and Jared scaled the hill again to no avail. When we got back, we started on the algebra. I felt deep down that the tree frog’s croak was intentional and he approved of my decision.
“Strategic Partnerships” represent an unfortunate trend of the past few decades in US education policy. I learned about them directly when I worked at ACT (2007-2009). I was supposed to be the one writing their policy reports–the big, heavily promoted reports they used to make their claim to be a player in US education policy debates. My drafts were deeply researched and honest. Then, they would go up the chain of command and were reviewed by an editor with no policy background or experience, whose job was to make sure they aligned with our strategic partners’ talking points. ACT’s strategic partners included at times the Education Trust, Mark Tucker’s Center on Education and the Economy, and, always, the Gates Foundation. The end result was that my manuscripts were gutted and replaced with trendy and superficial ideas du jour and citations limited to widely known celebrity researchers, with popular inaccuracies added to the content. Fortunately, my name is nowhere to be found in the reports. In return, ACT’s strategic partners would promote ACT products. The only time I ever attended a presentation by Mark Tucker was around this time and he did, indeed, promote ACT products as the best. (Ironically, the chief sponsor of strategic partnerships at ACT then works at College Board now.)
Big foundations belong to strategic partnerships, too. A popular belief among them is that each one alone cannot effect the big changes they wish to see in society, but together they can. So, the Gates Foundation goes in one direction and a crowd of other big foundations follows. I call it “pack funding.” They also repeat each other’s talking points and collectively recruit and fund “opinion leaders” to promote their goals (and to hound, suppress, ridicule, shun, and ostracize those who disagree).
Unfortunately, pack funding for the Common Core Initiative pretty much bought everyone with influence and cleared the field of any possible consideration of feasible alternatives. Those who were bought are now invested in their claims and owe each other favors. Paul Peterson at Harvard (and his many celebrity researcher progeny), for example, benefited hugely from association with the Gates Foundation and their largesse. In return, see for example: https://www.educationnext.org/after-common-core-states-set-rigorous-standards/.
These days, if one wishes to be an education policy celebrity, one must access a good deal of money, which probably comes with strings. One must join a “citation cartel”—a group of scholars that promotes each other’s work while it ignores or dismisses that of rivals. As with membership in a street gang, there are rules: group loyalty is rewarded, and disloyalty punished.
The outfall is far from just personal: most useful and relevant ideas and evidence are hidden from policymakers, blocked by a wall formed by a few cliques that hoard all attention for themselves.
FOR IMMEDIATE RELEASE: December 10, 2019
Jon Loevy, Loevy & Loevy Attorneys at Law, 312.243.5900, email@example.com
Scott Drury, Loevy & Loevy Attorneys at Law, 312.243.5900, firstname.lastname@example.org
Andy Thayer, Loevy & Loevy Attorneys at Law, 773.209.1187, email@example.com
Student Testing Giant “College Board” Sued for Illegally Collecting & Selling Students’ Data
Parent filed a federal class action suit today against the College Board, a ubiquitous student testing organization, for deceptively collecting and selling students’ confidential personal information.
While formally a not-for-profit, the College Board has approximately $1 billion in annual revenues each year and highly compensates its slew of executives, including its president who received over $1.5 million in 2017 compensation. Much of the revenues come from administering the SAT, PSAT/NMSQT, PSAT 10, PSAT 8/9 and Advanced Placement Exams (“AP”).
According to the suit, the College Board ramped up these revenues using deceptive practices to market a “Student Search Service” to test takers, falsely making it appear as if the service would assist them in getting into colleges and universities. However, “College Board’s true purpose in obtaining the personal information was to sell it to third party organizations in order to increase its already substantial revenues.”
Each year, hundreds of thousands of Illinois students, and millions of students nationwide, take one or more standardized tests provided by College Board. The suit, which seeks nationwide class status, estimates that over 5 million students in the United States were damaged by the College Board’s actions.
The suit alleges that the College Board’s sale of students’ personal information violated Illinois’ consumer fraud and deceptive trade practices laws, and allowed the College Board to unjustly enrich itself and unlawfully invade students’ privacy. It further alleges that the College Board violated the Children’s Privacy Protection Act (325 ILCS § 17/20) when it sold data about students under 16 years of age without parental consent. The suit seeks to enjoin the College Board from any further sales of student data, as well as other damages.
The attorneys seeking to represent the classes are Michael Kanovitz and Scott Drury of Loevy & Loevy Attorneys at Law. Loevy & Loevy is one of the nation’s largest civil rights law firms and has won more multi-million-dollar jury verdicts than any other civil rights law firm in the country.
A copy of today’s suit, Mark S., on behalf of himself and as parent and guardian of his minor child, A.S., and on behalf of all other similarly situated individuals v. College Board, No 1:19-cv-08068, is available here.
A federal law protecting children under the age of 13, The Children’s Online Privacy Protection Act of 1998 (or COPPA), is about to be weakened by the FTC. Parents, teachers, those who care about children should pay attention. If you think parents should have a say in how their young child’s information is collected and shared and used on the internet– NOW is the time to speak up.
If you are not familiar with COPPA, this November 3, 1999 notice in The Federal Register summarizes the intent and purpose of COPPA when it was passed. Below are a few excerpts
“Congress enacted the COPPA to prohibit unfair or deceptive acts or practices in connection with the collection, use, or disclosure of personally identifiable information from and about children on the Internet.”
“The Rule implements the requirements of the COPPA by requiring operators of websites or online services directed to children and operators of websites or online services who have actual knowledge that the person from whom they seek information is a child
(1) to post prominent links on their websites to a notice of how they collect, use, and/or disclose personal information from children;
(2) with certain exceptions, to notify parents that they wish to collect information from their children and obtain parental consent prior to collecting, using, and/or disclosing such information;
(3) not to condition a child’s participation in online activities on the provision of more personal information than is reasonably necessary to participate in the activity;
(4) to allow parents the opportunity to review and/or have their children’s information deleted from the operator’s database and to prohibit further collection from the child; and
(5) to establish procedures to protect the confidentiality, security, and integrity of personal information they collect from children. As directed by the COPPA, the Rule also provides a safe harbor for operators following Commission-approved self-regulatory guidelines.” https://www.govinfo.gov/content/pkg/FR-1999-11-03/pdf/99-27740.pdf
Bottom line, the FTC has made changes to COPPA guidance in the past but is now proposing several potentially big changes to COPPA, including removing parent consent for when a child’s school asks the student to use online apps and platforms (edtech) such as ClassDojo, iReady, Google, YouTube, etc. See here (Section E. Question 23 covers the edtech consent exception) Exceptions to Verifiable Parental Consent:
“Should the Commission consider a specific exception to parental consent for the use of education technology used in the schools? Should this exception have similar requirements to the “school official exception” found in the Family Educational Rights and Privacy Act (“FERPA”)…?”
*Speaking of FERPA, we know that FERPA was also weakened in 2008 and 2011, and removed parent consent before collecting and sharing student information with researchers, companies, contractors, consultants, volunteers, and other parties. Gutting FERPA by removing parent consent usurped parental rights; we should absolutely not make that same mistake by removing parent consent in COPPA.
The FTC is accepting public comment on these proposed changes to COPPA; the deadline to comment is Dec 9, 2019. Below is a short, easy to share CALL TO ACTION with links on how to comment and how to contact your Congressperson. Please submit a comment and do SHARE this CALL TO ACTION widely. Thank you.
Click the link below to download the CALL TO ACTION.
In this post, I am going to attempt to address a number of issues related to the situation in Wake County, NC where the school district adopted the Mathematics Vision Project (MVP). The three main issues I hope to address have to do with the evaluation of the implementation of the Mathematics Vision Project (MVP), MVP’s lawsuit against a parent, and the parent voice in Wake County (as well as across the country). And for good measure, or bad, I’m likely to hit on other issues. I keep hearing, “It’s complicated,” being said about so many things. While this whole situation may be complicated, it doesn’t have to be and it shouldn’t be. Are the parents the only ones involved in this situation who have not lost sight of what’s important—the students, their education, and their future?
For more information see the linked articles and legal documents provided at the end of this post.
The Wake County Public School System (WCPSS or Wake County) adopted MVP as the math program to be used throughout the district. WCPSS appears to be the fifteenth largest school district in the country so the adoption of this program impacts a lot of students. In short, parents and students have expressed concerns in a variety of ways. In response, the school board hired MGT of America Consulting, LLC (MGT) to conduct an evaluation. MVP filed a defamation lawsuit against a Wake County parent. For more detailed information see the links at the end of this post for articles and legal documents.
Evaluation of the Implementation
An August 6, 2019 article says this about the Wake County Board of Education:
The board voted Tuesday to have an outside company, MGT of America Consulting, review MVP math. The review will include classroom visits, analysis of student work, in-depth data review, and focus groups. The total cost of the project will not exceed $125,000.
This is misleading. It indicates there will be a review of MVP math. It isn’t the MVP math program that will be reviewed.
The board did contract with MGT to conduct an evaluation. The contract with MGT says:
MGT of America Consulting will work with district staff to do a comprehensive evaluation of implementation during the fall of 2019. This evaluation will include classroom visits, staff interviews and student, parent and teacher focus groups.
MGT is not being tasked with evaluating MVP, which is a math curriculum/program. The contract clearly states the evaluation will be of the implementation of MVP. I think it is important to make a clear distinction between the program itself and its implementation.
In my eyes, evaluating the implementation does not address the problem and the questions parents in Wake County are raising. Decision makers often seem to blame poor implementation when problems arise and concerns are expressed. That blame gives reason for doubling down on implementation efforts.
What needs to be evaluated first is the concerns parents have about this program, why they have those concerns, and solutions they may propose. What are their concerns? What do they like and not like about the program? What kind of math education would parents like for their kids? What math program would they like to be used in their child’s math class? What is it parents want? What solutions would they propose if given a chance to have them really considered? Could the proposed solutions be put in place? If not, why?
It seems in Wake County’s case, an evaluation of parent and student concerns should take place. Instead, an evaluation of the implementation of MVP is being conducted. Why aren’t parent concerns being evaluated? Why isn’t an evaluation of the MVP program being conducted? It seems like that ought to come before evaluating the implementation. If the program is not acceptable to parents, regardless of whether it is effective or not, I doubt it would make any difference to parents as to whether the program is implemented well or not. And what if a program is not effective and is well implemented? In this case, I see effectiveness as being subjective depending on which camp one is in and on this issue there seems to be two camps. I would venture to say that each camp, and likely each individual, has their own effectiveness criteria.
From news accounts and a committee report, it appears WCPSS responded to formal complaints submitted by parents. A letter from the district’s Chief Academic Advancement Officer says it is in response to “your complaint about the selection and implementation of the Mathematics Vision Project (MVP) curriculum.” WCPSS established a curriculum review committee to review concerns, determine if any board policies were violated, and provide recommendations. From the committee’s report, it appears the committee members were all district employees. There is no evident indication the committee talked with, met with, or communicated with any of the parents who submitted formal complaints. The committee may very well have addressed the submitted complaints but it is hard to tell without seeing the actual complaints. Is it possible that parent concerns go beyond whether a board policy was violated? While the committee reviewed the formal complaints, it does not appear any in-depth evaluation of parent concerns has taken place.
Evaluating the implementation seems to be an expensive endeavor to appease parents by trying to fool them into thinking the district is looking into things.
MVP’s Lawsuit against a Parent
I want to start with a quote that I hope people will give serious thought to.
“Whoever would overthrow the liberty of a nation must begin by subduing the freeness of speech.” Ben Franklin
On July 5, 2019, lawyers on behalf of MVP filed a lawsuit against Blain Dillard, a Wake County parent.
This lawsuit is extremely important for all parents across the country. It needs to be taken seriously. I question how seriously MVP was in filing suit. I would hope someone filing suit would take the endeavor seriously enough to spell the defendant’s name correctly. The complaint filed by MVP is against Blaine Dillard. His name is not Blaine, it is Blain. I would think in a legal document it would be important to get the name of the person you are suing spelled correctly. I wonder if a grammatically concerned judge would dismiss the case on that count? Is the misspelling of the defendant’s name an indication someone is SLAPP happy?
A strategic lawsuit against public participation (SLAPP) is a lawsuit that is intended to censor, intimidate, and silence critics by burdening them with the cost of a legal defense until they abandon their criticism or opposition. Such lawsuits have been made illegal in many jurisdictions on the grounds that they impede freedom of speech. From Wikipedea
Many states have anti-SLAPP laws. It appears that Utah, home of MVP, has a weak anti-SLAPP law and North Carolina doesn’t have an anti-SLAPP law. In the absence of a strong anti-SLAPP law is it okay to SLAPP someone? Morally and ethically would someone end up with a red face?
I have heard many questions raised and comments about this lawsuit. One question I have heard asked is who funded the development of MVP and is someone funding their lawsuit. I just bet they aren’t raising funds on GoFundMe.
Is this a lawsuit about corporate rights to make a profit vs parental rights in directing the education of their children which may include expressing concerns in many forms and venues? Starting in the 1800s, the court system gradually began viewing corporations as “people” with many of the same constitutional rights as individual citizens (See here and here). Citizens United seems to be the most recent capstone. Is it possible that this contributes to the boldness of corporations to file suits against parents for exercising their first amendment rights? Are corporate interests to be protected at the cost of individual first amendment rights?
Tom Loveless, a former director of the Brown Center on Education Policy at the Brookings Institution, replied to Sandy Joiner and Barry Garelick on a twitter post with this statement:
This is a first. In all my years of studying parent protests over curriculum, I have never heard of a publisher taking legal action against parents. MVP will not emerge from this looking good. Neither will the Wake County admin and school board.
I agree with Tom—no matter the outcome of the lawsuit, I do not think it will serve MVP well in the long run. Is it possible they may have done more damage to themselves by filing this lawsuit than anything any parent may say or write about MVP?
Like Tom, I am not familiar with any publisher suing any parents. I am familiar with lots of parent criticism of lots of math programs, but no related lawsuits. The only thing close to this I have seen has to do with cease and desist letters being sent to some individuals on behalf of Istation.
Kieran Shanahan, an attorney representing Istation, has sent cease and desist notices to several critics of the new contract. In a statement Monday, Shanahan said those people are “misrepresenting Istation by making false, misleading and defamatory public statements” and are unfairly harming and maligning the company.
“Istation was legally and appropriately awarded the contract in North Carolina and has a proven record and reputation as an industry leader in early education assessments across the country,” Shanahan said. “The cease and desist notices provided are a lawful and appropriate starting point to end the misinformation, set the record straight, protect Istation’s interests, and let the state move forward.”
The cease and desist letters are to people in a different part of the food chain than parents. Links to more info and articles about this issue are provided at the end of the post. One link includes copies of three of the letters.
On page 4, in item 28, and again on page 5, item 37, of MVP’s complaint (lawsuit document), MVP claims Dillard made statements with the intent to harm MVP. They claim he knew statements were false. Did he? If the statements are in truth false, how does MVP know whether or not he knew they were false? How does MVP know what his intent was? Is it possible his real intent is to have a good solid math education provided to his kids and others in Wake County? If MVP knows Dillard so intimately as to know his intent and whether he knows something is false or not, how come they don’t know how to spell his name?
Item 29, page 4, of the complaint reads:
29. The publication and/or public speaking of these statements harmed MVP. Part of MVP’s business involves submitting proposals for education-related contracts with private schools, public schools, school districts, government entities, and other entities. Dillard’s statements harmed MVP’s reputation as well as perceptions of the efficacy of the products and services that MVP provides. Upon information and belief, MVP has been unable to enter into contracts, and/or has not been invited to make proposals for contracts, and/or has been forced to enter contracts on compromised terms, and/or has been denied extensions on contracts, and/or has been forced to accept contract extensions on compromised terms, and/or has been unable to attract employees and/or consultants, and/or has been forced to invest more resources than otherwise would have been necessary to consummate a contract, and/or has otherwise been harmed.
I would like to think that a great program will stand on its own merits and those merits would override and rise above any criticism or possible falsehoods made of the program. Could it be that by filing this lawsuit, MVP has harmed itself to a greater degree than the possible harm of a parent’s statements? At this point, if harm has been done, how would one ferret out whether the harm, or how much harm, is caused by MVP’s own actions or by the statements of a parent? If harm is caused by MVP’s own actions, would they sue themselves?
Since harm is at issue here, let’s ponder a bit. Suppose MVP has been harmed. Suppose they prevail with their lawsuit. Where is the greater harm? The supposed harm to MVP? Or the harm to the willingness of parents to speak out in the interest of their children’s education? Will parents not speak out and express themselves out of fear of being sued? Could the outcome of this lawsuit open the door for corporations to completely shut down the Parent Voice?
It appears that MVP posted Clarifications Regarding Our Work in Wake County on their website around September 20, 2019. One could argue that this is damage control. While a link to their lawsuit is provided, I found it interesting that no mention was made or links provided for the Answer and Counterclaim and Motion for Judgment on the Pleadings documents. Those documents are well worth reading, especially the Motion for Judgment. Does the counterclaim make a good case that MVP hasn’t proven harm? Those documents were filed on behalf of Blain Dillard on September 9, 2019. MVP’s Clarifications post spells his name Blaine. Is the misspelling intentional? Is the intentional misspelling of a name a form of microaggression? An adult bullying tactic? We may never know, but the “e”, or lack of, is interesting.
MVP does state in their Clarification post they are a five-person organization and not a big corporate publisher. Even though it is small, MVP is an LLC which shields its members from personal liability. Is an individual parent shielded from personal liability? And while MVP may be a small, five member LLC, its website says it has partnered with Open Up Resources. MVP does not seem to list any funders or supporters but Open Up Resources lists their Philanthropic Supporters as Leona M. and Harry B. Helmsley Charitable Trust, Bill & Melinda Gates Foundation, William and Flora Hewlett Foundation, Draper Richards Kaplan Foundation, Charles and Lynn Schusterman Family Foundation.
I wonder about a lot of things related to this whole situation. I wonder… Did MVP have a conversation with the parent about his concerns and claims before filing their lawsuit? Or was it a nonversation? If a conversation did take place, how come we haven’t heard about it? How come we haven’t heard of any efforts to resolve this prior to the lawsuit being filed? Lots of parents speak out critically, even with false claims possibly, about their kid’s teachers. Ever hear of a teacher suing a parent for defamation? I am not aware of any cases but I can imagine it has happened. I wonder… Are there reasonable steps one might take in advance of filing suit that render a suit unnecessary?
One last comment related to that “e”. Failure to use one’s preferred gender pronoun seems to become a civil or human rights issue these days. What about the addition of an “e” to a person’s name?
Does this lawsuit subdue the freeness of speech?
For Parents and the Parent Voice
Here’s another quote. This one is for parents all across the country.
“Make yourself sheep and the wolves will eat you.” Ben Franklin
It appears the situation in Wake County is a part of the most recent phase of on going Math Wars. To learn more about the Math Wars, I recommend reading two documents. The documents are lengthy and informative. Math Wars, by Alan H. Schoenfeld, is from the perspective of the progressive reform math camp and A quarter century of US ‘math wars’ and political partisanship by David Klein is more from the perspective of an explicit math instruction camp.
While it has been reported that the WCPSS received formal complaints from 16 parents, that’s just the formal complaints. It is my understanding there’s more than 1400 Wake County parents with concerns enough to connect with each other.
Parents, take responsibility for your child’s education. That includes math. If you have concerns about or find the program being used is not satisfactory to you, teach your child math at home, single subject home school if allowed by your district and state, hire a tutor, or enroll in a tutoring or learning center. If your child receives help outside school, you may want to consider opting out of assessments. If your child scores well on assessments the school and others will credit it to the school program without considering the outside help.
It appears Wake County has school choice options. It would be nice if parents/students had a math program choice: a progressive reform math program or a more traditional explicit example based instructional program. In a district as a large as Wake County, that could work. If they say they can’t do this, would it be because they are unable or unwilling?
Are Wake County parents up for the challenge of identifying potential candidates and supporting them in successful campaigns for the Wake County Board of Education.
The education system is supposed to work for parents and the community. When will that system start listening to the parent voice? What will have to happen to get the system to listen and act based on the parent voice? And parents, are you willing to be a part of the parent voice? Are you willing to take back control over your child’s education? Are you willing to be a part of the rebellion it will take to regain local control?
Links to Related Articles and Information
Sites for Wake County Parents and Other Interested Parties
Wake County Parent Page Website
Wake MVP Parent Blog
Parents of MVP Math Students in WCPSS Facebook Closed group
Parent Rights for All Website by friends and supporters of Blain Dillard
Wake County Math Parent Legal Defense Fund Go Fund Me
MVP lawsuit documents
Answer and Counterclaim Sept. 9, 2019
Motion for Judgment on the Pleadings Sept. 9, 2019
News articles or posts
Clarifications Regarding Our Work in Wake County c. Sept. 20, 2019 on MVP’s website
A Few Facebook Comments—Abusive Litigation at its Worst Sept. 15, 2019
The Accidental Advocate August 9, 2019
Is An Education-World War Coming? August 1, 2019
MVP math suing Wake County parent for ‘libel and slander’ after he criticized program July 30, 2019 updated July 30, 2019
A Rising Parent Voice Gains Attention April 29, 2019
Related to Cease and Desist Letters
Company awarded K-3 reading contract sends cease and desist letters ‘to end the misinformation’ July 15, 2019 updated July 16, 2019 includes copies of three cease and desist letters
Editor’s note: This is the twelfth chapter 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.” The previous chapters can be found here:
This will be the last chapter for a while since school is starting up next week. Enjoy the intermission; the story will resume and conclude at a later date.
Ch 12 A Classroom Observation, an Evaluation and Sense-Making Again
The nice thing about being observed by someone in administration is that the students are well-behaved for fear of being punished. Students are receptive, answer questions, and cooperate. Such was the case at my previous school during my second year there. The Superintendent informed me that he would be observing my seventh grade class on a particular day. The lesson that day was on multiplying decimals. The lesson was straightforward. I didn’t have them work in groups or do posters at the back of the room as I had done for Diane. I thought I’d see if that affected my evaluation—I live an exciting life.
A week later I met with the Superintendent in his office to go over the results. He handed me his filled out form, had me read it, and asked if I had any questions. The evaluation was all very positive, going beyond what was observed in the classroom and ending with the following: “Mr. Garelick has done a good job of being a professional who takes care of business without stirring up unnecessary controversy or conflict.”
“So, do you want to come back next year?” he asked.
“I think so,” I said.
“Well I hope you will; you’ve been doing great. The students like you; I hear good reports from the parents, you teach well. And I can get things going to make you permanent,” he said.
“I thought I couldn’t be permanent unless I was full-time,” I said. I taught two classes and a remediation session.
“No, you don’t have to be full-time. We can make you permanent.”
“Sounds good,” I said. “Would I be teaching the same classes next year that I’m teaching now?”
He pointed to a schedule he had on the wall, showing that my classes would be the same.
“Sounds good,” I said again.
“Let’s do it.”
The next day I ran into James in the copy room and, feeling in a somewhat confident mood, said “I had my evaluation yesterday and found out we’ll both be teaching the same classes we’re teaching this year. So since you’ll be teaching Math 8 again, I’ll be writing up my observations of my seventh graders so you know how best to work with them.”
“I haven’t heard anything about that,” he said. Talking with James at times was like walking in a mine field; you never knew what was going to tick him off.
“Well, he showed me the schedule.”
“He hasn’t talked to me about it,” he said.
“OK, fine,” I said and acted like I suddenly remembered something that I had to do, and left.
Three weeks later, the Superintendent called me in to his office.
“I hate to tell you this,” he started, “but I need to because it will come up at the next school board meeting, and I didn’t want you to hear it from someone else.”
Call me a pessimist but I knew that this couldn’t possibly be good news.
“We’re going to have to let you go, and I want you to know it has nothing to do with performance. You’re doing great as I told you, but the way schools work, last one hired is the first one to go in situations like this.”
I asked the most logical question I could think of: “What is the situation?”
“I’m not at liberty to say. But under contract rules I have to give you this notice prior to mid-March. It could be rescinded if things change, but I have to issue this notice now.”
“I don’t know what to say,” I said.
“I’m sorry,” the Superintendent said and that ended the meeting. He did not look happy.
A week or so later, after the School Board met, the Superintendent gave me a copy of the Board’s vote to eliminate a position; 4 to 1 in favor of elimination. The document included the rationale: because of declining enrollment, the number of students would fall below a certain level. By law the number of permanent positions had to be reduced. And—as the Superintendent had told me—last one hired is first one fired.
He had me sign it and said I could request a hearing if I wanted to appeal it, but he advised against it. “The chances of convincing the board to reverse the decision is pretty small,” he said.
At my weekly meeting with Diane, I told her the news. “I’m sorry to hear that,” she said. “But when I was a principal, I had to sign a lot of those notices, and they were rescinded in the fall. So there may be a chance.”
“It doesn’t look like it, what with declining enrollments,” I said.
“Well, you never know. But it sure doesn’t help to have that happen. Have you told anyone?”
“No,” I said. “I don’t want to make an issue of it, and I certainly don’t want the students to know.”
“Good decision,” she said. “Good decision.”
“I have a question, though. I don’t know too much about teachers unions and all that—.”
“Consider yourself lucky,” she said.
“—but shouldn’t the union rep have been there at the meeting when the Superintendent told me the news?”
“He wasn’t?? You didn’t tell me that.”
“No,” I said.
“That doesn’t make sense.”
“You’re starting to sound like my students,” I said.
“Has James talked to you about it at all?”
“He’s continuing to not give me the time of day.”
“Are you planning on talking to him?”
“No,” I said. “It doesn’t sound like there’s anything he can do. And even if he could, something tells me he wouldn’t.”
“Hard to say,” she said. “Well, maybe not that hard. I hope it gets rescinded.”
I told none of the teachers nor the students. My classes went as normal. Normal for me being struck by a kind of stage fright before the start of each class. I’m like an actor before the curtain goes up, suddenly struck with panic that he has forgotten all his lines and even what the play is about. But once the students come into the room, the curtain is up and I am too busy tending to my immediate task than to worry about school politics and its various nuances.
Editor’s note: This is the eleventh chapter 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.” The previous chapters can be found here:
Chapter 11: More on Making Sense and a Fickle Bookseller
What making sense in math means varies for different people. For Lucy, a lot of the time it was often the monotony of the process. Same for most of the seventh graders I’ve taught, though there are other “nuances” depending on the person and at what level of silliness or seriousness they are operating on any particular day.
My Math 7 class at St. Stevens was a mix of different abilities and personalities. John was an aspiring athlete who had difficulty with math facts and remembering procedures. He worked earnestly and trusted me, but felt that ultimately math wasn’t something he would need. His vision of the future was that he would be a superstar in the sports world and have enough money to hire people to do various chores—math being one of the things.
While Lucy from my algebra class might utter “That doesn’t make sense”, John was more likely to say “That’s a lot of work” when faced with tedious procedures like adding or subtracting large mixed numbers.
He once asked in all seriousness why I assigned so many problems. I asked if there was a particular play in baseball that he had to practice a lot. There was—it was a tricky play that first basemen had to perform automatically and perfectly. “It’s the same thing in math,” I said. “We have to practice certain procedures so we can use them automatically to solve problems.”
Two second pause; then: “But Mr. G., I like baseball.”
My reply was performed automatically and perfectly. “You don’t have to like math; you just have to know how to do it.”
Donna, another student in that same class had a different idea of sense which vacillated between childish whimsy and pubescent whimsy.
Example of childish whimsy: After I explained that letters representing numbers were numbers going by different names, she proclaimed that the number 10 should be called “Jerry”.
Example of pubescent whimsy: I had passed out a worksheet that had on it a problem asking for the area of the shaded portion of the figure below:
Upon seeing the figure, Donna shouted “What the?!” and covered her mouth to stifle a giggle. When I came over to see what was the matter she turned the paper over so the figure would be out of sight. She did not disclose the source of her outburst to anyone in her class, but started to work on the problems.
Looking at the picture a few minutes later, I could see that one could interpret it to be any of two portions of human anatomy, one of which lacked nipples.
A completely different facet of the word “sense” came from my student Jimmy at my previous school. In an earlier chapter I described his penchant for asking questions during a lesson on multiplication of negative numbers. Before I could teach multiplication of negative numbers, however, JUMP Math required covering how to evaluate expressions such as 3-(2-x).
Knowing how to multiply by negative numbers would make this a lot easier. But JUMP decided on a micro-scaffolded approach which in retrospect I would not choose to do again. JUMP’s JUMP Math’s approach was to first look at something like 10-(5-2).
“We know we can do this easily by just doing the subtraction in the parenthesis first,” I said. “So we get 10 – 3 or 7. But suppose I wanted to do it by distribution.”
“Why would we want to do that when we can just subtract what’s in the parentheses?” Jimmy asked.
“Because pretty soon we’re going to evaluate expressions like 3 – (2-x) where we don’t know the value inside the parentheses.”
This quieted him for the moment so I went on. I decided to make up a story to go along with the problem. “Say you visit a book seller and he says to Jimmy, ‘I’m going to give you a special deal. I’m going to reduce the price of this $10 book by $5.’ ”
“Yeah, that would be a good deal,” Jimmy said.
“Yes, it is but then at the last minute he says ‘I changed my mind. I’m only going to take off $3.’ ”
“Wait a minute, he said he was going to take off $5,” Jimmy said.
“Right. So you’re going to pay more aren’t you? Originally you would have paid 10 -5 which is $5. But he reduced the discount by $2. So how much more are you going to pay now?”
Jimmy thought a minute. “Two dollars more.”
“Right,” I said. “If I wrote it now as 10 – (5 – 2), we can see that you end up paying two more dollars than what you would have paid had he not changed his mind. And what you end up paying can be written as 10 – 5 + 2.”
The whole idea being that we evaluated the expression using an intuitive approach, thereby sidestepping multiplication of each number by – 1. As I say, I wasn’t fond of the approach. Jimmy was strangely silent.
“Now, let’s suppose at the last minute the bookseller says, ‘Wait, I changed my mind; I’m going to take off $7.’ Now you’re paying less than you would have if he only took off $5. How much less?”
“Two dollars,” he said with a sigh.
I then summarized it as a rule: the signs of the numbers inside become the opposite. The homework problems were to evaluate various expressions in this manner, including those with variables, like 10 – (5-x).
“It just doesn’t make sense,” Jimmy said.
“What doesn’t?” I asked.
“I don’t understand why he would give less of a discount than he said he would. The guy said he would take $5 off, and then he only takes $3 off. Why would he do this? What sense does that make?”
“The bookseller is a bit strange, I admit,” I said. “But on the other hand, he also took off $2 more than he said he would. So he’s not all bad.”
“I don’t trust him,” he said. “I wouldn’t come back to his store.”
With Jimmy it was hard to tell whether his questioning was serious or a means of wasting time. Either possibility made sense.
Editor’s note: This is the tenth chapter 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.” The previous chapters can be found here:
Ch 10: Not Making Sense, and a Conversation I Never Had
“Math doesn’t make sense.” This was the chief complaint that Lucy evinced when seeking help with algebra. She was a bright girl in my eighth grade algebra class at St. Stevens.
Lucy’s statement will no doubt serve as evidence for those who view me as an unbending traditionalist hell-bent on teaching procedures at the expense of “understanding”. While I do provide the underlying concepts to procedures, there are students, like Lucy for whom math had always come easy and the connection between procedure and concept was obvious. With algebra the level of abstraction ramps up and things were no longer as obvious. Lucy thought that if math didn’t come easy then either something was wrong with her, or math made no sense.
The range of abilities in the St. Stevens algebra class was much wider than my previous classes, and likely more typical of most schools. There were about five students at St. Stevens who were at the very top of the class. At the lower end there were about four or five. Lucy was starting to fall into that lower group. She made a good effort in my algebra class in the beginning but increasingly got caught in waves of confusion starting with multiplying and dividing powers.
She had begun to make a good comeback with factoring of trinomials such as x²+5x+6 into two binomials: (x+2)(x+3). She even volunteered to do a problem at the board. But the next day we had more complex trinomials like 6x²-5x-6. Students were having a hard time with these and Lucy was back to sitting with arms folded, answering questions I asked of her with a shrug and a response of “I don’t know” laden with teenaged insouciance.
I had taught this particular type of trinomial by using a trial and error method in which you try various factors like 2x and 3x, and 6x and x to get it to work. (If you’re curious, the factorization of 6x²-5x-6 is (2x-3)(3x+2).
There is another method, sometimes called the “diamond method”, which involves some steps that I won’t go into here, but results in the trinomial being expressed as 6x²-9x+4x-6. This can then be expressed as 3x(2x-3) + 2(2x-3). Since (2x-3) is a common factor, this now can be expressed as (2x-3)(3x+2). I’ve tried to teach this method in the past with mixed success; many find it difficult. Given the problems I was having with Lucy and others, I decided to stick with the trial and error method.
I allotted time in every class for students to start on their homework to allow me to offer help and guidance. She accepted my help grudgingly. After working through a problem I asked “Does it make sense now?”
She gave her usual response. “Sort of.” I took this as “no”.
Katherine would sometimes use that period to catch up on paperwork, and in so doing would observe what was going on in class. She never offered any criticism or comments on anything that happened unless I asked. (And when you get down to it, that’s how I like to be mentored.) When I saw Katherine later that day I told her “I’m at my wits end with Lucy.”
“I know,” she said. “One look at her body language tells you she’s given up.”
“I’ve tried everything,” I said. “I’ve communicated with her mother, let her know she can get help, but she doesn’t even try. I feel like saying ‘I’m bending over backwards for you; the least you can do is show some respect and make an effort.’”
“You should tell her that,” she said. “Just talk with her and tell her what you told me, and what your expectations are. She’ll be real honest with you, but you need to reach an understanding.”
I lost sleep that night, rehearsing how that conversation would go. I decided I would pull her aside when the rest of the class was doing their warm-up questions, have the talk. But when I arrived in the classroom, I was greeted by a very cheerful Lucy who offered to help me pass out the day’s warm-up questions to the class. She then excitedly told me “I found a way to do the factoring.”
She showed me. It was the diamond method I had decided not to teach because I thought it would be too confusing for her.
“Where did you learn this?” I asked.
“I looked it up on the internet. It’s really easy.”
“Fantastic,” I said. “Do you want to show the class how it’s done?”
She didn’t want to, so I demonstrated the method. There were the sounds of people getting it as I put some problems on the board for them to work. I left the class elated that Lucy had taken the initiative and was getting it.
I ran into Katherine after class was over and excitedly told her about Lucy’s miraculous turn-around. As it turned out, after Katherine had talked with me the previous day, she decided to talk with Lucy at the end of the day.
“That explains her change in attitude,” I said.
“I should have told you,” she said. “I’m sorry. But she was in the classroom getting something so I just talked to her.”
“What did you tell her?”
“I told her that her body language is telling us she’s given up.”
“I said ‘Mr. Garelick thinks you don’t like him.’”
I wished she hadn’t said that. “What did she say to that?” I asked.
“She said ‘Oh no, that’s not true.’ She felt bad.”
That evening, my wife, who was brought up Catholic, said this was part of Catholic guilt. I have chosen to remain agnostic on such matters.
In the end, the top students were able to work the diamond method, while the other students relied on the trial and error method. Lucy would forget the procedure she had found on the internet and even simple trinomials would elude her despite the fact that factoring trinomials doesn’t go away in subsequent lessons.
There is an advantage to continued practice should anyone have their doubts. It leads to proficiency and eventually can connect with the understanding and “sense” that Lucy felt was lacking.
She would continue to be a challenge. And I would learn to take my victories if and when they occurred.
Editor’s note: This is the ninth chapter 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.” The previous chapters can be found here:
Ch 9. A Cathartic Discussion, Putting the Bell on the Cat, and Business as Usual
My meetings with Diane at my previous school were not always confrontational. Sometimes we got into my interactions with other teachers which I found fairly enjoyable. While it’s not quite gossip, it does have cathartic benefits.
Shortly after James and I met with the moderator who wanted us to meet for six two-hour sessions and collaborate on how best to teach math (see Chapter 6) Diane asked “Are you getting along with James any better?”
“Well, he was definitely friendlier towards me after that meeting.”
“So there’s been a breakthrough.” Diane said.
“I wouldn’t go that far,” I said. “He was friendly for a few days. He’s back in his non-talkative passive-aggressive mode.”
“I’ve met his wife,” Diane disclosed. “She works as a counselor at a high school near here. She’s very nice,” she said and sipped her coffee while looking at me out of the sides of her eyes. “Except when she isn’t,” she added.
“Sounds like a marriage made in heaven,” I said. She almost spit out her coffee.
“I find when I talk to teachers, that one of the biggest complaints about teaching is not always the teaching itself. It’s frequently about getting along with other teachers,” she said.
This made a lot of sense. One event in particular came to mind when she said that. During my first year at the school, the Superintendent was pushing for having seven periods rather than six. This meant that our classes would be forty-five minutes long instead of fifty-five. It would be even shorter on Wednesdays when we were dismissed early because of the weekly staff meeting.
The seven period day, in fact, was the topic of discussion at one such staff meeting, led by the Superintendent. Prior to the meeting, two of the teachers were in the room, and they agreed with me that shorter class times were not a good idea. “You’re right, Barry,” one of the teachers said. “It would really end up forcing us to cram a lot of things in.” She said she would speak out against it.
When our meeting began, the Superintendent talked up the benefits of the new schedule since it would allow students to now have two electives instead of just limiting them to one. And an elective could also be two periods long: sixth and seventh periods. With more electives, this could open up more teaching opportunities—an important consideration, given that the largest class was graduating and enrollment numbers were dwindling.
“But I want to hear from you now,” he said. “What are your feelings about this schedule?”
The silence that followed reminded me of Aesop’s fable about which mouse was going to put the bell on the cat.
Given the discussion prior to the meeting, I felt I was on safe ground to start the discussion.
“I’m not for it,” I said.
All eyes were suddenly on me.
“A shorter class period will make it difficult to teach. Right now Wednesdays are my worst day because class length is 45 minutes and I often don’t get done what needs to be done. With seven periods, every day will be like Wednesdays are now—and Wednesdays will be even shorter.”
“So I take it that you would be voting ‘no’ on this?”
I wasn’t aware that this was a vote, but now so informed I replied “That would be safe to say.”
Discussion continued. The Drama and PE teachers concurred with me, and then it was James’ turn.
“I think this would be a good step forward,” he had said. “I would like the opportunity to reinvent myself as a teacher…” and other words to that effect.
After he spoke, others now seemed to approve of the seven period day including the teacher who had previously agreed with me that it was a bad idea.
“I can’t blame her,” I told Diane. “She’s worried about her job and didn’t want to be against the Superintendent. Plus I think James being the union rep kind of makes him the thought leader.”
“Don’t get me started on teachers’ unions,” she said. “I’m starting to get a whole different take on this now.”
The union influence, such as it was, didn’t hold a candle to the history teacher’s final words on the subject. He had taught at the school for 30 years and was well respected. Although he voted in favor of the seven period day he offered this reflection after the yeas were seen to outweigh the nays: “I think it’s a shame that we’ll be going into the next school year with some people not happy about this change and a cloud hanging over them. So I propose we think about this some more.”
Apparently the Superintendent did. At the next staff meeting he announced that the current six period schedule would remain, though he was disappointed in the reaction. I guess he wanted unanimity. Apparently James was disgruntled about it as well.
“I don’t know if he’s held it against me,” I told Diane.
“He might have,” she said. “It’s hard to say.”
It’s hard to say a lot of things that go on in any school. I recall another time—this one a party—James was talking with the third grade teacher who mentioned the downward trend of state test scores on math at the school.
James gave a reason for that. “It’s because we don’t have students collaborate with each other enough,” he told her. She nodded in agreement at what is accepted as educational wisdom. Perhaps James thought there wasn’t enough collaboration in my classroom. Who knows? Hard to say.
In any event, I decided to not bring up that particular conversation at this session with Diane. Despite her dislike of unions and distrust of people who represent them, she was likely to say “Well he does bring up a good point; what are your thoughts?”
Our conversation turned to the usual business of filling out her online checklist. There were plenty of avenues for her to pursue what I thought of dubious practices, so no need to give her ideas.
Editor’s note: This is the eighth piece 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.” The previous chapters can be found here:
Chapter 8: The General This ‘n That Shop, Negative Numbers, and Faith
I went to school at University of Michigan in the late 60’s/early 70’s, long before the proliferation of 24 hour 7/11’s, Starbucks, and other brand name franchises. A few blocks away from me was a small mom and pop grocery store that was fairly new called “The General This n’ That Shop”. During my senior year I noticed that the items in the store were dwindling. On a particularly cold day in December, I stopped by to find that most of the shelves were bare, and on one, a single loaf of bread remained, which I bought.
“Are you going out of business?” I asked the cashier.
Her response: “I hope not.”
It is this type of optimism that I try to instill in my students. And among my seventh grade students the first such test has been negative numbers.
I do not like to prolong the topic. I once observed a teacher taking three weeks to teach it. After two weeks of adding and subtracting negative numbers and the students had it down fairly well, the teacher introduced a new explanation using colored circles. While the approach can be effective, its use at this point only caused confusion. One girl asked “Why are we doing this?”
The teacher answered “I know you know how to add and subtract with negative numbers. Now I want you to understand why it works.”
The girl’s response: “I don’t want to understand!”
This incident was not unique. I’ve found that a lot of the confusion with the addition and subtraction of negative integers is that students are given more techniques and pictorials than are really needed. They are left with the impression that it is a complex process and that there are many different ways to do it. This is ironic considering that subtraction is an extension of addition. In mathematical terms, a – b = a + (-b) where a and b can be positive or negative.
I keep it relatively straightforward with the first day spent using number lines with arrows to compute addition of negative numbers. The next day, the addition is done without pictures.
I then introduce subtraction. I tried this my first year teaching at my previous school with an accelerated seventh grade class. I asked them to compute 6 + (-4) which they knew how to do from the previous lesson. Two was their answer. I then asked them to compute 6 – 4. They saw the connection almost immediately, leading to the general rule of “adding the opposite”.
While it worked well with my accelerated class, I thought maybe I wouldn’t have the same success the next year with the seventh grade class which had large deficits in their math knowledge. But the technique worked just fine, with Kyle shouting out: “Adding a negative number is the same thing as subtraction”. This became a quote that I posted on the quote wall.
The only rub in all this is the subtraction of a negative number. I used to introduce this by first asking if anyone could solve 10 – (-5), and then linking the question to football for those who liked or played It.: “After a loss of 5 yards, how many yards do you need to get a first down?” As I mentioned in an earlier chapter, Jimmy had answered “Can’t you just punt it?” I have since changed my tactics. I specify that the ball has to be run and then use any number of non-football examples such as: “It was -10 degrees yesterday and 20 degrees today. By how much did it increase?”
My goal in teaching adding and subtracting of negative numbers is to achieve a level of automaticity, so that students can ultimately solve a problem like 3 – 7 without using pictures or writing it as 3 + (-7). At the same time, I try to get them to develop a number sense as to whether their answer is going to be negative or positive. I give them models to use such as: “If I gain 3 yards and lose 7 am I ahead or behind and by how much? If I earn $3 but owe $7, am I ahead or “in the hole” and by how much? They do get it, though they need reminders through the year.
And as far as multiplying negative numbers I provide an illustration of why things work as they do. I use an example of making a video of someone riding a bike backwards, and running the video backwards.
“What if they were skateboarding?” Jimmy asked.
“Whatever you want,” I said.
If the backwards rate is represented as -3 mph and we run the video backwards at 2 times the normal speed—represented as -2—the person appears to be riding a bike or skateboarding forward at 6 mph. A similar model can be used to show why a negative number times a positive is a negative number. (For the more curious students, and certainly in accelerated classes and in eighth grade algebra, I show the proof using the distributive rule.)
While my backwards video example generally does the job, it didn’t with Jimmy even when I used skateboarding rather than a bicycle rider. He tended to be quite literal. “That’s in a video; does it work in real life?” he asked thus opening up the question of whether mathematics can apply to images. He finally accepted the example used in JUMP Math where someone on a mountain is descending at a rate of 30 ft per minute or -30 ft/min. The example asks how one would represent where the mountain climber had been relative to his present position 3 minutes earlier, or -3 min. Jimmy agreed that the person would be higher 3 minutes previous and further accepted that the situation is represented by -3 x -30, or +90.
While Jimmy understood it, a girl said she did not understand either example.
“For now, just work with the rule,” I said. “You’ll get it the more you work with these kind of problems.” The girl did understand the examples a few days later. “Sometimes you just have to have faith in the math,” I told her. She evinced no expression so I said nothing more. Which is a good thing because I doubt she really cared about how we’re all sometimes like the cashier at the General This n’ That Shop.