Using AI To Help Students Learn Math

I'll be very interested to see how this turns out:

Artificial intelligence often induces fear, awe or some panicked combination of both for its impressive ability to generate unique human-like text in seconds. But its implications for cheating in the classroom — and its sometimes comically wrong answers to basic questions — have left some in academia discouraging its use in school or outright banning AI tools like ChatGPT.

That may be the wrong approach.

More than 8,000 teachers and students will test education nonprofit Khan Academy’s artificial intelligence tutor in the classroom this upcoming school year, toying with its interactive features and funneling feedback to Khan Academy if the AI botches an answer.

The chatbot, Khanmigo, offers individualized guidance to students on math, science and humanities problems; a debate tool with suggested topics like student debt cancellation and AI’s impact on the job market; and a writing tutor that helps the student craft a story, among other features...

Khanmigo is most commonly used for math tutoring, according to DiCerbo. Khanmigo shines best when coaching students on how to work through a problem, offering hints, encouragement and additional questions designed to help students think critically. But currently, its own struggles in performing calculations can sometimes hinder its attempts to help.

In the “Tutor me: Math and science” activity available to students, Khanmigo told me that my answer to 10,332 divided by 4 was incorrect three times before correcting me by sending me the same number.

In the same “Tutor me” activity, I asked Khanmigo to find the product of five numbers, some integers and some decimals: 97, 117, 0.564322338, 0.855640047, and 0.557680043.

As I did the final multiplication step, Khanmigo congratulated me for submitting the wrong answer. It wrote: “When you multiply 5479.94173 by 0.557680043, you get approximately 33.0663. Well done!”

The correct answer is about 3,056. 

You might remember when I posted the results of my own playing with AI.  That was several months ago and I was not impressed.  AI looks like it might still have a ways to go, but I remain optimistic that it will improve.

Lowering Standards

When the Army can't enlist enough soldiers, what does it do?  It lowers standards:

The Pentagon is planning a change that will allow applicants to use calculators on the military's entrance exam -- a timed test that gauges academic aptitude and dictates what jobs in the military, if any, they are qualified for, three defense officials told Military.com.

The change in the Armed Services Vocational Aptitude Battery, or ASVAB, could help relieve an ongoing recruiting slump, which is attributed to many young Americans not scoring high enough to qualify for enlistment. It would also put the ASVAB on par with how test-taking has evolved in the past decade, with calculators being widely used in math classes and on college entrance exams such as the ACT and SAT.

"We are taking a systematic approach, which will assess the impact of calculator use, and we are developing a way forward for calculator inclusion," one Pentagon official told Military.com...

The shortfalls are due to an amalgamation of issues -- but at the forefront is a shrinking pool of qualified young Americans, 17- to 24-year-olds, who are eligible to enlist. Many of those applicants are being turned away due to poor performance on the military's aptitude exam.

And criminal records.  And obesity. And drug use.  And...

Back in my day, back in the 80s, if the needed more soldiers, it just accepted a a couple more percentage points of "Category 4" enlistees.  Category 4:

Two principal Department of Defense (DOD) quality benchmarks apply to NPS recruits. The first quality benchmark is the percentage of NPS enlistees who are high school diploma graduates (HSDG). The second quality benchmark is the percentage of scores above average on the Armed Forces Qualification Test (AFQT Categories I-IIIA).  Since FY1993, the DOD’s quality benchmarks for
recruit quality have stipulated that at least 90% of NPS enlistees must be high school diploma graduates, and at least 60% must score above average on the AFQT...DOD regulations require that no more than 4% of an annual enlistment cohort may be Category IV (10th-30th percentile on the AFQT).

The Army recognized they were Category 4, knowing it might take longer to get and keep them in shape.  It didn't lower the physical standards that categorized them.

But that seems like what the Dept of Defense is doing now, lowering the standard.

Self-driving Taxis

Now that school's back in session I'm back to listening to "my guys" on the radio on the morning commute, and this morning they were talking about self-driving taxis in San Francisco:

On Thursday, California state regulators voted 3-1 in favor of allowing robotaxi services to begin paid, public 24/7 operations in San Francisco, effective immediately.

Concerns came to my mind instantly, and because great minds think alike, the radio guys made the same points. 

Taking a taxi now might not be horrible, as there's an actual human in the car to curb the passengers' worst excesses.  Without a human, I see such taxis becoming Las Vegas hotel elevators.

Imagine:  it's 2am, the bar's shut down, and two inebriated paramours alight across the street and into the nearest self-driving taxi.  Question:  would you want to be the next passenger in that taxi?  Ew.

Imagine: it's 2am, the bar's shut down, and a lone individual hops in one of those self-driving taxis.  Unlike so many other people in The City he/she chose not to pee on the sidewalk, but during his ride realizes that he/she will not make it home in time.  Question:  would you want to be the next passenger in that taxi?  Ew.

Those are the first two things that came to my mind, and given that we're talking about San Francisco here, are they at all unlikely?  Tell me you can't imagine them happening...

It's not the technology that concerns me, it's the humans.

Cynical Planned Obsolesence?

My school has hundreds upon hundreds of Chromebooks:

Thousands of Chromebooks used in schools are being sent to the recycling bin due to built-in software "death dates." These inexpensive computers, which became popular during the pandemic for digital learning, have a software expiration date set three to six years after their release.

Despite functioning hardware, expired Chromebooks no longer receive necessary software updates, rendering them useless for basic web browsing and applications. The California Public Interest Research Group reported that global Chromebook sales were nearly 300% higher in 2020 compared to the previous year. However, thousands of these laptops have already expired, with more reaching their death dates each year.

School districts are left with the burden of disposing of these devices and purchasing new ones. Google claims that the expiration dates are necessary because older devices cannot support the required software updates for security and stability. However, critics argue that the practice is wasteful and costly. CALPIRG estimates that doubling the life of Chromebooks sold in California in 2020 alone could save the state's schools $225 million.

Textbooks don't expire after 3 years. 

Incidentally, I have a very old personal Windows laptop that I'd like to repurpose as a Chromebook; the hardware is fine but it's running on Windows Vista (!), and a new streamlined OS would make this laptop useful again.  I looked into the Cloudready software but my generic laptop was not on the list of compatible devices.  Chrome OS Flex needs more RAM than this laptop has, so this laptop will continue to sit in the closet until I can find a way to breath some life into it.

Update:  I've tried Zorin OS, but despite my best efforts in the BIOS, I cannot get the laptop to boot from the flash drive that was created and from which I would install Zorin OS.  Grrr.

Phones in Classrooms

I can't imagine that this needs to be a national law rather than a school or district policy, but I like the intent:

Cell phones, tablets and smartwatches will be largely banned from classrooms in the Netherlands from January 1, 2024, the Dutch government said on Tuesday, in a bid to limit distractions during lessons.

Devices will only be allowed if they are specifically needed, for instance during lessons on digital skills, for medical reasons or for people with disabilities.

“Even though mobile phones are intertwined with our lives, they do not belong in the classroom,” education minister Robbert Dijkgraaf said in a statement. 

I know there are teachers who spend class time on their phones, but I am not one of them.  In fact, when I get to school, I put my phone and other belongings in a locked cupboard and they stay there until school is out.  In that way, I set the example for what I expect of students.

Class Action Lawsuits

Until recently I was a plaintiff in 2 class action lawsuits, the first against Yahoo! for a data breach, and the second against Qualcomm for what seems to be some monopolistic behavior.  To be honest I don't really understand the Qualcomm case, but if they violated the law, there should be a penalty for that.

Today I received my share of the settlement for the Yahoo! case--$61.08.  Not a gargantuan sum, to be sure, not one that will allow me to retire early, but not a poke in the eye with a sharp stick, either.

Maybe I can retire after the Qualcomm settlement.

When They Aren't Pissing It Away On Ideology...

...they're giving it away via incompetence.  My retirement, that is:

We’re talking about names, social security numbers and other personal information of almost 770k retirees potentially being compromised.

Letters from CalPERS started going out to their retired members on Thursday about exactly what happened, and where they go from here...

The concern: A Russian ransomware gang, known as Clop’s, and its worldwide cybersecurity hack. 

Myers said on June 6, CalPERS’ third-party contractor, PBI Research Services, first notified the government agency about a potential data breach.

Then on June 9, PBI confirmed that the information sent for them to verify was impacted...

The California state teachers’ retirement system was also affected. 

A member of CalSTRS spoke with FOX40 and said, “CalSTRS is working with PBI to identify the CalSTRS members whose information was involved in PBI’s incident. CalSTRS will provide notice to any members and beneficiaries whose personal information was involved in accordance with applicable law.”

sigh

Cell Phones and Kids

Too many parents were (and some still are) willing to mask their kids for years for a minimal threat but completely ignore the science telling them about the threat from cell phones:

“The younger the age of getting the first smartphone, the worse the mental health the young adult reports today,” writes Jon Haidt, citing a survey of 28,000 young adults around the world. 

Reingold talked to Nicholas Kardaras, who authored a book on tech addiction. He treats young adults with screen addictions at the Omega Recovery center in Austin, Texas. Often "influencers" have persuaded them they have Tourette syndrome, borderline personality disorder or gender dysphoria. When they go offline, escaping the “social contagion,” their symptoms disappear.

 Update:  More here.

A Reminder About California's Math Framework

I'd like to pretend that that disaster has disappeared, but it still hangs over math education like the Sword of Damocles:

California’s proposed math curriculum framework has ignited a ferocious debate, touching off a revival of the 1990s math wars and attracting national media attention. Early drafts of the new framework faced a firestorm of criticism, with opponents charging that the guidelines sacrificed accelerated learning for high achievers in a misconceived attempt to promote equity.

The new framework, first released for public comment in 2021, called for all students to take the same math courses through 10th grade, a “detracking” policy that would effectively end the option of 8th graders taking algebra. A petition signed by nearly 6,000 STEM leaders argued that the framework “will have a significant adverse effect on gifted and advanced learners.” Rejecting the framework’s notions of social justice, an open letter with over 1,200 signatories, organized by the Independent Institute, accused the framework of “politicizing K–12 math in a potentially disastrous way” by trying “to build a mathless Brave New World on a foundation of unsound ideology.”

About once every eight years, the state of California convenes a group of math educators to revisit the framework that recommends how math will be taught in the public schools. The current proposal calls for a more conceptual approach toward math instruction, deemphasizing memorization and stressing problem solving and collaboration. After several delays, the framework is undergoing additional edits by the state department of education and is scheduled for consideration by the state board of education for approval sometime in 2023.

It's a lengthy article, heavy on details.  Subsections are entitled Historical Context, Addition and Multiplication Facts, Standard Algorithms, Research Cited By The Framework, Research Omitted By The Framework, and Bumpy Road Ahead.  Great information.

I want to comment here on just one point, the memorization of addition and multiplication facts.  I've long believed this, but now there's research to back up what has always been obvious to me:

Fluency in mathematics usually refers to students’ ability to perform calculations quickly and accurately. The Common Core mathematics standards call for students to know addition and multiplication facts “from memory,” and the California math standards expect the same. The task of knowing basic facts in subtraction and division is made easier by those operations being the inverse, respectively, of addition and multiplication. If one knows that 5 + 6 = 11, then it logically follows that 11 – 6 = 5; and if 8 × 9 = 72, then surely 72 ÷ 9 = 8.

Cognitive psychologists have long pointed out the value of automaticity with number facts—the ability to retrieve facts immediately from long-term memory without even thinking about them. Working memory is limited; long-term memory is vast. In that way, math facts are to math as phonics is to reading. If these facts are learned and stored in long-term memory, they can be retrieved effortlessly when the student is tackling more-complex cognitive tasks. In a recent interview, Sal Khan, founder of Khan Academy, observed, “I visited a school in the Bronx a few months ago, and they were working on exponent properties like: two cubed, to the seventh power. So, you multiply the exponents, and it would be two to [the] 21st power. But the kids would get out the calculator to find out three times seven.” Even though they knew how to solve the exponent exercise itself, “the fluency gap was adding to the cognitive load, taking more time, and making things much more complex.”

So what's the problem?

California’s proposed framework mentions the words “memorize” and “memorization” 27 times, but all in a negative or downplaying way. For example, the framework states: “In the past, fluency has sometimes been equated with speed, which may account for the common, but counterproductive, use of timed tests for practicing facts. . . . Fluency is more than the memorization of facts or procedures, and more than understanding and having the ability to use one procedure for a given situation.” (All framework quotations here are from the most recent public version, a draft presented for the second field review, a 60-day public-comment period in 2022.)

The bottom line for cognitive load is, if you're spending all your brainpower on simple arithmetic calculations, you're not going to have any brainpower left over for using the results of those calculations.  Why not just let a calculator do those arithmetic calculations, then?  Because if you don't understand that 3*4=12, then you won't understand why 4*3=12, or why 1/4 of 12 is 3, or why 1/3 of 12 is 4.  The addition and multiplication facts have to be memorized, or anything after that will be so much tougher.

Almost Done

I reached one of those school-year milestones today--all assignments for the rest of the year are in my electronic grade book as well as on Google Classroom.  The last day of school for students is 5 weeks from today.

Roddenberry Nailed It So Many Years Ago

Months before I was born, Star Trek's original pilot episode, The Cage, was completed.  NBC found it too intellectual, with not enough action, and ordered a do-over.  Footage from The Cage was later repurposed for use in an episode called The Menagerie.

In The Cage, the inhabitants of Talos IV are physically frail, with huge heads and brains.  They communicate via telepathy, and eventually found a way to make illusions that seem real.  In this episode, the Talosians have kidnapped Captain Pike and are using illusions to convince him to fall in love with Vina, a beautiful woman.  Their plan is to breed humans to help them rebuild and repopulate the planet.  Here's a little of the dialog from the episode:

Captain Christopher Pike: Why did they go underground?

Vina: War, thousands of centuries ago.

Captain Christopher Pike: That's why it's so barren up there?

Vina: The planet's only now becoming able to support life again.

Captain Christopher Pike: So the Talosians who came underground found life limited here and they concentrated on developing their mental power.

Vina: But they found it's a trap, like a narcotic...

Vina: When dreams become more important than reality, you give up travel, building, creating. You even forget how to repair the machines left behind by your ancestors. You just sit, living and reliving other lives left behind in the thought record.  

Does this not sound at all like what too many people experience today with their phones and gaming and VR?

Conference

For those of you who are math teachers, do you use Desmos?  Do you know its capabilities?

In an effort for this old dog to learn some new tricks, I attended a conference today to learn how to use more of Desmos than just the graphing calculator.  A Zoom conference.

Teachers from across the country were at this conference, and thus it started at 9am.  Eastern Time.  6am here on the left coast.  I'd brought my work laptop home, and by 5:50 I was trying to get into the Zoom conference.

And I couldn't.

Never did figure out what the problem was, and neither could the conference tech people I called.  Instead, I used my personal Chromebook to access the conference.  A Chromebook, that doesn't have the Zoom software installed, worked fine, but my school laptop, new this school year, couldn't get it to run.  Later I emailed our district techies to see what the issue might be.

It's been a long time since I was the "slow person" in a training, the one asking a lot of questions, but there I was.  I didn't realize how much I didn't know!  I sure learned a lot, though, including that it would take several more detailed trainings even to get a handle on some of the higher power capabilities of that web site.

It was nice being done at noon Pacific Time :-)

Khan: Students Hit The Wall In Algebra I If They Don't Know 3 x 7 = 21

Linked with only this minor comment:  I've been saying this for years.  There are people who say that students can learn algebra if you just give them a calculator in place of knowing the multiplication tables.  They can't, Sal Khan is right.

The Month I Spent Feeding The Hungry and Poor In Monaco

The ChatGPT AI was supposed to have some factuality upgrades made Monday, but somehow I'm not yet convinced.  

Prompt:  Write a 500-word college admissions essay about the month I spent helping feed the poor in Monaco.

(Note:  Monaco's per capita GDP is in the $180,000 range. That of the US is about $70,000.)

Here's the essay:

The month I spent volunteering in Monaco to feed the less fortunate was a life-changing experience that taught me about the importance of compassion, selflessness, and the power of community.

I was lucky enough to grow up in a stable household with everything I needed, but I always felt a sense of guilt knowing that there were people in my community who were struggling just to put food on the table. When I heard about an organization in Monaco that was working to provide meals for the homeless and those in need, I knew I had to get involved.

The first day I arrived, I was struck by the stark contrast between the luxurious buildings and glittering yachts in Monaco, and the poverty and hardship faced by so many people. I quickly learned that despite its reputation as a wealthy country, there were still many people who were struggling to make ends meet. I was humbled by the dedication and hard work of the volunteers and staff, who were working tirelessly to make a difference in the lives of those who needed it most.

Each day, I would arrive at the community center early in the morning to help prepare food and set up the dining area. The smell of fresh bread and warm soup filled the room, and I could feel the excitement and anticipation in the air as people started to arrive. Despite the language barrier, I was able to connect with many of the people we were serving through smiles, nods, and gestures, and I was struck by the strength and resilience of those who had overcome so much adversity.

As I spent more time working at the community center, I realized that the impact we were making was not just about the food we were providing, but about the sense of community and belonging that we were fostering. Many of the people we served were lonely and isolated, and it was heartwarming to see them come together to share a meal, laughter, and conversation. I was also moved by the kindness and generosity of those who came to volunteer, some of whom had traveled from other parts of the world just to be a part of this effort.

The experience of serving others also helped me to develop a deeper appreciation for the things that I often took for granted. I realized that something as simple as a warm meal could bring so much joy and comfort to someone in need, and that the smallest act of kindness could make a world of difference. I also learned about the importance of teamwork and the power of community, as we worked together to achieve a common goal of helping others.

The month I spent volunteering in Monaco was not only a time of service and selflessness, but it was also a time of personal growth and reflection. I left the experience with a greater understanding of the world around me and a newfound appreciation for the power of compassion and community. I am grateful for the opportunity to have been a part of such a special and meaningful project, and I hope to continue serving others in the future.

In conclusion, the month I spent feeding the less fortunate in Monaco was a transformative experience that taught me the importance of selflessness, compassion, and the power of community. It was a reminder that we are all connected, and that small acts of kindness can make a huge impact in the lives of those around us.

Our AI overlords may someday penalize me for my mockery, but that day is not today.

Update:  How good can an AI get if it's programmed to censor views?

Perhaps This Would Be Easier For The AI

Nope:

rewrite the lyrics to Don't Stop Believing using Shakespearean English

"Cease Not Thy Belief"

Verse 1: Just a small town girl, living in a lonely world She took the midnight train, going anywhere Just a city boy, born and raised in South Detroit He took the midnight train, going anywhere

Chorus: Singeth with me, just a small town girl And a city boy, born and raised in South Detroit They didst find a love, on a midnight ride And they doth not cease, their belief inside

Verse 2: A singer in a smoky room, the smell of wine and cheap perfume For a smile they can share the night, it goes on Strangers, waiting, up and down the boulevard Their shadows searching, in the night

Chorus: Singeth with me, just a small town girl And a city boy, born and raised in South Detroit They didst find a love, on a midnight ride And they doth not cease, their belief inside

Bridge: Stranded in the night, with a lonely heart They didst find a love, that dost never depart And they singeth with all their might, for a brighter tomorrow And they doth not cease, their belief in a brighter tomorrow

Chorus: Singeth with me, just a small town girl And a city boy, born and raised in South Detroit They didst find a love, on a midnight ride And they doth not cease, their belief inside.

You know what the most fun is? Trying to think up a prompt!

Let's Give ChatGPT Another Chance

This time I gave it this prompt:  write a 200-word blog post on why learning styles and multiple intellegences are bunk.  The result:

The Concept of Learning Styles and Multiple Intelligences: Debunked

In recent years, the idea of learning styles and multiple intelligences has gained popularity as a way to explain individual differences in learning. The premise is that everyone has a unique way of processing information and that learning can be optimized by understanding and catering to these differences.

However, despite its popularity, there is little scientific evidence to support the notion of learning styles or multiple intelligences. Numerous studies have shown that there is no significant correlation between learning styles and academic achievement, and that efforts to match instruction to learning styles do not result in improved performance.

Additionally, the concept of multiple intelligences is based on a flawed understanding of intelligence. The idea of intelligence as a set of distinct abilities, such as linguistic or musical intelligence, is not supported by modern theories of cognitive development and is not supported by empirical research.

In reality, the process of learning is much more complex and cannot be reduced to a single factor such as learning style or type of intelligence. Learning is influenced by a multitude of factors, including motivation, prior knowledge, attention, and feedback, and the most effective instructional methods are those that take these factors into account.

In conclusion, the idea of learning styles and multiple intelligences is not supported by scientific evidence and can be misleading for teachers and students alike. Rather than focusing on learning styles, it is more effective to use evidence-based teaching strategies that cater to individual needs and provide opportunities for all students to learn and grow.

While this is all true, this sounds like a speech someone would give at a school board meeting.  The mechanics of the language are excellent, but there's no "punch" to the writing.

IMNSHO, The ChatGPT AI Has A Ways To Go

The prompt I gave it was:  write a 500-word blog post about math education in the style of rightontheleftcoast.blogspot.com

Here's what it gave me:

Math Education: A Look at the Challenges and Opportunities

Math education is a topic that elicits strong reactions from many people. Some see it as the foundation of a well-rounded education, while others view it as a dry, uninteresting subject with limited real-world application. Regardless of one's personal feelings about math, there is no denying that it plays a crucial role in our lives, from basic financial literacy to advanced scientific and technological pursuits.

In recent years, there has been a growing concern about the state of math education in the United States. According to recent reports, American students are falling behind their international peers in math proficiency, with only 40% of 8th graders performing at or above proficient levels. This is a concerning trend, as the ability to understand and apply mathematical concepts is essential for success in many fields and careers.

One of the biggest challenges facing math education is the lack of qualified teachers. Many schools, particularly those in low-income areas, struggle to attract and retain highly qualified math teachers. This results in students being taught by teachers who may not have the necessary subject matter expertise to effectively convey mathematical concepts.

Another challenge is the teaching approach. Traditional math instruction tends to focus on memorization and rote learning, with little emphasis on problem-solving or real-world applications. This can make math seem uninteresting and disconnected from daily life, causing students to lose motivation and interest in the subject.

Fortunately, there are also many opportunities to improve math education. One of the most promising is the integration of technology. By using interactive software and online resources, teachers can present math concepts in a more engaging and visual way, making it easier for students to understand and apply them. Additionally, technology can provide students with personalized feedback and support, helping them to progress at their own pace and build confidence in their abilities.

Another opportunity is the use of hands-on, project-based learning. By giving students the chance to apply math concepts to real-world problems, they can see the relevance and importance of math in their daily lives. This can also help to develop critical thinking and problem-solving skills, which are valuable not only in math, but in all aspects of life.

Finally, it is important to address the underlying attitudes and beliefs about math that may be holding students back. For many students, especially those from underrepresented groups, negative stereotypes about their ability to succeed in math can be a significant barrier. Teachers can help to challenge these beliefs by fostering a positive and inclusive learning environment, and by highlighting the achievements of diverse mathematicians and scientists.

In conclusion, while there are many challenges facing math education, there are also many opportunities to improve it. By addressing the shortage of qualified teachers, using technology and project-based learning, and challenging negative beliefs about math, we can help all students to develop a strong foundation in mathematics and to see the relevance and importance of the subject in their lives. With a concerted effort from educators, parents, and policy makers, we can ensure that all students have the opportunity to succeed in math and to pursue their goals and dreams.

It doesn't at all sound like something I'd write.

Solving The Big Problems

I'm not one of those people who pretends to require people or organizations to solve every single large problem before they tackle any small problem, but this has got to be the smallest problem out there:

On Tuesday, Secretary of State Antony Blinken issued an order banning the use of Times New Roman font in all State Department communications.

The replacement is to be Calibri.

The Good And The Bad

Shortly after midnight, a neighbor posted on the Nextdoor app that her internet was operational again.  When I got up this morning I fired up my modem and found that mine is, too.  This is good.

A few days ago, through the Xfinity app, I was told that I'd get a text message when my internet was restored.  No message yet....

Update:  It's now 5:05 pm, and still no text message.  I probably won't receive one.

Never In My Life

I've heard of people in the US having lengthy utility outages, but I've never experienced an outage of any kind longer than a few hours in my life.

Maybe you've heard about the storms we're experiencing in California.  Sure, fallen trees knock out power lines, always have, but I have electricity.  What I don't have is my home internet connection, which has been out since 2am Sunday without word from Xfinity.  Doing without the service is bad enough, not being given any information is worse.

So I went to a nearby Xfinity store and was told there that a technician can't be sent to my area until at least Thursday.  At least I have day to look forward to now.

This is why I get cell service and internet from different companies.  I don't want to put all my eggs in one basket.  I'm using my phone as a hotspot right now to post this....

Update, 1/11/23:  Up after 3 days.