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[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. To learn about Spies and Analysts, I recommend watching this webinar (with elementary, middle, and high school versions) or reading this blog post.]
 
In March 2001, Russia’s Mir space station was falling out of orbit and was going to crash into the Pacific Ocean. Taco Bell used this as an bizarre marketing opportunity and placed a 40′ x 40′ sign in the middle of the ocean with a target on it that said “Free Taco Here!”. If the Mir hit the sign on the way down, everyone in the United States would get free tacos.

Here’s a short video to refresh your memory:

LSOP History: Mir Space Station Taco Bell Target - YouTube

So overall, this is a fairly wild proposition. But I want you to think about this from Taco Bell’s perspective. Sure, they would get great advertising for this stunt (and Mir did not ultimately hit the sign), but what if the space station hit the sign and Taco Bell had to pay up? Would that cost thousands of dollars? Millions? Billions? How would you even figure it out?

What Taco Bell ultimately decided to do was take out an insurance policy from SCA Promotions, a company that guarantees prizes. What this means is that SCA Promotions charged Taco Bell a fee, and if the Mir hit the target, Taco Bell would not have to pay anything more. In fact, Taco Bell was probably hoping and praying that it hit the target as it would have boosted sales and cost them nothing.

Consider though what SCA Promotions had to do to figure out how much to charge Taco Bell. If they charged too much, Taco Bell wouldn’t feel like it was worthwhile. If they charged too little, it wouldn’t be worth the risk to make the deal. If the Mir missed the target, they’d get all the money. If the Mir hit the target, their company could go bankrupt!

So, what if you worked for SCA Promotions and you were asked you to figure out how much to charge Taco Bell for this insurance policy. Where would you begin? What information would you want to know? What would you do with that data once you had access to it? These are the topics I’m exploring in my spies and analysts post. I want to walk you through the process so that you can better appreciate the complexities of mathematical modeling.

The first part of the process requires the spies. So, I want you to stop and take thirty seconds to think about what information you would use to figure out the cost of the insurance policy. Would you look at how how big the sign is? The speed of the Mir? The number of people in the United States? The cost of a taco? The number of people who like tacos? The time of day? As I hope you realize, the list of questions could go on and on. So, think about what information you’d pick if this was your job. Once you’ve determined what information you’d want, keep reading.
 

Spies
SCA promotions does not specify the exact information they used, but here’s what we have:
  • The sign was 40′ by 40′.
  • In 2001, there were an estimated 281 million people living in the United States and the cheapest Taco Bell taco cost 60 cents. Taco Bell estimated the cost of the free tacos at $10,000,000. Accordingly, that seems to assume that about 6% of the population would actually take advantage of a free taco.
  • According to the video, the area that the Mir was expected to crash into was approximately 3600 miles (5794 km) x 120 miles (193 km) by of the that the Mir

What’s important to realize is that the only solid fact is the size of the sign. The cost of the tacos and the size of the area where the Mir might crash are estimates. That being said, based on the video, it sounds many of the factors I thought of were included. So, how do you take all those factors and turn them into an amount of money to charge Taco Bell?

This is where the analysts come in. Their job is to take the data, figure out what parts are more or less important, and break it down in such a way that it becomes useful. Take 30 more seconds to think about how you might even begin to work with the data.

 

Analysts
First, let’s assume that the Mir has an equal likelihood to land in any part of the crash zone. In reality, I suspect that it may be more likely to land closer to the middle and less likely towards the sides of the rectangle.

If that’s the case, then the area of the sign is 1600 square feet while the area of the crash zone is 432,000 square miles. Converting square miles to square feet gives us an area of 12,043,468,800,000 square feet for the crash zone. This results in a ~0.0000000133% (or 1 in 7,500,000,000) chance of hitting the target. So now what? How much do you charge Taco Bell?

The way I see it, a ~0.0000000133% chance of having a $10,000,000 payout leads to an expected value of having to pay $0.001 on average. So, I guess that charging anything over a penny should earn you money over the long run. I don’t know what Taco Bell was actually charged, but with odds like this, I’m surprised that they didn’t just cover the costs themselves.

 

Conclusion
I’m hoping that at this point, you have a better appreciation for the complexities of mathematical modeling. Once the spies and analysts are done acquiring the information and putting it together, they still have to determine whether the formula (or mathematical model) they come up with is any good. So many assumptions were made here that are likely incorrect. For example, we don’t even know for sure whether the sign was placed inside of the crash zone! This may seem like no big deal, but SCA Promotions has to take it seriously or it could bankrupt the company.

At this point, there are no computers or calculators that can figure this out on their own. This is where the jobs are at. If we truly want to focus our time and energy in a skill that will really help our students become college and career ready, mathematical modeling is where we need to be.

The post Math Modeling Can Tell Us If We Get Free Tacos appeared first on Robert Kaplinsky.

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Have you ever noticed that you can accept tough feedback from one person, but if another person gave you the exact same tough feedback, it would make you feel judged or criticized? Giving tough feedback is challenging and may feel like an impossible choice: say something and offend the recipient or sugarcoat your message into irrelevance.

As educators, it’s our job to give students and other colleagues feedback. So, what if there was something you could do so that the feedback you gave was much more likely to be well received? What if the choice between offending someone and sugarcoating was artificial and there was actually a way to share constructive criticism without damaging the relationship? Would you be interested in learning about it? If so, keep reading because I’m going to share a strategy I’ve used for years that is much better than what I was initially doing.

 

John Gottman’s Research
John Gottman studied married couples to figure out what made them happy or unhappy. He observed that couples that had balance between positive and negative interactions were much happier than couples that did not have this balance and were more likely to end in divorce.

So, the key here is that relationships need to have balance. You might expect that this balance would be 1:1 meaning an equal amount of positive and negative interactions. This was very far from the reality though. Gottman found a “magic” 5:1 ratio of positive interactions to negative interactions resulted in happier, stable relationships while much less than that often resulted in divorce.

Think about what this means because it makes sense. While positive interactions like a kind word, a shared laugh, or a hug are all valued, a negative interaction like an argument has a much more significant impact. A kiss and a compliment does not make the negative interaction disappear from their memory. What you may be realizing is that this 5:1 ratio exists outside of marital relationships as well and applies to relationships between friends, siblings, parents, children, and especially colleagues and students.

 

Implications for Education
I was a teacher specialist for Downey Unified School District when I first learned about this research from my amazing boss, John Harris. It was simultaneously intuitive and something I would have never thought of on my own.

Over the years, I’ve observed hundreds of lessons where I was supposed to give non-evaluative feedback. This was rarely easy to do. I was nobody’s boss, and was grateful to be invited to observe. I was very aware that if my initial feedback was too harsh, I ran a very high chance of never being invited back. So, what could I do?

I looked at my notes and categorized what I observed as either:

  • something positive that the teacher should be recognized for and encouraged to continue
  • something negative that the teacher should work on

I then took my feedback and implemented the 5:1 ratio. This was much more challenging to do in practice than in theory. For every piece of negative feedback I wanted to discuss with the teacher, I had to find five positive things as well. If I could not find five positive things, I could not share my constructive criticism about the negative thing either. Similarly, if I wanted to share two constructive criticisms, then I had to find ten positive things! This forced me to think to myself “Of all the things I want this teacher to work on, which is absolutely the most important?”

 

Psychology Tangent
Humans are pretty bad at keeping track of growth over time. For example, when I look at my 5th grade son, he looks the same as he always has. Obviously this can’t be true, but it takes looking at pictures from a year earlier to realize how much he’s changed. This happens because I see him every day and it’s hard to recognize the little changes that are constantly happening.

Similarly, we’re pretty bad at noticing professional growth over time. We don’t have easy access to “pictures” of how our teaching looked from a year earlier to realize how much we’ve changed. So, I have to make a concerted effort to appreciate teachers’ growth. I force myself to think about what classrooms looked and felt like when I was a student. Everyone was in rows. The teacher talked. We listened. We did lots of classwork.

So, any classroom that is not doing that has made some progress that can and should be acknowledged. Be intentional about being appreciative of growth and not taking anything for granted.

 

Conclusion
I constantly try to share genuine positive observations whenever and wherever. Obviously, this is never a bad thing and strengthens all relationships, helping the recipient understand that you have their best intentions in mind. When you do give feedback, it will be much more likely to be well received and even appreciated.

In the context of observing a single lesson, always stick to Gottman’s the 5:1 ratio. If you’re lucky enough to have more than five positives, include those as well. When sharing your feedback, make sure to lead with some of the positives. Then share your one concern and suggestion. Then continue with any additional positive feedback you may have. If they ask to see your notes and what else you wrote down, think twice before showing it to them. Unless you have a strong relationship built on years of positive interactions, this might backfire, throwing the 5:1 ratio out of whack, and making the recipient question your intentions.

What do you think about these ideas? What do you agree with? What do you see differently? Please let me know in the comments below.

The post My Secret For Giving Other Teachers Feedback appeared first on Robert Kaplinsky.

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As I’ve mentioned in many blog posts, I struggled a lot in my first years as a teacher. I began my teaching career at a time when schools were desperate for math teachers. I got an emergency credential and was allowed to teach before ever taking an education class or doing any student teaching.

I really had no business being in a classroom, and I basically replicated the same troubling experiences I remembered from being a student over the previous decade: the teacher lectures and the students repeat what they heard. I’m not proud of it, but it’s where I came from and it helps me realize how far I’ve come.

When I look back and think about moments that helped me fundamentally change my teaching philosophy, reading the article Never Say Anything A Kid Can Say by Steve Reinhart is near the top of the list. It woke me to possibilities I had not considered. It painted a picture of what a classroom could be, which was not the classroom I had. Even almost two decades later, the strategies he shares still ring true.

So, this blog post is basically a short love letter of the reasons why I treasure his article and why I think everyone should read it (though I’m guessing many of you have already read it and love it too).

 

Reasons Why I Love His Article
  • What struck me first was that he writes like he’s one of us, not our superior. He talked about his struggles, his realizations, and his quest to be better. He said things like “Making changes in instruction proved difficult because I had to learn to teach in ways that I had never observed or experienced.” Wow! That statement is just as true in 2019 as it was in 2000! Thinking about it now, he probably inspired me to be transparent when talking about my own struggles because the way he wrote made me feel normal for not having it all figured out. Remember that this was published in 2000, which was a time before most educational blogs when the only things that seemed to get published were success stories and not struggles.
  • He succinctly articulated a massive paradigm shift when he said “My definition of a good teacher has since changed from ‘one who explains things so well that students understand’ to ‘one who gets students to explain things so well that they can be understood.'” When I read that I totally knew he was right and that it would take a lot of work to accomplish.
  • He shared five straight-forward steps for making this happen (I’m only sharing the names of the steps so you’ll have to read his brilliant article for details)
    • Never say anything a kid can say!
    • Ask good questions.
    • Use more process questions than product questions.
    • Replace lectures with sets of questions.
    • Be patient
  • He was a huge proponent of think-pair-share. If you’ve ever seen me work with students or teachers, you’ll know that strategy plays a huge role in my teaching. I can’t remember if I learned it from him, but it certainly made me use it more.
  • He introduced me to the idea of a “warm call” where you prep a student for being a part of the conversation. He said, “Asking a shy, quiet student a question when I know that he or she has a good response is a great strategy for building confidence and self-esteem. Frequently, I alert the student ahead of time: ‘That’s a great idea. I’d really like you to share that with the class in a few minutes.'”

 

Conclusion
Honestly, I could go on and on about why this article was so good. He gave me the vision and steps to become the teacher I wanted to be long before I was even ready to understand the significance of what he shared. So, if you do any sort of professional reading this month, please check out his article.

What part of the article resonated with you? Did it make an impact in your career too?. Please let me know in the comments.

The post Never Say Anything A Kid Can Say appeared first on Robert Kaplinsky.

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I recently finished reading George Courous’ book The Innovator’s Mindset and enjoyed his storytelling as well as many thought provoking moments. One in particular stands out, and I wanted to explore it more in this blog post. He wrote:

If worksheets were handed out as professional learning, some teachers would be bored to tears, yet in many cases, we do the same thing to our students. That type of learning is not about what is better for kids but what is easy or because it’s the way it has always been done.

 
When I read this, I thought, “He is so right!!” I loved how thinking about it this way made it easy to realize that this would be absolutely unacceptable to do with teachers, yet is common practice to do with students.

He explains that this “type of learning is not about what is better for kids” and then provides two potential explanations:

  • We use them because it’s easy to teach that way
  • We use them because it’s the way we’ve been doing it for years

I often mention that I’m shocked that I wasn’t fired in my first few years of teaching. While I tried hard and loved my students dearly, I didn’t really know what I was doing. I used many worksheets with them, especially those kinds that have the riddles you can solve by answering problems.

In retrospect, I didn’t use them because I thought they were the best way to teach students, but rather because I didn’t know any better ways. I was overwhelmed. I worked from 6 am to 6 pm every school day and a bunch on the weekends. It was simply easier to do it this way.

I used them because that’s what I remembered doing when I was in school. I was following the status quo, and continuing to do it the way it had always been done because I was most familiar with it.
 

Conclusion
Perhaps a good way to think about Courous’ metaphor is to think about everything we do in education and whether a similar version in professional development would be well received. If it wouldn’t, maybe it’s a time for us to step back and reconsider the possibility that the topic could be taught differently.

What do you think? Were there any other parts from his book you enjoyed? Do you see this metaphor applying elsewhere? Please let me know in the comments below.

The post What If They Made Us Do Worksheets At Professional Development? appeared first on Robert Kaplinsky.

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What if you could predict which students would struggle before they do? What if your predictions were so accurate that they let you to focus your attention on those who truly needed your help? What if this enabled you to put support programs in place that made learning more equitable? This doesn’t have to be a “what if?” because this tool currently exists.
 

Academic Support Index
I first heard David Stevens speak about his Academic Support Index (ASI) at a conference in San Diego. My colleagues and I were so impressed by the potential that he was hired to help implement the program in my district, Downey Unified School District. For years I’ve wanted others to know about his research, so that’s why I’m writing about it on my blog.

The ASI is a tool to help identify students who need academic support as well as what level of support they likely need. David uses the metaphor of a ship at sea that has “tailwinds” which push it forward and “headwinds” that impede its progress. The ship can make more progress either by increasing the tailwinds or decreasing the headwinds. He goes on to say:

All students enter school with a combination of “headwinds” and “tailwinds”. Tailwinds are the things that make school easier for students: Parents with high education levels, cultural capital, stable homes, good attendance, and past academic success are examples. Headwinds are things that might make success in school more difficult: Having a learning difference, being an English Learner, a history of academic struggles, or low socio-economic status. Some students come to us with a lot of headwinds and some students arrive with a lot of tailwinds.

 
With the goal of minimizing headwinds and increasing tailwinds, he set out to statistically determine which factors strongly affect students’ success. His results, which he incorporated into a mathematical model called the Academic Support Index, give each student a score that helps educators determine “the likelihood that [a student] will require additional academic support to fully realize his or her learning potential.”

 

Applications
The ASI has helped identify ~400,000 students at a variety of school districts. What he learned was that the ASI had an effect size that was “almost twice that of other factors such as parent education level and socioeconomic status making it a strong predictor of student performance.” The results were so exceptional that they were accepted by the national research society American Educational Research Association (AERA) an astounding three times in 2015, 2017, and 2018.

This is a game changer people. I have not heard of anything like this that can reliably give us this kind of information. The ASI can help you answer the following questions:

  • How can we tell if our programs or interventions are actually making a difference in student outcomes?
  • How do we predict in advance which students might struggle academically so we can provide them with appropriate support?
  • How can we more effectively and efficiently use our limited resources on the students most in need?
  • How can we address the achievement gap without contributing to stereotype threat?

 

Conclusion
If the potential to support the students who need us the most excites you as much as much as it excites me, I highly encourage you to go to David’s website (academicsupportindex.com) and contact him (DavidStevens@AcademicSupportIndex.com) to learn more about how you can set this up at your school or district.

The post A Crystal Ball To Predict Student Struggles appeared first on Robert Kaplinsky.

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Have you ever noticed that sometimes people don’t realize how others perceive them? This can be problematic if they don’t realize their potential or conversely don’t realize that they are rubbing people the wrong way. This blog post uses a tool called the Johari Window that will help you make sense of it all and provide a context that can help us fix these problems.

The Johari Window is a way of exploring a person’s traits based on what they are aware of and what others are aware of. The image below helps you visualize what I mean.

You can think of the four quadrants as:

  • Open – These are the traits that you and others agree upon. I find it to be the least interesting quadrant because you know you have these traits and others do as well. For example, everyone knows that you are helpful or that you are cranky in the morning.
  • Hidden – These are traits that you believe you possess but others do not. This is an interesting quadrant as the different perceptions might be because you have a personality trait you hide from others or because you see yourself differently than others. For example, you might know that you are depressed but others may not or you might think you are hilarious and no one else does.
  • Blind Spot – These are traits that you are not aware of but others are. Again, this could be a positive or negative situation. For example, you might not realize that others see you as a leader or conversely that others see you as unreliable.
  • Unknown – These are traits that neither you nor others are aware of. This quadrant is a bit peculiar, because it seems strange that a person might possess traits that neither she nor others are aware of. However, consider what happens in extreme situations like moments of severe duress. You often read about unlikely heroes who do something extraordinary like lift up a car to save a child underneath or tackle an active shooter. The person exhibits traits that nobody knew existed because there hadn’t been a time when they were needed.

 

Applications in Education
So, what does this meant for educators? I’ll share my initial thoughts but I’d love your perspective in the comments. Where I think we could apply this knowledge most effectively is in moving traits from the “Blind Spot” quadrant to the “Open” quadrant. More simply, we should make sure people know about their positive traits.

Often we see people in ways that are fundamentally different from how they seem themselves. How many times have you heard a version of the story where a teacher reached out to a student, told her about the potential the teacher saw in her, and altered that student’s life for the better forever? I can tell you that however many times you’ve heard that story, it’s not enough.

There are so many students who don’t see themselves as learners with unlimited potential. As a society, we focus too often on what we’re missing rather than what we have. Educators can accomplish so much by telling students about the qualities students have in their blind spots that they are unaware of.

Sadly, for many people, this may be the first time that anyone has acknowledged this positive trait. You might think that telling the student or teacher is unnecessary because she probably already knows about it. I’d challenge that view because even if the student does already know, hearing it from you just reinforces a positive self-image.

Realize that this can apply to everyone, not just students. Imagine how it would make your day for a colleague to let you know how others see you positively. So, there is no reason you can’t do the same for others. Whether it’s administrators, support staff, students, or parents, I think we can always do more to let people know how they’re perceived and encourage positive growth.
 

Conclusion
Again, my call to action is to let other people know about the positive traits that might live in their blind spots. No one loses here. This is an act of empowerment, like I mentioned in my ShadowCon talk. The person receiving this information will certainly win and may forever see you as someone who positively shaped her life. I love it!

I’d like to know what you think. Have you told someone about a positive quality in her blind spot? If so, how’d it go? Do you see other applications of the Johari Window in education? Please tell me all about it in the comments below.

The post Do You Know What Other People Think About You? appeared first on Robert Kaplinsky.

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Whenever I plan to teach a lesson, I try to anticipate the foundational skills students will need to know to complete it. For example, if students have to determine which slope is steeper, I think about how they will have to compare fractions to see which had a greater value.

In my first years of teaching, I’d review these foundational skills before we began the lesson. I didn’t really have a clue as to whether or not the kids actually needed this preventative help. I just believed that the lesson would go more smoothly if the students were more familiar with the skills they needed.

At that point I didn’t have the perspective to see all the problems I caused with my way of thinking including:

  • By not giving students a chance to work on the problem before I began the intervention, I potentially wasted time reviewing a concept students may have already understood.
  • I turned what could have been a good discovery lesson into a game of “let’s mindlessly use the skill Mr. Kaplinsky just showed us because why else would he show it to us?”
  • I made it much harder to distinguish between students who truly understood the concept and students who were robotically repeating what I had just reviewed.
  • Perhaps most importantly, I lost the opportunity for students to realize that there was something in mathematics that they wanted to understand but did not. This would have allowed them to ask for help, have a small intervention, and then realize that they learned something that helped them make sense of mathematics. Dan Meyer summarizes this succinctly with the metaphor “If math is the aspirin, what is the headache that would have ever made them want it.”

 

Fixing This Problem
This reality had been bouncing around in my head for quite some time, but I didn’t have an easy way to articulate all of it until seeing Juli Dixon present at a Solution Tree conference in San Diego. There, she spoke about just-in-time scaffolding versus just-in-case scaffolding.

She describes the difference between the two by stating:

One way to provide differentiation for each and every student is to offer scaffolding that students need at the appropriate time. When you provide scaffolding “just in case” students need it rather than “just in time” —i.e., when students demonstrate the need—you are shortchanging the learning process and failing to provide the rigor that today’s standards demand.

 
The naming was so perfect that it immediately hit me that I had been a “just-in-case” scaffolder early on in my career. I thought, “These kids might struggle during this lesson, so I am going to review what they need to know, just in case they do.” While I meant well, this was truly about what was more convenient for me and not what was best for students.

What I came to realize (though not label so perfectly) was that students instead need “just-in-time” scaffolding. To me, just-in-time scaffolding is so much better for students than just-in-case scaffolding. After all, would you prefer to have a doctor that prescribed medicine before you met her or a doctor who learned about you and then diagnosed your illness (if you even have one!) before prescribing medicine?

The reality though is that just-in-time scaffolding is more work for the teacher. For example, not every class will need the same amount of scaffolding (and some may not need it at all). So, if you teach multiple periods of the same class, you may find that each of the classes ends a lesson in different places, making it harder for you to manage.

 

Conclusion
I believe that the benefits (potential time savings from not doing the intervention at all, students who realize they need a specific help and ask for it, etc.) outweigh the costs. What do you think though? What do you agree with? What am I missing something on? Please let me know in the comments below.

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There’s a scene from The Matrix which I absolutely love as a metaphor for the choices we make and the ignorance we can choose to turn on or off as it suits us. Watch the scene or read the dialogue below.

Morpheus (Laurence Fishburne) explains to Neo (Keanu Reeves) that the Matrix is an illusory world created to prevent humans from discovering that they are slaves to an external influence. Holding out a capsule on each of his palms, he describes the choice facing Neo:

“This is your last chance. After this, there is no turning back. You take the blue pill—the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill—you stay in Wonderland, and I show you how deep the rabbit hole goes. Remember: all I’m offering is the truth. Nothing more.”

 

Basically Neo is presented with a choice where he can swallow the blue pill and live a comfortable life where he can believe whatever he wants. Or, he can swallow the red pill, trade away that blissful ignorance, and gain a deeper understanding of reality. Honestly, it’s not an easy choice.

For a less serious and very funny example of what this choice between blissful ignorance and harsh reality looks like, listen to about a minute of this short clip from my favorite comic, Jim Gaffigan, where he talks about our denial when we stay in hotel rooms. What I’ve started to wonder is whether this same choice between blissful ignorance and harsh reality might apply to education.

 

Application to Education
Based on my experiences and interactions as an educator and consultant over the last 15 years, I believe that less than 15% of American math teachers have actually read and understood their grade level math standards. This might seem ludicrously low, but what I’ve found is that most people either use their textbooks in lieu of their standards or use summaries of the standards that have been written by someone else.

Believe me, I’ve done the same thing myself. In fact, as a 7th grade math teacher, for four years I taught a standard that was actually an 8th grade standard because it was in my textbook and I didn’t ever think to look and see whether it was actually a part of my standards. I just assumed that if it was in my textbook, it must be a part of my standards. Boy was I angry at myself when I discovered that. It was such a pain to teach that standard and it had taken away time from other topics I could have spent more time on.

This reality is simultaneously understandable (because many states’ standards are so challenging to read) and really scary because it means that there’s a reasonable chance that teachers are not teaching what they should be teaching.

For example, there are subtle differences between standards at various grade levels. What’s the difference between dividing fractions in 5th grade versus dividing fractions in 6th grade? What about ratios and proportions in 6th versus 7th? What about the difference between solving systems of equations in 8th grade versus Algebra 1? These differences can be challenging to figure out even when you have both standards side by side. If you don’t have them and are comparing problems listed in textbooks from two grade levels, it can be darn near impossible.

 

Conclusion
When I look back at my experiences as a new teacher, I cleaaaarly chose to take the blue pill. What can I say? It was a combination of being naïve and lazy. I chose blissful ignorance. Nowadays I choose to take the red pill. Whenever possible, I read the standard and learn more details. It can be a royal pain to make sense of it all, but I’ve realized that it’s critical to focusing on the right things.

It’s rarely an easy choice when deciding on whether to swallow the red or blue pill. Each have their advantages and disadvantages, but it’s important to realize when we are making that choice as it has consequences.

What do you think? What am I wrong about and where am I misguided? Where else do you see people choosing which pill to swallow in education?

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My favorite of all the Depth of Knowledge (DOK) levels, as I define them in these matrices for elementary and secondary mathematics, is DOK 3. I’ve always found it challenging to give a short and sweet reason as to why I felt that way… until I heard Bushnell’s Law.

This “law” was created by Atari founder Nolan Bushnell and was used to describe his ideal video game. He said:

All the best games are easy to learn and difficult to master. They should reward the first quarter and the hundredth.

 
When I first heard his law, I thought “That is exactly why I love DOK 3!!” Yes, I realize how nerdy that is, but I’ve learned to embrace it. To explain what I mean, try solving the problem below:
 
Using the digits 1 to 9, at most one time each, place a digit in each box to make a sum that is as close to 1000 as possible.

 

This is the kind of problem that takes people many attempts to figure out. So, when you’re ready to see the answer to this problem, head over to Open Middle.

 

Easy To Learn
Beginning this problem is fairly straightforward. Just place the nine digits in their own box and find the sum. As a result, every person begins with success. So, this problem is “easy to learn.”

 

Difficult To Master
However, you quickly realize that randomly choosing digits won’t be effective in the long run and so you have to think strategically by using your conceptual understanding of place value. For example, lets say you get a sum of 1044, how do you change your digits so that you don’t get even farther from 1000? So, this problem is also “difficult to master.”

 

Conclusion
I used to describe DOK 3 problems like the one you just tried by saying they had a very low floor (so that anyone can attempt them) but very high ceilings (so that they challenge even the most advanced students). That wasn’t so bad, but there is something elegant about describing them as “Easy to learn and difficult to master.”

What do you think? How do you describe problems like these? Let me know in the comments.

The post Let’s Make Math Easy To Learn And Difficult To Master appeared first on Robert Kaplinsky.

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I believe that schools and districts waste a lot of time and money on initiatives that never go anywhere.

Perhaps it happens when a district spends over a billion dollars on new iPads and changes its mind. Perhaps it’s less publicized and happens when teachers are sent to a conference, students get an expensive software, or policies change district wide. Often times it begins with high hopes… but nothing really seems to change and after a while people stop talking about it or doing anything with it.

Thinking about how much time and money gets spent on the latest shiny gadgets or hip training that go nowhere can be mind blowing. Yet, this pattern seems to keep happening without an end in sight. I don’t think it has to be this way though, and I think that applying some business principles to education may be a start.

 

The Lean Startup
Imagine that you have an idea for a new app for people’s phones. You think it could be a game changer, but you’re not sure as everyone hopes that their new app will be a game changer. What should you do? Should you spend $50,000+ and make your dream app? Or, is there a way to get a better idea about whether your idea will even work before you jump right in?

I’m guessing that many of you would want to figure out if it would work before you jump in. However, change the context to being a new app for students at a school district, and it seems like too many districts would just cut a check and maybe later figure out if it made a difference.

This is really scary to me, as it wastes crazy amounts of money and leads to burnt out teachers. So, let’s talk about two ideas I learned from the book The Lean Startup that have applications in education.

 

Minimum Viable Product
Before schools and district implement a big initiative, they should think about the assumptions they’re making that have to be true for the initiative to work. For example, with the Los Angeles USD iPad fiasco, I’m sure that the idea of every student having a device sounded amazing, but for it to work correctly, there were many assumptions that would have to prove true including:
  • Infrastructure like WiFi would have to be installed and working in schools
  • The bandwidth would have to be high enough to support all the devices being used at the same time
  • Teachers would have to find the iPads to be helpful or would not use them
  • Teachers would have to be trained on how to use them with their students
  • The iPads would need to be highly reliable or would require never ending maintenance
  • Students would have to keep them in good condition so they don’t break
  • There would have to be apps that could do what teachers wanted
  • There would have to be money to buy those apps
  • The devices would need a lifespan long enough to be worthwhile

I could go on and on, but the point is that if even one of those assumptions turned out to not be true, the whole project would fail. What good are iPads you can’t connect to the internet? What good are iPads that no teachers want to use?

The process of testing assumptions is absolutely critical, and in the Lean Startup model, the idea of a minimum viable product (MVP) allows you to test assumptions before moving on. Here’s a real example of it from business.

Zappos founder Nick Swinmurn wanted to test the hypothesis that customers were ready and willing to buy shoes online. Instead of building a website and a large database of footwear, Swinmurn approached local shoe stores, took pictures of their inventory, posted the pictures online, bought the shoes from the stores at full price after he’d made a sale, and then shipped them directly to customers. Swinmurn deduced that customer demand was present, and Zappos would eventually grow into a billion dollar business based on the model of selling shoes online.

 
The idea that 20 years ago people were skeptical about selling shoes online may be hard to understand today, but the reality is that it would have been very risky to build a whole company out of an idea that relied on many assumptions. Instead, Swinmurn minimized his risk by testing his assumptions in the “minimum viable” way.

Sure, it was very inefficient to take picture of shoes and then ship them directly to customers. However, by doing this, he could find out whether his assumptions were true. If they weren’t, then he could figure it out before he wasted lots of time and money.

How do we do this in education? Can we pilot a program at a grade level or school to see how it works before we scale it far and wide? What valuable issues or concerns might we uncover? What we have to realize is that this is a process.

Going back to the LAUSD example, for me to commit to such an enormous expenditure, virtually ever assumption would have to be tested. Maybe I’d begin with rolling out iPads for a single school. How does the WiFi hold up? How much training do teachers need? How often are the iPads are utilized? What apps are purchased but not used? What evidence shows that the iPads make a difference?

Once those issues were resolved, then I’d scale it up and see what new issues come up. I’d repeat this until it was clear it was set up for success. While I’ve never been an administrator, it’s hard for me to understand how some of these decisions are allowed to happen.

 

Split Testing
Here’s a tough question to ask: how do we know that we’re making the right decisions before we commit to them? How do we know whether the decision we’re making is better than the alternatives?

This is something that happens in the online world all the time without you ever noticing. For example, let’s say that a website wants people to click on a button. They have some ideas about what the button could say (maybe “BUY NOW!” or “GET YOURS!”) and what color the button should be (red or blue), but they’re not really sure which is best. This is where split testing comes in.

They will set up their website to randomly pick one of the two phrases and one of the two colors. Then they will sit back and collect data on what phrase and color leads to the most clicks. If one combination of color and text results in more clicks, then they will choose that phrase and color as the permanent color of the button.

It doesn’t have to end there. They could even test the button’s shape, placement, or any other factor. The process of split testing provides data that people can use to turn their hunches into something quantifiable. So how do we do this in education?

I saw it done in my own school district when piloting a new textbook. Teachers who were unsure about which textbook was better took their two favorite books and tested them out for a nine week period. Half the teachers got book A while half got book B. After the nine weeks, they switched and got an additional nine weeks with the other book. After each nine week period, we collected data to quantify what teachers learned. This resulted in helping teachers make a more informed decision.

Continuing with the iPad example, perhaps Los Angeles USD could have given some teachers online training and some in person training and examined the results. Maybe some schools could have had one app while others had another to see what was more effective. I’m not saying that I have a perfect way of setting this up, but that by testing our options, we’re more likely to make a decision we are happy with.

 

Conclusion
Unfortunately, I believe that people make worse decisions when they’re spending other people’s money. I think that we need to be more practical about the big choices we make and look for ways to better ensure success ahead of time. My hope is that this blog post provides two options to consider if you find yourself in a similar position.

I’d like your pushback though. What am I naive about? What am I missing? What other ways could these techniques be applied? Please let me know in the comments.

The post Here’s How Schools Can Waste Less Time and Money On Initiatives appeared first on Robert Kaplinsky.

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