Rethinking Math Concepts for Marginalized Students

Introduction: 

An introduction to what sparked the original thought, but this essay has not gone where I originally intended it to go. 

A thought, not intended to reflect on anyone, especially not myself as I tend to be very insensitive. I prefer to deemphasize the money aspect of, “poor families”, and say “intentionally marginalized communities”. The trends we see in neighborhoods such as these aren’t from lack of money, or color of skin, or religion, or music, or drug/alcohol use, or anything that could be considered personal failures, it comes from the structure of our political and economic system that seems to require that certain groups get held back in contrast to others. (maybe this already happens I don’t know)

I happen to work in one of these marginalized neighborhoods. I don’t think public education is serving my students very well. The lack of change that I have been able to bring about, heck, the lack of discussion on how to educate our children, is one of the strongest drivers of my unhappiness not just in work, but in life itself. 

I read on page 146 and 147 of Fair Isn’t Always Equal by Rick Wormeli:

“I worked for several years in a low-performing school with a high concentration of students from poor families. Many students were also involved in violent gangs. When I later moved to a school with students from more affluent families, I realized how much lower my expectations had been for the students in the first school. The truth is that I didn’t know how to teach them well, and I was just plain tired of fighting all the battles. It seemed kinder and easier to not expect as much from them. I look back on that experience and I cringe. (emphasis mine)

This quote comes from Section III GRADING Chapter 11 “The Relative Nature of Grades and Their Definitions” 

I’d summarize the chapter as basically:

• Grades are a terrible measure of learning
• Grades often are confused with tools for motivation
• An “A” can mean above standard or meeting standards depending on the school or teacher
• Grades are often used as feedback when they are supposed to represent post-learning achievement (Grades aren’t part of learning)

It was about 11 years ago when I was drawn by the idea that you can teach calculus to a 5 year old. (https://www.youtube.com/watch?v=rNx6G-9GKPE). So the idea that I can teach 8th grade math to anyone willing to learn doesn’t seem like an impossible task. As Dr. Nellie Deutsch was developing her family math website and refining this very concept. I used those tools with my own kids and once or twice with nieces and nephews. https://naturalmath.com/goods/ 

While the last of those kids is in high school and all of them have decent math skills (one niece is even majoring in math) I doubt that my introductions to advanced math concepts had anything to do with it, especially because the nieces and nephews only saw me at most once a year. More likely they are all successful students because they all grew up in non-marginalized communities. (Source: Many discussions I’ve had with my brother-in-law on the nature of education and the quality of schools our children were enrolled in). Sure they all have parents who love them, they have supports, they all have everything you’d hope all children had, meaning they will require a good bit of therapy to become normal, but should be able to get decent jobs and live at least moderately happy lives. More importantly for this essay, they were all at or above grade level for at least most of their educational careers. 

Thoughts on Teaching:

First a note. If you’ve never taught you may not understand that teaching a class is not particularly difficult. What is difficult is getting to know students and adjusting for them. That is what this essay is about. I spent a good 8-10 hours on day 1 writing this, then a couple more hours on day 2 and 3 trying to finish up. The hard part is thinking about what or how this will impact my classroom. Because, this is a real problem that has been consistent. A sizable number of my students struggle with slope. It seems so simple: steepness of a line, ratio of how far a line goes up or down vs the distance over. 

I’ve thought about it in the past and tried different things, none of which has been very successful. What I’m thinking about today, who knows if it will be successful later this year. It is frustrating to teach what seems to be a relatively easy and straight forward concept only to have students just forget it the next day. 

Why? I don’t really have an answer for this. I wish I did because it keeps happening to me and my students. This is where the essay turned from; “offended that teachers are going easy on kids because they are poor”, to, “do I really know what I’m doing? Let’s examine a common complaint about how my lessons aren’t working and try to revise that basic lesson.” 

A simple example

Take the basic concept of slope of a line. It starts simply as rise over run riserun. Take two points on a line and count up from one point then over to the other set that as a ratio and you’re done. Draw a little picture on the board of a slope triangle for visuals and it really seems simple. Slope formula follows as a logical extension if you don’t happen to have a graph handy, or your coordinate points aren’t composed of nice whole numbers you can still find slope by thinking of how far up or down vs how far over. Starting with a simple picture of a triangle seems like it should be easy to remember and picture in your head when doing work in the future.  

How students do it wrong? 

First, students can’t find two points on the line. They just stick a dot anywhere. (While they are technically correct it does no good here.)

Second, students don’t draw a right triangle or often not a triangle at all. For example, they tend to draw too far up so when they go over they are above the second point, then they draw down to the second point. This is not a triangle, just an irregular four sided figure. 

Expectation	Reality
Slope of 412 reduced to 13	Slope of 510 or something

Reflection

From this example I can really see that I’m assuming students have a base of knowledge, but I’m also assuming that I’m breaking down a concept to its purest form, when I’m doing neither of those things. (Give me a moment I’m learning what I’m doing as I’m writing this). 

Why does this happen?

1. Students aren’t using the points with whole numbers and coordinates that we can identify.
   1. It is possible they do this because they aren’t comfortable finding and naming coordinate points on a graph. 
2. Students don’t make points on the graph lines so they ignore the coordinate plane and focus on connecting the points. 
3. Do students realize it should be a triangle?
   1. Do students realize a right triangle is important?
4. While ratio isn’t supposed to be a confusing word, it really is (Sometimes texts use the word quotient, but that is even worse.)
   1. Should I say make a fraction with the numbers? I’ve tried.
5. This is how to find a slope, it does nothing to help students understand what the concept of a slope is. It feels like we are teaching what slope is, but all we are really doing is telling students slope is the ratio of change in the value of y and the change in the value of x, then showing that slope can be the triangle made when we pick a point on a line and then go up and over to a second point on the line. 

Finding the slope of a line didn’t start out disconnected. Generally I start with a line or two and ask, “How do we find a way to determine which line is steeper than the other?” I probably didn’t give enough time to think about the question, “What do we mean by steepness?” I probably just took a bunch of lines and said which is steeper, which everyone could do. Then said how do you know and jumped on the first kid who said something along the lines of this line goes up faster. Then it’s here is the up and here is the over the more up and the less over and you got steeper. 

When a teacher has students with a solid 7th grade math background this is enough. When a teacher has students without any solid math background it’s enough for today, but not for holding in memory to be used tomorrow. 

I stopped here and asked chat GPT: how would you teach finding slope of a line using inquire based methods to 8th grade students who are more than 3 grade levels below in math achievement

Lesson here 

The AI is making a lot of the same mistakes. 

So what am I doing that needs to change:

1. Assuming knowledge (Yep, students should have some base knowledge, so where can we start assuming they know something? Yeah, diagnostics, but my students test between kindergarten and 5th grade in many classes so again where do we start assuming knowledge)
   1. When taking things to a graph make sure to connect coordinates with values. Maybe show in some way that we cannot know the exact coordinates of a point not on a grid.
   2. Maybe show that measuring distance between two points on the graph can be done but one point not on a graph line then it can’t be done. 
   3. Name it slope triangle right away.
      1. Making the triangle isn’t required for understanding or doing, but will be useful sometimes in the future so exposure is nice, it just isn’t the goal of the lesson.
2. Not spending enough time exploring the concept of steepness and instead leading students towards the answer you want riser/un
   1. One of the ways to compensate for lack of background math knowledge is to start very concrete and let the students dictate when we move more abstractly.
   2. Start with simple proportional ratio problems from 7th grade
      1. How can we write the ratios
      2. How can we compare two different ratios
      3. Ask questions about which is increasing faster
3. Where and when does practice fit in?
   1. Seriously, students who most need practice don’t. 
   2. Most of class is spent introducing this idea often because the background math isn’t there so we are building from the very bottom.
   3. Homework generally isn’t done.
   4. Stop using I do, we do, you do
      1. Build from concrete
      2. Write notes with examples
      3. Finish with what did I learn
      4. Prove it with intentional practice

Rethinking the concept 

I’m starting to think that we don’t know how to teach “these” kids because we aren’t building a curriculum for them. We have a curriculum for “regular” students, but not students who have been going to school designed to marginalize them. 

When exploring advanced math concepts to my own kids I didn’t really think about building a base of knowledge and I knew there was nothing to build on. I also didn’t care if it connected with anything because for the most part they weren’t even in school. In the classroom most lessons are built with the assumption that there is something to build on and that something else will come after. While there is always something to build on with students, where that solid ground starts is often variable. The point of entry must be open.  

When teaching a concept we start with the basic concept, but also need to explore edge cases. 

• What if both start with zero? Or a million?
• What if the slopes are almost the same? 
• What if I don’t have access to numbers? 
• Really big slopes. 
• Really small slopes. 
• Comparing slopes. 
• Slopes with whole numbers. 
• Negative slopes. 
• Zero slope. 
• Vertical slope. 

Also: When will we use this concept? 

• What are the ways we will use the concept? 
• Where does it fit in on the total range of math education? 
• What came immediately before? 
• What will come next? 
• What is the larger concept(s) we are teaching related to this?
• Is there a specific strategy that students should know (slope triangle)?

Let’s just think of the seemingly simple concept of using a slope triangle to find slope, but connecting it to what is slope and how will we make the leap to using the slope formula.

The slope triangle isn’t important in itself, as a method to find slope. It is an algorithm such as you would use to multiply larger numbers, but that algorithm can be useful for comparing slopes, and proving that slopes on a straight line are the same all over, and that triangles are similar, but not congruent. So the triangle is important, but not required. Our lesson objective then would be along the lines of: using a graph to determine the exact slope of a line. 

I have kind of a lesson from here till almost the end, but not something I would teach from. Think of it as a proto-lesson. An idea I’ll save until we get closer to this point in the curriculum and flesh out then.

Warm up

Starting with the first point assuming knowledge. When we make things more concrete then they become more manageable for students with less background knowledge. Sometimes it is called a lowering barrier of entry. I want to start with comparing the steepness of two lines with an objective measurement. 

Which line is steeper?	What do we need to do to help? Zoom in ok?	What makes this so much easier?	Can you give a number for the steepness? The number has to tell me which line is steeper even if I can’t see the lines.

The last picture and question are important in building a purpose for the inquiry to follow.

Inquiry 

Exploring steepness

This is the part of the lesson where the big mistake is thinking too much about what the students are doing. They are doing, but the doing is supposed to help them think. The doing has to lead to thinking and the thinking has to be specific?

We need to have a reason for slope or it won’t be remembered. Students may not realize that a line on the graph represents more than just an object floating out in space (cannot assume knowledge). At this point we want to bring in the axis lines and labels of our graph to add context (This is like character development in a story and helps us remember the overall story line). Students don’t have to talk about lines and points and steepness. They can talk about the number of plants per square feet. (This is even better if you can use real data on any two ratios. The problem with real ratios is often that they are not pretty and don’t use  whole numbers. The problem with not using real ratios is we start ugly then adjust our numbers to make it pretty and that has all sorts of problems, like the question, why are we doing this?). Comment: Notice the steeper line is mostly under the other line, this is so we don’t accidentally equate steepness with on top. 

I really want students to think and be able to answer the basic questions 

• What is the steepness of each of the lines? 
• How can you communicate that steepness without showing the graph? 
• Is that communication intuitive?
  • Like if you tell me blue is something steep and orange is something steep, can I know that orange is steeper than blue?
• If it is more steep how do I know without you telling me? 

For this particular graph I might ask questions like:

• Which is better for a small apartment but I love plants? 
• Which one is better if I want the biggest garden ever and space is not a problem?

What answers might the students come up with? Where will the students be working? How will we get everyone to the correct answers? This case being rise/run?

At this point I realized the last 30 minutes or so of work will probably be tossed. I’ll keep the warm up, but go in a slightly different direction for discussion.

The thing is with a problem like this student answers will come fast and they will want to know if they are right or wrong right away? I need a good question or questions that have an answer that is intuitively correct, but is not obvious. 

Now I’m looking at the graph and thinking I want to change a couple of things so I can develop a better question. What if I changed the axis to height and distance and instead of talking about plants we were talking about wheelchair ramps? Now my students will care about how steep the line is because they have to figure out if it is too steep to push a wheelchair. If we had time and resources we could even play around with a wheelchair. We could at least say engineers did this in real life. I should also look up how steep a standard wheelchair ramp is (it is a 1:12 ratio). 

Maybe I can’t get to a question that gets them to a slope directly. Instead I might say that the ADA has a requirement that the slope of a wheelchair ramp cannot exceed 1:12. What does that mean?

I saw a sign on the road telling me to slow down, there was a 14% grade up ahead? What does that mean?

I’ve got it as a colon and a percentage. I need it as a fraction for future work. I’d also like the slope triangle thrown in there. 

Recap a bit for myself because it’s been a few days. Warm-up with a couple of lines and ask students which is steeper and how can you tell me if I can’t see the lines. Followed by slope from ADA wheelchair ramps and road signs. What do they mean and how are they the same and different from our warm up?

If we put the three examples next to each other we can talk a couple of minutes about how they each are excellent for their particular use case. Then decide that the use of graphs leads us naturally towards the use of difference in y-coordinates and x-coordinates. This requires the knowing of where the point is on the line, the use of the graph lines, and the creating of a triangle.

I have smaller whiteboards on the walls so I might give groups a couple of lines and ask them to tell me the slopes. Each group can have a different line. They have 5 minutes to determine the slope. Then one by one we can have groups tell us the slope and what number to start on the y-axis and see if the other groups can draw their line correctly. A different person each time for each group. 

Ask generally what were the key points making sure we generally describe drawing a slope triangle. Have students take notes in their notebooks, including at least two examples. Name today’s notes, “finding slope on a graph with the slope triangle strategy.” 

At home practice with answers on the LMS to check.  

Yea, thanks for taking this journey with me. Now how do I put all of this thinking into the hour a day I have for lesson planning?

Conclusion

This essay is getting so long and taking so much time because it has morphed. The problem is I focused first on the second half of the sentence “…I was just plain tired of fighting all the battles.” (Wormeli pg 147). I hear complaints all the time about these battles; students not doing their homework, not paying attention in class, talking in class, reteaching the same lesson a million times in a row, because the students are just not getting it. When it turns out I should have been paying closer attention to the first part of the sentence. “The truth is that I didn’t know how to teach them well, …”

I don’t want to say I don’t know how to teach the students, or how to differentiate, or simply how to teach. The thing is, often I’m afraid that is just the simple truth. It’s not just me though, I don’t think education is built for my students. Which brings us back to the beginning. Students in intentionally marginalized neighborhoods do not get the education they need.  

Standardized Testing: Equity in Education

Yesterday I finished 6 hours of curriculum work. This is tied to the 6 or 12 hours I spent the summer before and the hour I spent listening to a paid consultant. All of this was planned so that we can improve the achievement of our students as measured on standardized tests.

This is supposed to be good for our students and I’m sure it will show some measurable gains. Yes, we talked about students all the time. We said things along the lines of, last year our students struggled with this, and whatnot. The thing is our students were not the center of our discussion. Improvements on the standardized test was the goal.

I am absolutely sure that if I read that sentence to my building principal or superintendent they would deny that was the main purpose. I’m sure they would push back and tell me that students are always first.

However, as far as I’m concerned everything we use to measure success in schools is built on the sand castle of structural racism. Measures of success are built on what well funded white school districts can and have done. They test well, they go to college, they have time and money for extra curricular activities, parents work regular jobs, in many instances one parent can and did stay home during the day, they usually read books by white authors, they generally listen to music by white musicians, look at art by white artists, discuss poems by white artists, etc….

In majority non-white districts, with lower income, less funding for schools, less stable housing, different priorities, these measures of success aren’t always the same. When we talked about students in our curriculum meetings we talked about how they could be successful in increasing their ability to succeed on tests of the specific standards that will most likely be tested. We did not start our conversations with what do our students need.

I’m not a researcher. I’m not going to spend most f my day digging up information so I can write a receipt and drop it on you like a microphone. Just start with this YouTube short and imagine English class revisited to explore the difference between Standard American English with local dialects.

Another Reason Democrats Keep Losing

This is why I think democrats are missing the mark. 

They claim to be for the people, but let’s use my recent example of interaction with the government for the people. 

I opened an account with an online bank almost 5 years ago.  They were FDIC insured so I thought I would be ok. 

About 6 months ago they went bankrupt. I was one day late in transferring my money out, damn. 

After almost 6 months of little or no useful information I’m finally told I will be informed of a way to get my money back. 

During this time senators on the banking committee were aware of this farce and supposedly on top of it. I made a complaint with several different government agencies. I also wrote a letter to my congressman. 

I got a form response from one government agency, telling me they were aware of the situation, but could not give me any specific information on my particulars. I got other responses saying they didn’t deal with banks. 

Finally, I got the long awaited email saying I could apply for my money back. This bank, which claims to be cleaning the mess left by the original bank. They made a point to tell me they spent months trying to figure out the balance sheet. It was oh so hard and they did this at their own expense. 

They also made a point of telling everyone that you could appeal but if you did so they probably wouldn’t accept said appeal based solely on the record of transactions. 

They offered me 1/3 of the money in my account. There was no justification for it, except their word that they went through all of the messed up records and this was my actual true balance. 

Now I assume I have to find all of my old pay stubs and prove that the amounts on them are equal to the amounts of deposits made at about the same time. I’m not sure how I’m going to prove that the withdrawals that are there are the only withdrawals. Perhaps there are others that were not recorded. I doubt it. 

What has my congressman done? Well after the third email where I started with this is the third time I’ve written to you, someone contacted me. Nothing since, but hey its a start. I actually worked with her a few years back with some IRS troubles and she got someone from the IRS to call me and explain what was wrong.  I haven’t heard back from either senator. 

Why hasn’t the FDIC stepped in and just said make people whole because they are insured and stop whining? Why don’t my representatives respond to me? Why does a large corporation get to just dictate terms to me without any proof whatsoever? Why is it on me to prove what they owe me? Why don’t they have to prove that they owe me less than what the official record is?

Democrats have created rules and safeguards to protect the average citizen. Those safeguards make it more difficult for smaller independent entrepreneurs to get started unless they borrow tons of capital from predatory investors. Then when they fail those safeguards are ignored and the regular citizen is left twisting in the wind and then dumped on. What do our representatives do? So far nothing? I imagine if I didn’t write to my congressman I’d have no hope at all to get my money back. Currently all I have is a glimmer. 

Fractions

Why is it so difficult to understand the addition of fractions. Part, I think comes from the way we define fractions.

The introduction of fractions is usually this many colored parts out of this many total.

Two fifths is two boxes out of five colored in while three fourths is three out of four boxes colored in

Two fifths is two boxes out of five colored in while three fourths is three out of four boxes colored in.

Looking at it like this we can forgive students who then say two of five plus three of four is five of seven.

Creating basic fractions by coloring in two cells our of five to make two fifths and three out of four to make three fourths.

We tell students that we cannot add fractions of different denominators. Therefore we have to find equivalent fractions for both so that they have the same denominators.

Why this is done is often glossed over.

Skip counting the first fraction five times we get to fifteen twentieths. Skip counting the second fraction four times we get to eight twentieths. Added together we have a total of twenty three twentieths. he equivalent fractions

To find the correct answer we tell students that we can only add fractions of the same denominator, and then we only add the numerators.

We often say skip count by numerator and denominator until both fractions have the same denominator.

How many times to skip count each is a guess most of the time.

Sometimes it might be easier to do if we separate the numerators and the denominators.

Skip counting the first fraction five times we get to fifteen twentieths. Skip counting the second fraction four times we get to eight twentieths. Added together we have a total of twenty three twentieths.

This way we can see when the denominators are equal.

Imagine adding five sevenths and seven eights. This quickly becomes unwieldy as the denominators become larger, especially if they are relatively prime.

Another common way to add fractions is a percentages.

Some fractions are easily converted to percentages.

This is actually a nice step in the transition between fractions as how many boxes are colored out of the total. You’re asking what percent has been colored in so this becomes a fraction out of 100.

These fractions can be converted to percentages fairly easily by dividing 100 by the denominator and multiplying by the numerator. We end up with 40% plus 75%. converting 115% back to the simplest form might be more difficult.

For basic fractions like these the transition to percentages is fairly easy. Maybe you don’t know what percent two out of five is, but you can divide 100 by 5 and get 205 for each block quickly.

Three fourths is even easier because a quarter is 25 cents and 3 quarters is 75 cents. (Very US centric)

Now imagine trying to add five sevenths and seven eights. How much is 7 parts of 100?

The model quickly falls apart with the introduction of more difficult fractions like five sevenths and seven eighths.

100 divided by 7 is 12 point something????

Comparing the images for two fifths and three fourths when the over all length is the same is the same as comparing them as wholes

Here we might want to separate the numerator and the denominator again.

Images of two fifths and three fourths combined together show that the cells making up the numerator are longer than the cells of a whole but we don’t know how much because it is just part of a cell hanging over.

When we add them together we can see the numerators add together to make a bit more than a whole. How much more we don’t know because a part of the numerator hangs over the whole and we need to figure out how big that part is.

As we double each fraction we can see two fifths becomes four tenths and three fourths becomes six eights, but the overall length doesn’t change.

Each time I double a fraction I keep it as part of the whole and each whole is the same size. As I multiply each fraction the overall length doesn’t change so each cell must shrink until they all fit. In essence the denominator is shrinking in size, as the number is multiplying. (The total number of pieces it takes to make a whole is increasing, but the whole isn’t changing size so the size of each piece shrinks).

There are rules so each fraction changes by a multiple of the numerator and a multiple of the denominator because the fraction is a part of the whole and we want to keep the same part of the whole. (Equivalent fractions)

As I work my way up, I continue until each cell is the same size or each denominator is the same number. (Same as we did the first time, but now we are thinking of it as parts of a whole.)

Multiplication of each fraction shows we end with four groups of the two fifths and five groups of the three fourths.

Now that all of the denominators are the same I can simply combine all of the parts in the numerator that have been colored. I have eight of twenty in the first fraction and fifteen of twenty in the second fraction.

Illustrating we are adding eight twentieths and thirteen twentieths. Eight colored cells on top of a total of twenty and thirteen colored cells on top of a total of twenty. combined together we see 23 total colored cells above 20 cells making up a whole.

When I add them together they still hang over the edge, but now I can see the exact amount that hang over the edge.

Ending page illustrating with cells we have 23 in the numerator and 20 in the denominator.

Soft Bigotry of Low Expectations

That was the justification for George W. Bush’s No child Left Behind Legislation. His premise was that teachers and schools in low income districts just didn’t expect their students to be able to achieve so they didn’t push them very hard.

If we would give everyone a standardized test he could objectively tell which districts and which schools were doing better and parents could then choose a better school. And the government could stop spending money on failing schools.

First of all, most schools are chosen by where you live. If you live in the low income neighborhood you get the low income school that comes with it.

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Yes the number of students in schools of choice (read charter) increased by 5%, but the quality of the schools hasn’t changed. Which is bad for charter schools because they don’t have to take the most difficult students.

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Second, that school probably sucks because school funding in America is almost always tied to personal wealth. (So we should reduce funding for these schools?)

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Our current system for funding public schools shortchanges students, particularly low-income students. (Economic Policy Institute)

Check out the wide variety in public school funding for yourself.

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Finally, standardized tests are a horrible way to measure the quality of a school.

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Effects of standardized tests on students and teachers.

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Pretty much everything that was done since has made the first two problems worse.

I was working in a low income school district when NCLB was enacted. We knew our schools were below par. We did our best, but the combination of high staff turnover rate, lack of funding, and lost faith in education combined to keep our kids down. It wasn’t the schools, the teachers, or even the parents (as so many people would like to blame), so much as straight out hard bigotry.

When funding is tied to family wealth and families have been cut out of the wealth building apparatus for generations, well you will have almost no funding.

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Racial wealth gap today is legacy of vastly unequal wealth for Black and White Americans following Civil War

Racial wealth gap has been stagnant for last 40 years due to differences in Black and White households’ wealth portfolios

Federal Reserve Bank of Minneapolis

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We also know that after Brown V. Board of Education white folks fled the cities and took their wealth with them. It is said that many school districts today are more racially segregated since.

What do we need to do to change education? There isn’t a silver bullet that fixes everything in every school district, but if their were it would be people.

Further reading

The Soft Bigotry of Low Expectations … Through Mathematics Education

The Racial Wealth Gap

How the racial wealth gap has evolved—and why it persists

Public education funding in the U.S. needs an overhaul

School Choice in the United States: 2019

Adolescent Brain Development

A review or summary of

Understanding brain development: Investing in young adolescents’ cognitive and social-emotional development Katie Jansen & Sarah M. Kiefer

In case you didn’t know some of the hallmarks of the adolescent years are a lack of impulse control, a yearning for independence, emotional swings, disorganization, and poor decision making skills. The prefrontal cortex, the brain itself is growing and changing more than it has since the first 5 years of life.

On top of all this brain reorganization everyone hits puberty and discovers what hormones can do. Social structures are rearranged. Close friends often change, and peer groups gain much more influence.

These are things that all middle school teachers know.

Often when talking about teaching in middle school I’ll tell people that teaching content takes a back seat to teaching social skills. Jansen and Kiefer come right out in the 2nd page of the article saying, “teachers who recognize adolescence as a critical time to invest in students adopt research-based, equitable, developmentally responsive strategies that support cognitive and social-emotional development” (pg 18)

What they are leading towards is that if we develop a safe environment for growth and help students have positive experiences they can develop higher brain functions quicker. In other words, they mature faster.

While this might seem like a minefield for most people what it actually is, is an opportunity. “young adolescents are at an ideal age for teachers to provide explicit learning strategies and support for self-regulated learning skills” (pg 20)

Students come into middle school with no real idea of how to learn. Teachers can and should take time to teach effective strategies. Teaching review strategies by incorporating it into lessons. frequent low-stakes quizzes (formative assessment). They can incorporate spaced retrieval and regularly include previous material on tests, as well as explicitly teaching skills such as planning and organization.

The goal is to get students to do their own self-regulation, but that is a skill that can be taught. Students will not know how to evaluate their own learning. They won’t know how to organize anything. They won’t know any effective study techniques. And they will be deeply afraid of making mistakes, especially in front of their peers.

It will be easy for teachers and other adults to mistake immaturity and lack of cognitive development as behavior issues. Especially when some of their peers will seem to have no problem with self regulation, because they have matured faster, or are in a different stage of development. It is important to keep a high ratio of positive feedback, and empathy. Authoritarian or behaviors that could be construed as controlling will often inspire an oppositional behavior from middle school students.

While students are growing and developing emotionally and physically teachers and schools can help by providing opportunities for healthy exploration of a variety of experiences. This allows students to funnel their impulsive and sensation seeking behaviors towards positive activities instead of risks.

In the end the goal is to build students capacity for self regulation, and critical thinking by allowing more autonomy, and challenging work. Asking students to challenge themselves in an environment that is safe and failure is an accepted part of learning.

If it’s too good to be true, then it probably is

Effect Sizes and the 10-Foot Man

To AI or Not to AI

That is the question everyone is asking isn’t it?

Seems like most of the folks talking about AI are talking about either how to stop students from using it or what they can use it for to lighten their own load.

Of course what is a tool for anyway, but something to be used to help do something better, easier, or new.

Wait new?

What can AI allow me to do that is new?

I’m not really sure. When we ask these AI to write something or answer a question it isn’t creating anything new. It’s stealing bits and pieces from different places on the web and cobbling them together.

I read this blog post by NomadWarMachine this morning and I agree the list of activities a person should do to get started on a creative task is fine. It was a list created in seconds. Probably even faster than you or I could do. The problem is to know and understand most people need to do.

My point is this, if what you wanted was a list this was the way to do it. However, if what you wanted was to set yourself on a path of creativity. This was the wrong way to go about it. If what you wanted was to learn how to build a habit of activities that help you stimulate creativity, this was the wrong way to do it.

We don’t learn very well by reading about something. We don’t change behaviors by glancing through a bulleted list (or numbered because the AI got that wrong). We learn by, well there are 6 or 7 or more major theories about learning. Most of them will likely require you to do your own research. Like in #etmooc2 I’m gathering a lot of information about AI by reading, but I don’t start making sense of it until I start putting it into practice. I have to play around with the various AI models, write blog posts like this, ask myself questions, ask questions in the group discussions, and so on.

The other blog post I want to mention is from Multilitteraus Incognitus. If we don’t want our students to use AI, but then we decide to use AI to help grade our students, are we being hypocritical? “Ultimately it’s the learner who needs to sweat and feel the burn.” but it’s also our responsibility as teachers to build those relationships with our students because learning and learners are social. (Vygotsky)

A month ago my son was frustrated because he keeps being asked to do solo’s on saxophone in his high school jazz band. The advice he seemed to keep getting was to do more. So he was frustrated because he didn’t know what that meant. I suggested he practice his solos. Get a few riffs down that he can play off of. His response, I drop the little brother of at class and practice for an hour before school.

The problem was he was practicing alone. He is technically good at his instrument, but he wasn’t creative. So here’s me, not a musician, giving him advice, but it was pretty simple. Find a friend and practice with them. He did and below is the result of just a week of practicing with friends and not alone.

He is the smaller sax player, the other guy was his mentor come back from college to support his friend. Also the blonde trumpet player is the younger son. He probably should get a shutout from his dad too.

A forget the name of the song (I should probably ask an AI to identify it) so just enjoy

Getting the band back together

I”m pretty excited. #ETMOOC2 has been organized. Learn more about it here.

I almost missed it because I’ve been off of twitter for most of the last couple of months. (It’s weird though, the mastodon retweeting service I signed up for sometimes works and sometimes doesn’t even though the twitter API is supposed to be pay only now.).

Whatever, I look forward to learning a bit more about AI. I haven’t gotten too much into it, but I know it is more than just a fad. I mean the AI out there for public use really isn’t an intelligence, but used correctly it can be a powerful tool. Time to explore it a bit and figure out how to use that tool for myself.

If you’re out there and looking for something to do, join us. This is a constructivist MOOC. That means you won’t be a passive learner, but creating the learning with the rest of us. If you’ve never joined a cMOOC. I highly suggest trying it out.

Register here

Back to Blogging I Hope

I recently wrote a post here. Then decided I need to get back to writing. I know my writing isn’t the greatest and I never had much readership, but it is a good way to organize my thoughts. The choice is do I do my writing here, or at my https://philosophywithoutahome.blogspot.com/ blog.

I’m not keen on the brown theme there anymore so I really have to get that changed.

Maybe I’ll publish on both. Though the blogger blog is more connected to my online name of dendari and the powers that be in my district seem to like to look for subversive activity to write up. I think I might lay low over there for a while.

Then again maybe not. I certainly have a backlog of unpublished thoughts I might want to revisit.