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Did you know robots can help us develop growth mindset?  It’s true.  Machine learning means that not only can robots learn, they can teach us too.  To see how, check out this post on Byrdseed.  I have no idea why watching videos of robots making mistakes is so funny, but my students and I were all in helpless hysterics after the first minute of this one…

After a quick discussion to refresh our memories about growth mindset and fixed mindset (which I introduced in the fall using this activity), I followed Ian’s suggestion to have the students write letters to the robot.  One from each mindset.  I collated them into two letters (shown below), which I will bring back to the students tomorrow.  All of this feeds into a major activity about writing good quality feedback, and the regular weekly practise of students writing feedback to themselves on their quizzes.

I didn’t show the second minute of the video until after everyone had turned in their letters.  But I like Ian’s suggestion of doing that later in the week and writing two new letters… where the fixed mindset has to take it all back.

Fixed Mindset

Growth Mindset

Dear robot, try not flipping pancakes.  Just stop, you suck.  Why don’t you find a better robot to do it for you? You are getting worse.  There is no chance for improvement.  Give up, just reprogram yourself, you’ll hurt someone. Perhaps you weren’t mean to flip pancakes. Try something else.  Maybe discus throwing. Dear robot, please keep trying to flip the pancake. At least it left the pan on attempt 20.  Go take a nap and try again tomorrow.  Practise more. Don’t feel bad, I can’t flip pancakes.  Keep working, and think of what can help.  I see that you’re trying different new techniques and that’s making you get closer. Maybe try another approach.  Would having another example help? Is there someone who could give you some constructive feedback? Or maybe have a way to see the pancake, like a motion capture system. That would help you keep track of the pancake as it moves through the air. Keep going, I believe in you!




Siobhan Curious inspired me to organize my thoughts so far about meta-cognition with her post “What Do Students Need to Learn About Learning.” Anyone want to suggest alternatives, additions, or improvements?

Time Management

One thing I’ve tried is to allow students to extend their due dates at will — for any reason or no reason.  The only condition is that they notify me before the end of the business day *before* the due date.  This removes the motivation to inflate or fabricate reasons — since they don’t need one.  It also promotes time management in two ways: one, it means students have to think one day ahead about what’s due.  If they start an assignment the night before it’s due and realize they can’t finish it for some reason, the extension is not available; so they get into the habit of starting things at least two days before the due date.  It’s a small improvement, but I figure it’s the logical first baby step!

The other way it promotes time management is that every student’s due dates end up being different, so they have to start keeping their own calendar — they can’t just ask a classmate, since everyone’s got custom due dates.  I can nag about the usefulness of using a calendar until the cows come home, but this provides a concrete motivation to do it.  This year I realized that my students, most of them of the generation that people complain is “always on their phones”, don’t know how to use their calendar app.  I’m thinking of incorporating this next semester — especially showing them how to keep separate “school” and “personal” calendars so they can be displayed together or individually, and also why it’s useful to track both the dates work is due, in addition to the block of time when they actually plan to work on it.

Relating Ideas To Promote Retention

My best attempt at this has been to require it on tests and assignments: “give one example of an idea we’ve learned previously that supports this one,” or “give two examples of evidence from the data sheet that support your answer.”  I accept almost any answers here, unless they’re completely unrelated to the topic, and the students’ choices help me understand how they’re thinking.

Organizing Their Notes

Two things I’ve tried are handing out dividers at the beginning of the semester, one per topic… and creating activities that require students to use data from previous weeks or months.  I try to start this immediately at the beginning of the semester, so they get in the habit of keeping things in their binders, instead of tossing them in the bottom of a locker or backpack.  The latter seems to work better than the former… although I’d like to be more intentional about helping them “file” assignments and tests in the right section of their binders when they get passed back.  This also (I hope) helps them develop methodical ways of searching through their notes for information, which I think many students are unfamiliar with because they are so used to being able to press CTRL -F.  Open-notes tests also help motivate this.

I also explicitly teach how and when to use the textbook’s table of contents vs index, and give assignments where they have to look up information in the text (or find a practise problem on a given topic), which is surprisingly hard for my first year college students!

Dealing With Failure

Interestingly, I have students who have so little experience with it that they’re not skilled in dealing with it, and others who have experienced failure so consistently that they seem to have given up even trying to deal with it.  It’s hard to help both groups at the same time.  I’m experimenting with two main activities here: the Marshmallow Challenge and How Your Brain Learns and Remembers (based on ideas similar to Carol Dweck’s “growth mindset”).

Absolute Vs Analytical Ways of Knowing

I use the Foundation for Critical Thinking’s “Miniature Guide To Critical Thinking.”  It’s short, I can afford to buy a class set, and it’s surprisingly useful.  I introduce the pieces one at a time, as they become relevant.  See p. 18 for the idea of “multi-system thinking”; it’s their way of pointing out that the distinction between “opinions” and “facts” doesn’t go far enough, because most substantive questions require us to go beyond right and wrong answers into making a well-reasoned judgment call about better and worse answers — which is different from an entirely subjective and personal opinion about preference.  I also appreciate their idea that “critical thinking” means “using criteria”, not just “criticizing.”  And when class discussions get heated or confrontational, nothing helps me keep myself and my students focused better than their “intellectual traits” (p. 16 of the little booklet, or also available online here) (my struggles, failures, and successes are somewhat documented Evaluating Thinking).

What the Mind Does While Reading

This is one of my major obsessions.  So far the most useful resources I have found are books by Chris Tovani, especially Do I Really Have to Teach Reading? and I Read It But I Don’t Get It.  Tovani is a teacher educator who describes herself as having been functionally illiterate for most of her school years.  Both books are full of concrete lesson ideas and handouts that can be photocopied.  I created some handouts that are available for others to download based on her exercises — such as the Pencil Test and the “Think-Aloud.”

Ideas About Ideas

While attempting these things, I’ve gradually learned that many of the concepts and vocabulary items about evaluating ideas are foreign to my students.  Many students don’t know words like “inference”, “definition”, “contradiction” (yes, I’m serious), or my favourite, “begging the question.”  So I’ve tried to weave these into everything we do, especially by using another Tovani-inspired technique — the “Comprehension Constructor.”  The blank handout is below, for anyone who’d like to borrow it or improve it.

To see some examples of the kinds of things students write when they do it, click through:


I’ve been looking for new ways every year to turn over a bit more control to the students, to help them use that control well, and to strike a balance between my responsibility to their safety (in their schoolwork and their future jobs) with my responsibility to their personal and collective self-determination.

One tiny change I made this year is to use more “portfolio-style” assessments.  If you work for the same institution I do, you know that “portfolio” can mean a bewildering variety of things… I’m using it here in the concrete sense used by artists and architects.  So far this semester, that looks like doing in-class exercises where students work on 3-5 examples of the same thing. For example, our first lab about circuits required students to hook up 3 circuits, using batteries, light bulbs, and switches, and draw what they had built.  On the second lab day, I asked them to build the same circuits again, based on their sketches, and add measurements of voltage, current, and resistance.  On the third day, they practised interpreting the results, using sentence prompts.

But the “assignment” wasn’t “hook up a circuit.”  The skills I was assessing were “Interpret ohmmeter result”, “Interpret voltmeter results”, “Document a circuit”, etc.  So I asked them to choose from among the circuits they had worked on, and let me know which one (or two) best showed their abilities.

I haven’t reviewed the submissions yet, but I’m anticipating that they’ll need feedback not only on the skill of interpreting a circuit but also on the skill of self-assessment.

In support of this, I’ve had students evaluate the data gathered by the entire class.  Part of my hope is that seeing each other’s work and noticing what makes it easier or harder to make sense of will help them better assess their own work.  What suggestions do you have for helping students get better at choosing which of their work best demonstrates their skills?

XKCD Comic: The erratic feedback from a randomly-varying wireless signal can make you crazy.I’m thinking about how to make assessments even lower stakes, especially quizzes.  Currently, any quiz can be re-attempted at any point in the semester, with no penalty in marks.  For a student who’s doing it for the second time, I require them to correct their quiz (if it was a quiz) and complete two practise problems, in order to apply for reassessment. (FYI, it can also be submitted in any alternate format that demonstrates mastery, in lieu of a quiz, but students rarely choose that option).

The upside of requiring practise problems is eliminating the brute-force approach where students just keep randomly trying quizzes thinking they will eventually show mastery (this doesn’t work, but it wastes a lot of time).  It also introduces some self-assessment into the process.  We practise how to write good-quality feedback, including trying to figure out what caused them to make the mistake.

The downside is that the workload in our program is really unreasonable (dear employers of electronics technicians, if you are reading this, most  hard-working beginners cannot go from zero to meeting your standards in two years.  Please contact me to discuss).  So, students are really upset about having to do two practise problems.  I try to sell it as “customized homework” — since I no longer assign homework practise problems, they are effectively exempting themselves from any part of the “homework” in areas where they have already demonstrated proficiency.  The students don’t buy it though.  They put huge pressure on themselves to get things right the first time, so they won’t have to do any practise.  That, of course, sours our classroom culture and makes it harder for them to think well.

I’m considering a couple of options.  One is, when they write a quiz, to ask them whether they are submitting it to be evaluated or just for feedback.  Again, it promotes self-assessment: am I ready?  Am I confident?  Is this what mastery looks and feels like?

If they’re submitting for feedback, I won’t enter it into the gradebook, and they don’t have to submit practise problems when they try it next (but if they didn’t succeed that time, it would be back to practising).

Another option is simply to chuck the practise problem requirement.  I could ask for a corrected quiz and good quality diagnostic feedback (written by themselves to themselves) instead.  It would be a shame, the practise really does benefit them, but I’m wondering if it’s worth it.

All suggestions welcome!

I’ve written before about using Diana Hestwood’s slide deck on growth mindset.  It’s called “How Your Brain Learns and Remembers,” and it uses an explanation of neuron biology to promote a growth mindset.  I found the slide deck pretty self-sufficient — it was complete enough not to require a presenter.  In the spirit of “Presentation Zen,” I converted it into a handout and asked students to complete the questions embedded in it.

Note: my students needed a full 20 minutes to complete this thoughtfully without feeling rushed.  This year I didn’t give them quite enough time and their responses are less personal than they have been in the past.


Comments From Students

“It takes more than insight of studying for dendrites to grow, it will take practice.”

“Good exercise, I recommend it for future students.”

“Neurons are amazing!”


Here are the resources I’ll be using for the Peer Assessment Workshop.

Participant Handout

Participants will work through this handout during the workshop.  Includes two practice exercises: one for peer assessment of a hands-on task, and one for peer assessment of something students have written.  Click through to see the buttons to download or zoom.


Feel free to download the Word version if you like.

Workshop Evaluation

This is the evaluation form participants will complete at the end of the workshop.   I really like this style of evaluation; instead of asking participants to rank on a scale of 1-5 how much they “liked” something, it asks whether it’s useful in their work, and whether they knew it already.   This gives me a lot more data about what to include/exclude next time.  The whole layout is cribbed wholesale, with permission, from Will At Work Learning.  He gives a thorough explanation of the decisions behind the design; he calls it a “smile sheet”, because it’s an assessment that “shows its teeth.”

Click through to see the buttons to download or zoom.


Feel free to download the Word version if you like.

Other Stuff

In case they might be useful, here are my detailed presentation notes.

This week, I’ve been working on  Jo Boaler’s MOOC “How To Learn Math.”  It’s presented via videos, forum discussions, and peer assessment; registration is still open, for those who might be interested.

They’re having some technical difficulties with the discussion forum, so I thought I would use this space to open up the questions I’m wondering about.  You don’t need to be taking the course to contribute; all ideas welcome.

Student Readiness for College Math

According to Session 1, math is a major stumbling block in pursuing post-secondary education.  I’m assuming the stats are American; if you have more details about the research that generated them, please let me know!

Percentage of post-secondary students who go to 2-year colleges: 50%

Percentage of 2-year college students who take at least one remedial math course: 70%

Percentage of college remedial math students who pass the course: 10%

My Questions

The rest, apparently, leave college.  The first question we were asked was, what might be causing this?  People hazarded a wide variety of guesses.  I wonder who collected these stats, and what conclusions they drew, if any?

Math Trauma

The next topic we discussed was the unusual degree of math trauma.  Boaler says this:

“When [What’s Math Got To Do With It] came out,  I was [interviewed] on about 40 different radio stations across the US and BBC stations across the UK.  And the presenters, almost all of them, shared with me their own stories of math trauma.”

Boaler goes on to quote Kitty Dunne, reporting on Wisconsin Radio: “Why is math such a scarring experience for so many people? … You don’t hear of… too many kids with scarring English class experience.”  She also describes applications she received for a similar course she taught at Stanford, for which the 70 applicants “all wrote pretty much the same thing.  that I used to be great at maths, I used to love maths, until …”.

My Questions

The video describes the connection that is often assumed about math and “smartness,” as though being good at English just means you’re good at English but being good at Math means you’re “smart.”  But that’s just begging the question.  Where does that assumption come from? Is this connected to ideas from the Renaissance about science, intellectualism, or abstraction?

Stereotype Threat

There was a brief discussion of stereotype threat: the idea that students’ performance declines when they are reminded that they belong to a group that is stereotyped as being poor at that task.  For example, when demographic questions appear at the top of a standardized math test, there is a much wider gender gap in scores than when those questions aren’t asked. It can also happen just through the framing of the task.  An interesting example was when two groups of white students were given a sports-related task.  The group that was told it measured “natural athletic ability” performed less well than a group of white students who were not told anything about what it measured.

Boaler mentions, “researchers have found the gender and math stereotype to be established in girls as young as five years old.  So they talk about the fact that young girls are put off from engaging in math before they have even had a chance to engage in maths.”

My Questions:

How are pre-school girls picking this stuff up?  It can’t be the school system. And no, it’s not the math-hating Barbie doll (which was discontinued over 20 years ago).  I’m sure there’s the odd parent out there telling their toddlers that girls can’t do math, but I doubt that those kinds of obvious bloopers can account for the ubiquity of the phenomenon.  There are a lot of us actually trying to prevent these ideas from taking hold in our children (sisters/nieces/etc.) and we’re failing.  What are we missing?

July 22 Update: Part of what’s interesting to me about this conversation is that all the comments I’ve heard so far have been in the third person.  No one has yet identified something that they themselves did, accidentally or unknowingly, that discouraged young women from identifying with math.  I’m doing some soul-searching to try to figure out my own contributions.  I haven’t found them, but it seems like this is the kind of thing that we tend to assume is done by other people.  Help and suggestions appreciated — especially in the first person.

Interventions That Worked

Boaler describes two interventions that had a statistically significant effect.  One was in the context of a first-draft essay for which students got specific, critical feedback on how to improve.  Some students also randomly received this line at the end of the feedback: “I am giving you this feedback because I believe in you.”  Teachers did not know which students got the extra sentence.

The students who found the extra sentence in their feedback made more improvements and performed better in that essay.  They also, check this out, “achieved significantly better a year later.”  And to top it all off, “white students improved, but African-American students, they made significant improvements…”  It’s not completely clear, but she seems to be suggesting that the gap narrowed between the average scores of the two groups.

The other intervention was to ask seventh grade students at the beginning of the year to write down their values, including what they mean to that student and why they’re important.  A control group was asked to write about values that other people had and why they thought others might have those values.

Apparently, the students who wrote about their own values had, by the end of the year, a 40% smaller racial achievement gap than the control group.

My Questions:

Holy smoke.  This just strikes me as implausible.  A single intervention at the beginning of the year having that kind of effect months later?  I’m not doubting the researchers (nor am I vouching for them; I haven’t read the studies).  But assuming it’s true, what exactly is happening here?

This just in from dy/dan: Jo Boaler (Stanford prof, author of What’s Math Got to Do With It and inspiration for Dan Meyer’s “pseudocontext” series) is offering a free online course for “teachers and other helpers of math learners.”  The course is called “How To Learn Math.”

“The course is a short intervention designed to change students’ relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning. In the 2013-2014 school year the course will be offered to learners of math but in July of 2013 I will release a version of the course designed for teachers and other helpers of math learners, such as parents…” [emphasis is original]

I’ve been disheartened this year to realize how limited my toolset is for convincing students to broaden their thinking about the meaning of math.  Every year, I tangle with students’ ingrained humiliation in the face of their mistakes and sense of worthlessness with respect to mathematical reasoning. I model, give carefully crafted feedback, and try to create low-stakes ways for them to practice analyzing mistakes, understanding why math in physics gives us only “evidence in support of a model” — not “the right answer”, and noticing the necessity for switching representations.  This is not working nearly as well as it needs to for students to make the progress they need and that I believe they are capable of.

I hope this course will give me some new ideas to think about and try, so I’ve signed up.  I’m especially interested in the ways Boaler is linking these ideas to Carol Dweck’s ideas about “mindset,” and proposing concrete ideas for helping students develop a growth mindset.

Anyone else interested?

Michael Pershan kicked my butt recently with a post about why teachers tend to plateau in skill after their third year, connecting it to Cal Newport’s ideas such as “hard practice” (and, I would argue, “deep work“).

Michael distinguishes between practice and hard practice, and wonders whether blogging belongs on his priority list:

“Hard practice makes you better quickly. Practice lets you, essentially, plateau. …

Put it like this: do you feel like you’re a 1st year teacher when you blog? Does your brain hurt? Do you feel as if you’re lost, unsure how to proceed, confused?
If not, you’re not engaged in hard practice.”

Ooof.  On one hand, it made me face my desire to avoid hard practice; I feel like I’ve spent the last 8 months trying to decrease how much I feel like that.  I’ve tried to create classroom procedures that are more reuseable and systematic, especially for labs, whiteboarding sessions, class discussions, and model presentations.

It’s a good idea to periodically take a hard look at that avoidance, and decide whether I’m happy with where I stand.  In this case, I am.  I don’t think the goal is to “feel like a first year teacher” 100% of the time; it’s not sustainable and not generative.  But it reminds me that I want to know which activities make me feel like that, and consciously choose some to seek out.

Michael makes this promise to himself:

It’s time to redouble my efforts. I’m half way through my third year, and this would be a great time for me to ease into a comfortable routine of expanding my repertoire without improving my skills.

I’m going to commit to finding things that are intellectually taxing that are central to my teaching.

It made me think about what my promises are to myself.

Be a Beginner

Do something every summer that I don’t know anything about and document the process.  Pay special attention to how I treat others when I am insecure, what I say to myself about my skills and abilities, and what exactly I do to fight back against the fixed-mindset that threatens to overwhelm me.  Use this to develop some insight into what exactly I am asking from my students, and to expand the techniques I can share with them for dealing with it.

Last summer I floored my downstairs.  The summer before that I learned to swim — you know, with an actual recognizable stroke.  In both cases, I am proud of what I accomplished.  In the process, I was amazed to notice how much concentration it took not to be a jerk to myself and others.

Learn More About Causal Thinking

I find myself being really sad about the ways my students think about causality.  On one hand, I think my recent dissections of the topic are a prime example of “misconceptions listening” — looking for the deficit.  I’m pretty sure my students have knowledge and intuition about cause that I can’t see, because I’m so focused on noticing what’s going wrong.  In other words, my way of noticing students’ misconceptions is itself a misconception.  I’d rather be listening to their ideas fully, doing a better job of figuring out what’s generative in their thinking.

What to do about this? If I believe that my students need to engage with their misconceptions and work through them, then that’s probably what I need too. There’s no point in my students squashing their misconceptions in favour of “right answers”; similarly, there’s no point in me squashing my sadness and replacing it with some half-hearted “correct pedagogy.”

Maybe I’m supposed to be whole-heartedly happy to “meet my students where they are,” but if I said I was, I’d be lying. (That phrase has been used so often to dismiss my anger at the educational malpractice my students have endured that I can’t even hear it without bristling).  I need to midwife myself through this narrow way of thinking by engaging with it.  Like my students, I expect to hold myself accountable to my observations, to good-quality reasoning, to the ontology of learning and thinking, and to whatever data and peer feedback I can get my hands on.

My students’ struggle with causality is the puzzle from which my desire for explanation emerged; it is the source of the perplexity that makes me unwilling to give up. I hope that pursuing it honestly will help me think better about what it’s like when I ask my students to do the same.

Interact with New Teachers

Talking with beginning teachers is better than almost anything else I’ve tried for forcing me to get honest about what I think and what I do.  There’s a new teacher in our program, and talking things through with him has been a big help in crystallizing my thoughts (mutually useful, I think).  I will continue doing this and documenting it.  I also put on a seminar on peer assessment for first-year teachers last summer; it was one of the more challenging lesson plans I’ve ever written.  If I have another chance to do this, I will.

Work for Systemic Change

I’m not interested in strictly personal solutions to systemic problems.  I won’t have fun, or meet my potential as a teacher, if I limit myself to improving me.  I want to help my institution and my community improve, and that means creating conditions and communities that foster change in collective ways.  For two years, I tried to do a bit of this via my campus PD committee; for various reasons, that avenue turned out not to lead in the directions I’m interested in going.  I’ve had more success pressing for awareness and implementation of the Workplace Violence Prevention regulations that are part of my local jurisdiction’s Occupational Health and Safety Act.

I’m not sure what the next project will be, but I attended an interesting seminar a few months ago about our organization’s plans for change.  I was intrigued by the conversations happening about improving our internal communication.  I’ve also had some interesting conversations recently with others who want to push past the “corporate diversity” model toward a less ahistorical model of social justice or cultural competence.  I’ll continue to explore those to find out which ones have some potential for constructive change.

Design for Breaks

I can’t do this all the time or I won’t stay in the classroom.  I know that now.  As of the beginning of January, I’ve reclaimed my Saturdays.  No work on Saturdays.  It makes the rest of my week slightly more stressful, but it’s worth it.  For the first few weeks, I spent the entire day alternately reading and napping.  Knowing that I have that to look forward to reminds me that the stakes aren’t as high as they sometimes seem.

I’m also planning to go on deferred leave for four months starting next January.  After that, I’ve made it a priority to find a way to work half-time.   The kind of “intellectually taxing” enrichment that I need, in order for teaching to be satisfying, takes more time than is reasonable on top of a full-time job.  I’m not willing to permanently sacrifice my ability to do community volunteer work, spend time with my loved ones, and get regular exercise. That’s more of a medium-term goal, but I’m working a few leads already.

Anyone have any suggestions about what I should do with 4 months of unscheduled time starting January 2014?

I wrote recently about creating a rubric to help students analyze their mistakes.  Here are some examples of what students wrote — a big improvement over “I get it now” and “It was just a stupid mistake.”

The challenge now will be helping them get in the habit of doing this consistently.  I’m thinking of requiring this on reassessment applications.  The downside would be a lot more applications being returned for a second draft, since most students don’t seem able to do this kind of analysis in a single draft.

Understand What’s Strong

  • “I thought it was a parallel circuit, and my answer would have been right if that was true.”

  • “I got this question wrong but I used the idea from the model that more resistance causes less current and less current causes less power to be dissipated by the light bulbs.”

  • “The process of elimination was a good choice to eliminate circuits that didn’t work.”

  • “A good thing about my answer is that I was thinking if the circuit was in series, the current would be the same throughout the circuit.”


Diagnose What’s Wrong

  • “The line between two components makes this circuit look like a parallel circuit.”

  • “What I don’t know is, why don’t electrons take the shorter way to the most positive side of the circuit?”

  • “I made the mistake that removing parallel branches would increase the remaining branches’ voltage.”

  • “What I didn’t realize was that in circuit 2, C is the only element in the circuit so the voltage across the light bulb will be the battery voltage, just like light bulb A.”

  • “I looked at the current in the circuit as if the resistor would decrease the current from that point on.”

  • “I think I was thinking of the A bulb as being able to move along the wire and then it would be in parallel too.”

  • “What I missed was that this circuit is a series-parallel with the B bulb in parallel with a wire, effectively shorting it out.”

  • “What I did not realize at first about Circuit C was that it was a complete circuit because the base of the light bulb is in fact metal.”

  • “I thought there would need to be a wire from the centre of the bulb to be a complete circuit.”

  • “I wasn’t recognizing that in Branch 2, each electron only goes through one resistor or the other.  In Branch 1, electrons must flow through each resistor.”

  • “I was comparing the resistance of the wire and not realizing the amount of distance electrons flowed doesn’t matter because wire has such low resistance either way.”

  • “My problem was I wasn’t seeing myself as the electrons passing through the circuit from negative to positive.”



  • “In this circuit, lightbulb B is shorted so now all the voltage is across light bulb A.”

  • “When there is an increase in resistance, and as long as the voltage stays constant, the current flowing through the entire circuit decreases.”

  • “After looking into the answer, I can see that the electrons can make their way from the bottom of the battery to the middle of the bulb, then through the filament, and back to the battery, because of metal conducting electrons.”

  • “To improve my answer, I could explain why they are in parallel, and also why the other circuits are not parallel.”

  • “I can generalize this by saying in series circuits, the current will stay the same, but in parallel circuits, the current may differ.”

  • “From our model, less resistance causes more current to flow.  This is a general idea that will work for all circuits.”