Tag Archives: Teaching Philosophy

[MTBoS Blaugust] New Teacher Orientation, Day 4

Today was the last day of the new teacher orientation. I’d rank it below the previous days, but it had some necessary stuff: license renewal info and continuing education. One cool thing they did was talked about Growth Mindset!

MTBOSBlaugust2016.png

At my school in NM, I found out about growth mindset through the MTBoS (twitter & blogs). It’s something that I had talked with my students about, and would even go so far as to say that I convinced some of my class of the validity and value of having a growth mindset.

Most of the talk was great, I’m just going to nit-pick one small thing some people were saying. There was a line that went something like this: “A fixed mindset focuses on the grade or the outcome while a growth mindset focuses on the process.”

I think I understand the sentiment behind this, but I want to push back on this a bit (if for no other reason than to start discussion!). Here’s my example/justification: LeBron James has a growth mindset when it comes to basketball. He works incredibly hard and (correctly) believes that this hard work makes him better at basketball. However, he is laser-focused on winning the NBA Finals, as that is one of the main things that, for many, will put him ahead of MJ in the argument for “greatest player ever”. The NBA Finals is an outcome: either you win or you don’t. Sure, he understands the process of improving himself as a player and athlete, but his focus is on the “assessment”.

I think equating fixed mindsets with “too much focus on the assessment” detracts from the main point of fixed vs. growth mindset discussions. The real core of it is showing students that hard work can improve intelligence and ability (or math ability). So what if they’re doing that just to get a better grade?

Agree or disagree? Discussion is welcome: please comment below or on twitter with me (@newmanmath)!

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Getting ready for a new Job

After five years of teaching in Gallup, we just moved from New Mexico to Maryland to get closer to family. That means I’ve, fortunately, got a new job teaching 8th graders. Four classes of 8th grade math (2 “merit” and 2 “honors”[1]) and 1 class of Algebra 1.

I’m just trying to wrap my mind around the job because I’ve had trouble getting started on anything. Maybe it’s because we just moved to a new house, living with my wife’s parents, who are great. Maybe it’s because we’ve had 3 family vacations (4 if you count the move!) in the past month and a half. Or maybe it’s because there’s a baby that could decide it wants to come as I’m typing this, in which case I’ll finish this post after my wife has our second child.

So yeah, I’m scatterbrained.

Here’s a list of things that I need to do soon, in no order:

  • Set up my classroom:
    • Get posters
    • Think about seating (it’s been 5 years since I’ve had my own classroom!!)
    • Purchase things like manipulatives, whiteboards, trays & folders for papers, extra writing utensils, stamps, etc. (What am I forgetting?)
  • Plan the first day of class
    • Get to know you surveys
    • Jump right into problem solving/math task
  • Plan second day of class
    • Go over routines & expectations
  • Plan warm-ups and routines
    • Study Math Talks more
  • Look into available technology and make tasks using those when it’s productive
  • Create assessments (this should come before planning tasks/lessons)
  • Consider “early year” things I want to accomplish
    • Growth Mindset
    • Grades talk (go hand in hand with above), SBG
    • Problem Solving Strategies (Devil’s Bridge Crossing Problem)
    • Get-to-know-you sheets
    • Get routines established
      • Warm ups
        • Visual Patterns
        • Estimation180
        • WODB
        • Math Talks
      • Quote of the week (?)
      • How to take a quiz (self-grading!)
      • How to re-assess
      • Explain Lagging HW
      • Explain old standards showing up again on new quizzes/assessments
      • Plickers
      • Recognizing Birthdays
    • Ninja Wall
  • Learn what I need to stay up to date on accreditation of my teaching license
  • Learn about the PBIS system at my school (Positive Behavior Incentive School)
  • Learn about other discipline policies at my school
  • Learn all this little things (printer, laminator, etc.) at my school!
  • Figure out how the pacing guide for the county works
  • Read all the MS blogs compiled by Julie (ha…)

I’ve dropped by my new classroom and here are some pictures of the new room (no work done yet!).

I should post this and get to work!

 

[1] Though I’m trying not to put too much stock into the prior categorization of students.

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[2016 Blogging Initiative] Week Four: A Lesson Introducing the Unit Circle

My Relationship with Textbooks: “It’s Complicated”

My first several years of teaching I avoided the math textbook as much as possible[0]. One year I even waited to hand out textbooks to students until the second quarter. I assumed (incorrectly) that using the textbook would make me a lazy, bad teacher. However, at the start of this year I decided to embrace the textbook for the good resource that it can be: a bank of practice problems[1] not a replacement for my teaching[2].

Background: My Classroom 

One other thing I’m doing this year is flipping my classroom. The flip, however, isn’t just lecture. I’m trying to challenge my students do problem solving through the vidoes, and I hope to show how I’m trying to achieve that in this lesson. For one thing, I provide guided notes for the students to fill out as they watch the lesson. I also don’t do every problem: I ask them to pause the video and try some in the middle of the video. To that end, I’m also using EDpuzzle which pauses the video and asks them questions that I’ve created at a variety of levels.

When we get back together in class the following day, the students are randomly assigned into groups of 3 or 4. Students spend about 10 minutes going over the notes and making sure each students’ notes agree with one another and that students understand the topic. After that students work on practice problems, from the textbook, on the same topic. [3]

The Challenge

So we’re chugging along and we get to the Unit Circle. This is the first lesson that I disagree with how Blitzer (our textbook) approaches it. I’ve had success with students in the past by teaching special right triangles first because students see them in the Unit Circle. So I decided to create my own “chapter” and left the textbook, like old times.

The link below is a short (<13 minute) video so you can see what the students will do for HW prior to class. But you should watch it because that’s the interesting part of my lesson. 🙂

https://edpuzzle.com/media/56b43368fe5ccd81111fd654

Here’s the handout:

As you can tell from the video, I show students the special right triangles and where the values come from. My hope is that they use the Pythagorean theorem if they ever forget the shortcuts in the future, but most students will, unfortunately, probably forget that. I’m not sure how to share that with them differently.  However I only give students a few points from the Unit Circle, and ask them to “figure out the rest”. If they can figure it out on their own before coming to class, and they understand the special right triangles, then I think that it will be more likely that the Unit Circle will stick.

Since I’ve deviated from the textbook here, I had to find practice problems online, but that wasn’t too difficult. Students will go to my website and simply click on the worksheet links (complete with answers) to practice this in class. I’ll only print out the sheets for those students who want more practice beyond class and have no internet at home.

I’ve assigned the video (only 2 students have watched it so far), but we’ll meet in class Monday to see how well they did filling out the rest of the Unit Circle.[4]

Request for Feedback

How can I improve this approach? How can I teach special right triangles in the video so that they do more of the “heavy lifting”?

How are the quality of the questions in the EDpuzzle video? Are there others you thought of that I could do?

Is there a better way to approach the Unit Circle that you’ve seen/used other than special right triangles?

If you could answer any of the questions above, I’d greatly appreciate it. Thank you for reading! (and watching??)

 

[0] I still avoid it in Physics–I haven’t handed out a textbook in 3 years, with the exception of one student who begged for it. It didn’t help her.

[1] It’s also a good resource for ideas for 3-act lessons.

[2] I’ve seen some teachers teach how to read a textbook, which is a valuable skill, but one that I’ve decided pass on for now. I want my students to understand the math first and foremost. I’m still not sure how I feel about not teaching students to use a textbook effectively and efficiently.

[3] Because I believe that HW is practice, earlier this year (before I flipped), I don’t grade HW. Students also didn’t do the HW (with very few exceptions). Now, I still don’t grade that they watch the video, but I’m not afraid to email or call home if students are missing it chronically. Also when students get to class, they recognize that they’re responsible for learning the material at home, and so will work harder at the start of class to understand what they didn’t watch. It’s amazing how much more “HW” (practice) they’re doing now just because it’s happening during class.

[4] And if I’m on my blogging game, I’ll blog about how it went. Unfortunately it’s tennis season, so I probably won’t find time to soon.

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Reflections on a Grading System

This semester in Precalculus I used my own grading system that I created through Google Spreadsheets. The program worked well enough, but I am going back to ActiveGrade for a few reasons.

Screenshot from 2015-12-19 15-22-43

Left: Student View. Right: Teacher View.

Why I’m Leaving the Google Spreadsheet Grading

The students were confused with the overwhelming number of grades they had to wade through. The simplicity of ActiveGrade is also one of its strengths.

Occasionally the students couldn’t see their grades because the function ImportRange sometimes didn’t work.

The teacher view is every student’s assignment, so I can’t easily see where students stand on a given topic.

I initially liked separating skills and understanding concepts, but there are a few problems from it. For one, the skills and concepts are on different tabs, so it’s more cumbersome to input grades.

I separated the standards on each quiz, but through some teachers on Twitter I see the perspective of not putting standards on quizzes and having students figure out which standard is which. Breaking the standards into tiny chunks was good for encouraging students to “retake” standards.

One more advantage of ActiveGrade is the ability to send an e-mail to every student and parent with their grades. Currently our school sends a weekly grade e-mail to parents, but since I don’t keep my grades there, parents don’t see student’s grades.

Math Practices

I tried to keep track of certain math practices: (1) Good reasoning & explanations, (2) Checking work, (3) Math Modeling, (4) Asking good questions, and (5) Reasoning when doing estimations. I wasn’t good at “catching” (1) when students did it in class (that was supposed to be the primary way I got that one), students didn’t do well enough on quizzes to get to the point of (2) checking their work, and the system I had designed for (4) asking good questions didn’t allow for enough students to demonstrate their ability. The only ones that worked were (3) and (5). The (3) Math Modeling worked since they had to turn in the sheet to show that they worked during the 3-act lesson. The (5) estimations worked because it was a warm-up [1], once a week, and the students submitted responses into a Google form (bit.ly/rcsguess), which I could then plug in later. However, the warm-up took longer than I wanted (~15 minutes), so I think I’m going to drop it for 2nd semester.

Because of all this, the Math Modeling is the only Math Practice I’m going to keep grading. I’ll probably plug this into the school’s grading system and set it as %30 of a student’s grade. This should be a gimme for students that are present and turn in the work that they do in class, once a week, on block days.

The New Plan

I still want to emphasize understanding. I plan to do this on a case-by-case basis. I will no longer break one standard into sub-standards for grading purposes (e.g. 1.7 Combinations & Composition of Functions had the sub-standards 1.7A Combinations of Functions, 1.7B Function Composition, and 1.7C Function Decomposition) because I want students to know what a question is asking by reading the question, not the standard heading. However, it is often still helpful to introduce new ideas by breaking it down, so I’ll hold on to those names somewhere. Quizzes will be broken into 3 “sections”, and students receive a grade: 1, 2, or 3, for each quiz. To earn a 3 (Mastery), students will have to demonstrate understanding at some point[2]. I am still going to make “going beyond” available (trying to decide between making it a 3.5 and a 4) for students who want to reach and get an A. I’ve really appreciated the Nrich math problems to that end.

Drawbacks

Quizzes (or discussions) to demonstrate previous standards will take longer: to create, take and grade.

It will take more work for students to see which skill or understanding they need to focus on when going back over previous standards, since the standards aren’t broken into tiny sections anymore.

Students won’t see that “growth level” (and the video game characters to go with it!0 which I was so excited about. I think it accurately captured which students worked the hardest to improve in math in my class and I hope to find ways to encourage that kind of growth again.

Conclusion

Those are the only drawbacks? Grading should be faster to plug in, parents will know where students stand more frequently, and students will be required to recognize when a skill or technique applies rather than just memorizing a single skill and applying it. Why didn’t I make this change sooner? I’ve still got a ways to go, but hopefully I can start focusing on content more.

 

[1] Also, the Estimation 180 website is already created, and super cool!

[2] Before a 2 “felt like a 2” and a 3 “felt like a 3”. Now there 3 questions and it’s easier for a student to predict how well they’ll do based on their own grading of themselves after a quiz. From Chemistry I have appreciated making it clearer what a student will get based on how well they perform on each question.

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Growth Mindset Discussion

Getting students to have a Growth Mindset is something that I’ve been working on and improving every year I’ve taught. This year I had a discussion about it later in the year than I should (at the end of the 1st quarter), but it was still a very valuable discussion.

The Discussion

I started by giving them a Google Form with this question:

How does math work?

I only gave them two possible answers:

People are born with math skills or aren’t. How good you are at math mostly depends on that.

People who work hard in math class can get better at doing math. How good you are at math mostly depends on that.

I intentionally left off the “something in between” answer even though many students immediately complained they thought it was a combination of both. I wanted to see which they thought was more important. The results surprised me:

 

Growth Mindset Results

They surprised me because I thought a vast majority would vote for “people are born with math skills.” Perhaps my students are starting to believe the opposite of that simply because of the way my class works and the classroom culture I try to cultivate, despite not having an overt discussion on this topic before now? [1]

Me: Forget, for a second, whether Fixed Mindset (blue above) or Growth Mindset (red above) is true. Some scientists did a study and looked at whether students had a Growth Mindset vs. a Fixed Mindset, and who got better grades. Do you guys think one group of students had better grades?

Students: Maybe…

Me: Well it did affect it, significantly. Like, the students who had the Growth Mindset did way, way better, on average, than those with the Fixed Mindset. [2]

I asked for a little input on why people voted for the one they did, and some students spoke up. I confessed to them that I used to have a Fixed Mindset, well into college. And I told them about a student from a few years ago, who they mostly knew, who made the comment at her senior presentation “I didn’t think I was that good a student.” I explained that I could believe that because early on in her junior year, she didn’t really “stand out” from others beyond the fact that she worked really, really hard.

She’s the only student in the history of our school to get into the BA/MD program.[3]

I then showed them this cool diagram and we talked about how changing their mindset:

Reflection

I’m really glad we had this discussion, even if it was a bit late in the year. It was one of those times in the classroom where I could almost feel the students grabbing at the inspiration with their eyes and wanting to be better students and people because of the discussion. Or maybe that’s just all in my mind. Either way, the one thing I need to get better at is mentioning this discussion more often in the future whenever a student is bummed about a grade, frustrated with a problem, or envious of another’s success.

Already a few students have started coming in much more often to demonstrate standards. Wohoo.

 

[1] Or maybe that’s just wishful thinking.

[2] I can’t quote this study, but I’ve heard it before. If you know of the study, please leave it in the comments below so I can show my students!

[3] It’s a program at UNM (several school have it) where you receive admission to medical school prior to entering undergrad. Needless to say, it’s a very competitive application into the program.

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The Master Plan for Precalculus: (3) Skills

I’m changing things big-time next year. This is the third post. Click one of the links to go to the other posts.

  1. An Overview
  2. Math Practices
  3. Skills [this one]
  4. Understanding & Going Beyond

Although math classrooms over-focus on procedural skills, they should not be entirely cut from the curriculum. There’s a reason they’ve become so important in the math classroom. By making skills 40% of the grade, I can say “a majority of your grade does not come from skills” and yet “you must master a majority of these in order to pass this class” (70% is passing at our school).

Here’s a quiz that’s I’ve made for the near the beginning of the year:

Some things you may or not be able to notice:

Skill Standards are separated into pairs of questions

I don’t expect both questions to cover the entire skill, which is why I intend to give each standard multiple times. See the “Form C” in the top right? That means it’s the third iteration of this quiz. Their grade is then a 0, 1, or 2, depending on how many they show me they know how to do [1]. Their grade will then be either the mode or the latest grade, whichever is higher [2].

Each question is taken from or modeled by a question from the HW in the book

The more similar the questions are to students’ HW, the more likely it is that they’ll do their HW. Many of these are taken straight from their textbook and I’ll point this out frequently throughout the course so students start making the connections.

Each Skill Standard has 3 boxes for grades

One goal of SBG is for students to get better at self-assessment. The first box is for them to predict how well they’ll do, either before they’ve seen the questions or after they’ve tried them. The second box is for them to give themselves a grade as they grade themselves against an answer key [3]. Students are surprisingly bad at giving themselves a grade even though they have the answer key! The third box is the grade that I give them after checking after them. This should help them to get better at assessing themselves.

The Skills Standards are clearly grouped together in one larger box

I’ll explain more about the “understanding” standards, but this reinforces the idea that the skills are closely linked and students should be thinking about how these relate to one another. The final question is my attempt to tie these together in an over-arching “understanding” question.

Here’s how I plan on reporting this to students:

Gradebook: Student View

An older version, where you can see the “Math Practice” bar chart filled out on the right.

Student's View of their Grade

The newer version has a link with more practice material to the right of their grade (stars).

The coins are my gamification of their grade. I tried to group each set of coins (skills) into a star (understanding). One of the things that contributed to the growth level (at the top) is how much they “improve” from the first time they take a skill. This rewards students who don’t do well the first time around, but study and do better later times. I hope this little incentive encourages those who don’t always “get it” the first time around, as they’re the ones who often need encouragement in math class. Their growth level has no bearing on their grade.

In the next post I’ll explain more what the stars mean.

[1] NOT how many they “get right”. If they show their work, which students are more apt to do in a SBG system like this, they’ll get credit but lose a point in “Attend to Precision” from their math practices grade (see previous post).

[2] I wanted to do just mode, so if they take a quiz 3 times, get a 2, 2, then 1, I’ll reward them for their sustained ability the first two times. However, I didn’t want students to dig holes so deep that they couldn’t get out, so 0, 0, 0, 0 isn’t automatically a failing grade, hence the “latest grade” opportunity.

[3] An idea I’ve gotten from other blogs: orange pens in the back of the room along with an answer key. When students finish their quiz, they leave their own writing utensil at their desk and get instant feedback. They’re not just to mark “right or wrong” but they’re supposed to fix mistakes in work and write how to do it correctly in the orange pen.

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The Master Plan for Precalculus: (2) Math Practices

I’m changing things big-time next year. This is the second in a series of posts. Here are the others (links will be added as they’re written).

  1. An Overview
  2. Math Practices [this one]
  3. Skills
  4. Understanding & Going Beyond

Jo Boaler’s piece on complex instruction convinced me that my teaching (and assessment) should be “multidimensional”. That means that I teach more than just skills. I’ve tried to communicate this, but now it’s going to be a whopping 40% of the students’ grade, so I’m going to have to clearly define what it means to earn a grade here, and what assessment looks like. I’ve turned to the common core math practice standards to help me with this and I’ve settled on these 5 math practices for a few reasons. The main reasons are (1) I think they’re important math skills, (2) they are not assessed (easily) in a standard quiz, and (3) I think they are (more or less) easily assessed through an alternative method. Here are the five math practices that I’m assessing:

  1. “Explain Why”: Construct Viable Arguments and Critique the Reasoning of Others
  2. “Model”: Model with Mathematics
  3. “Check Work”: Attend to Precision
  4. “Good Questions”: Ask Good Mathematical Questions
  5. “Estimations”: Make Accurate Estimations

I’ll go into more detail for each of these below, but for assessment, students can earn a point in each of these practices in different ways. They can earn a total of 40 points, but can only receive a maximum of 10 points in any category. I mean to explain to them that “you should become really good at 3 of these (get 10 points), but nobody is awesome at everything, so I expect you to simply improve in the other two areas (say, 5 points each). If you can do this, you’ll get the maximum possible 40 points in this area by the end of the semester.” On their grade chart (Google Sheet), there is a bar chart for them to see how they’re doing in each of the five areas. Here’s how students earn points:

Explain Why

When working, students should constantly be demanding AND giving explanations and justification for their math. If I hear students either giving a good explanation why or if they are being persistent and asking why some bit of math works, from either a peer or myself, then they earn a point in this category. I’ll use something like Class Dojo to keep track of this during class and tally the points later. I already foresee students complaints: “I asked why but you didn’t hear me do it!” or “I gave a really good explanation but you didn’t see it!” I’ll be up-front about this aspect with them: “Explaining and asking why should become second-nature to you.  You ought to be doing it every day in class, so if you do it 90 times (once a day) and I see only 1 out of every 9 times you do it, you’ll reach ’10’ and make your quota. Don’t do it 10 times throughout the semester and expect me to see every time you do it. Make it become second-nature, like breathing, and I’ll catch you more than enough times! I only expect to get at best a quarter (1/4) of the times you do this. Do this so often that I can’t ignore you and you won’t have a problem.” I’ll also give them opportunities to come in outside of class and explain “why” on topics, or ask questions, and that should cover any problems of me missing some students entirely (“You never hear meeee!”).

Model

I’ll explain this more, but I plan on starting every unit possible with a 3-Acts lesson and working into the math after we’ve already go a situation. Students will have opportunities to model with the mathematics by doing multiple representations, both for projects and classwork. They will get a point for each good model they do (I’ll let them fix what’s wrong with projects to earn a point for the model if they wish) and turn in, and should easily have more than 10 opportunities throughout a semester.

Check Work

I always teach students how to check their work, but never assess them on it. This gives me an opportunity to do so without directly tying it to whether they can do the procedural skill or not. Every quiz where they have checked their work for every problem, they get a point in this area. I’m tossing around the idea of them losing a point for a “careless” quiz where they miss too many problems on a quiz due to careless errors (and not checking their work), making this the only math practice that they can lose points on. With at least 18 quizzes in a semester, there’s plenty of time to improve and get 10 points in this area.

Good Questions

Starting each “unit”/week out with a 3-acts lesson (roughly 18) should give students plenty of time to hone their math-question asking ability. We’ll start with Alex Overwijk‘s cool “What makes a good math question?” lesson, where students discuss & work out what it means to ask a good math question (not exactly this post, but something like this post). I’ve always typed out their questions before, now it’s just a matter of me doing that somewhere I can save it (Evernote) and putting their names next to questions (probably a good idea even if I don’t use it for a grade!). Each good question gets one point, so students will be clamoring to figure out what makes a question a good math question.

Estimations

Inspired by estimation180 and various teachers (Dan Meyer) talking about students getting “buy in” to 3 Act lessons by guessing has let me to realize that estimating a quantity is a mathematical skill that so many math students sorely lack. Especially when you look at “pick something way too high and way too low and then your best guess”, very often some students’ “way too high” is lower than other’s “way too low”, and visa versa. So I’m going to award points for good estimations (top 3 or within 10% is my current model–that’ll have them doing a bit more math!). This should increase their buy-in for the 3 Act lessons and have them reminding me to do estimation180’s at least every Monday (perhaps even a few each Monday, so that they can all have a chance to win and get points). I’ve seen students get excited without attaching a grade to it–should I not attach a grade so that it just remains fun?

That could go for all of these: should I even attach a grade to these things? In my (current) opinion I’m making the goal so low (only 10 a semester) that they can still have fun and see themselves as improving. I want them to see that I value when they do these things, not just when they can factor a quadratic. So I think it’s essential for me to give them credit for this, even if it’s super-easy to pass this part of their grade (and I hope that it is!).

In the next post, I’ll talk more about the procedural skills.

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