Tag Archives: Teaching Philosophy

End of the Year

As I’m getting ready for next year, I realized that I need to have closure on this past year.

Last summer (2016) my family moved back to Maryland from New Mexico and because of that, I needed to find a math teaching job. I was hoping for a high school position, but according to the county math specialist, it was a strange year because no HS math positions were opening up. They asked, and I said that I was willing to teach middle school, and before I knew it, I was teaching 8th grade math and Accelerated Algebra 1!

It was a big transition for me for several reasons: private to public, Christian to secular, high school to middle school; Precalculus, Physics, Chemistry to 8th grade math. In both schools I was fortunate to teach a very diverse group of students, though the makeup of the diversity changed[1].

One of the biggest changes was having an new boss/principal (who ended up being really awesome!) I didn’t know whether I would be allowed to continue my bizarre Standards Based Grading gradebook.

How I Graded This Year

Because of this, I graded differently in Algebra (where I was the only Algebra teacher in the school) than in 8th Grade Math (where I taught alongside an experienced teacher).

In both classes, we had quizzes/tests every Friday, for consistency, and the content of the assessment depended on where the students were in their understanding.

In 8th grade math, students could do quiz/test corrections, like I’ve done in the past, but there were not really standards in the gradebook and each quiz/test was one grade[2]. Classwork was a big chunk of the grade (~25%?) and by the end it was really just me grading their warm-up sheets weekly on effort.

In Algebra, I graded them out of 100, but they really could only usually earn multiples of 10 (50, 60, 70, 80, 90, or 100). Quizzes had fewer than 10 questions and I just took 10 points off for each one they got right (so getting 4 out of 6 right would be an 80). That was 95% of their grade and the other 5%, just like in the other class, was HW.

Where I’m Going

Next year, I’m going up to High School, and I’m moving to the local High School where my children will eventually attend one day!

I’ll be teaching two sections of year-long Algebra 1 and one section of Precalculus each semester.

Once again, I’m moving into unknown territory: I don’t know what the principal will allow. At least I’m a little more familiar with the gradebook, though I know it can’t do SBG the way I want it to (like ActiveGrade!).

One added challenge is that my “year-long” Algebra kids will really only have me for a semester because they switch all their classes around. So they’ll likely have two different Algebra 1 teachers. Also Precalculus is a semester course, so I’ll have a new batch in the Spring there too.

That means the weirder my grading policy, the more time I’ll have to spend explaining and the longer students will take to adjust to the new setup.

How I Want to Grade Next Year

I know I want to go back to more SBG than I did this past year. I need to have students see that grades are communication, not rewards/punishment. I need to give students second chances. And I need my classroom instruction to be driven by the focus that SBG brings. I need to work on what this looks like, so first up, I need to find well organized standards that are “just the right size”.

I also intend to flip the classroom. So much of my Algebra class left positive on that aspect of the class, more than I was expecting!

I also want to create a class website again. I used Google Classroom this past year and it was very effective for the middle school students, but it’s too difficult to find previous posts (even with the tagging system)[3] and the organization that a website brings is so helpful.


[1] In NM, 70% of my students were Native American, compared to in MD, roughly 1/3 of my students were African American and 1/3 of my students were Hispanic.

[2] Except for one time near the end of the year where I gave them a large quiz and wanted them to see that they were two different topics. I also wanted to reward them because I thought it was going to be a quiz that they’d do really well on. They didn’t. Oops.

[3] I still can’t believe that you can’t easily search within a Google Classroom yet. Makes no sense.


Leave a comment

Filed under Teaching

[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!


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)!


Filed under Teaching

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.

1 Comment

Filed under Teaching

[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. 🙂


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.


Filed under Teaching

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.


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.


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.


Filed under Teaching

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:


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.

Leave a comment

Filed under Teaching

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.


Filed under Teaching