Monthly Archives: December 2017

12/30/17: My Favorite Lesson: Area Formulas

This is one of my favorite lessons because it focuses on conceptual understanding, reassures students that memorization is not necessary, and it makes connections between formulas that students didn’t know were related. A lot of people take formulas for granted. They didn’t just appear out of nowhere; it had to be proven.

I first start with a little non-graded “quiz.” The purpose of this is because as stated in a previous blog post, I strongly believe that when students make mistakes first, it makes the learning much stickier. I ask them for the area formulas of a rectangle, parallelogram, triangle, trapezoid, kite, regular hexagon, regular octagon, and a circle.

I then reiterate the definition of area. The main noun of area is the *space* inside of a 2-d figure, measured in square units. Colloquially when we ask for the area though, we are asking for an amount.  New: through a tweet yesterday from Bobson Wong (@bobsonwong), I learned that I should say “calculate the area” never “find the area” so there won’t be any smart aleck answers of students pointing or circling the figure when we ask about the area.

I write on the board “Wait, ALL area formulas are related to the area of a rectangle?!” and then we derive each formula together.

To find the area of a rectangle, we would multiply the base by the height to find the amount of square units that would fit in the figure. Note: some books may use length and width, but I use base and height to emphasize that these two dimensions are perpendicular to each other.

I then move on to parallelogram to see that we can manipulate the figure into a rectangle. Boom. Parallelogram -> rectangle. (“->” will mean “relies on the area of”)


I have students draw a non-right triangle and ask them how we can use what we know to find the area of the figure. Students would say that we could cut the triangle into smaller triangles and “copy” those triangles to make a rectangle. So boom. Triangle -> rectangle


For trapezoids, I have students draw a non-isosceles trapezoid. Some students said that the trapezoid is composed of 2 triangles and others said that we could copy the trapezoid, rotate it, to create a parallelogram, which we know the area formula. Boom. Trapezoid -> parallelogram -> rectangle


I do the same discovery approach with kite. I draw a kite (with the diagonals) and ask them how we can use what we already know to find the area formula of a kite. Some say that we can manipulate the triangles to make a rectangle with base 1/2 d_1 and height d_2 and others see it as the image below. It surprises the students that we don’t even need to know the side lengths of the kite to find its area. Boom. Kite -> rectangle


For a regular hexagon, I break the figure into 6 triangles, “unroll” them, then place half of the triangles in the crevices of the other triangles to create a parallelogram. In order to find the area of this parallelogram, we need to know the height of the triangle, which we call the apothem. Boom. Regular hexagon -> parallelogram -> rectangle

Screen Shot 2017-12-30 at 10.04.29 AM

(found this pic on

I then have students find the area of a regular octagon with their groups. They see that with the same process, it is the same area formula as a regular hexagon (1/2 x apothem x perimeter)! Boom. Regular octagon -> parallelogram -> rectangle

For circles, I do two approaches, one being very similar to how we found the area of a regular hexagon and octagon, and the other “cutting” the circle so it becomes triangular. Boom. Circle -> parallelogram -> rectangle or Circle -> triangle -> rectangle. Check out these animations to see what I mean:

At the end, I have students reflect on their “quiz.” I reiterate that math isn’t about memorizing formulas; it’s about relational understanding.

Thank you for reading.

12/27/17: My Favorite Discovery Lessons Part 1

I have a lot of discovery activities that I’d like to share with you, and I’ll share them 1-2 at a time. I claim absolutely no ownership of any of these activities as I have seen them around before. I would just like to show you my “twist” to these activities. Here are two of my favorites:

Howie’s Hypothetical Ice Cream Shop (Permutations and Combinations)


For the entire period, I pretend that we are in “Howie’s Hypothetical Ice Cream Shop.” I have students come up with 10 ice cream flavors as a class, and I tell them our specials for today: they can choose either a permutation cone or a combination bowl, where they can pick three different flavors each. I first ask if the permutation cone or the combination bowl will have more arrangements and why, then I have them try to find out how many arrangements there are for the cone and the bowl.

Permutation cone is pretty easy to figure out, there are 10 choices for the bottom scoop, 9 choices for the middle, then 8 choices for the top scoop. Showing an example of a tree diagram will show us that we multiply 10x9x8 to get 720. Combination bowls are a little harder, where they will still have 10 choices for one scoop, 9 for the second, and 8 for the third, BUT there’s a slight difference between a permutation cone and a combination bowl: You need to eat the permutation cone in a certain order, top middle, then bottom, but a combination bowl, you can eat in any order you want. If you asked for a combination bowl of strawberry, vanilla, chocolate and your friend orders a bowl of chocolate, vanilla, strawberry, you’re getting the same bowl. I then I have students exhaust the arrangements of chocolate, vanilla, and strawberry, then we see that every group of 6 turns to 1 when we consider combination bowls. That is why combination will always be smaller than permutation. In this case, it would be 720/6=120.


I have students do this for 4 choices (where for combinations, every group of 24 (4x3x2x1) turns to 1), 5 choices, then 10 choices. Before I discuss the 10 choice option, we will have noticed that our number of arrangements keep increasing for both permutation cones and combination bowls. I ask them, “Do our number of arrangements keep going higher for both the permutation cone and combination bowl?” Sometimes they say yes, sometimes no, but we continue along.

After this, I show them that combinations are found in Pascal’s Triangle as well as ask the students what other patterns they see in Pascal’s Triangle. 


Triangle Inequality (with noodles!):

Before I go with the manipulatives, I have students draw what these triangles would look like if it had these side lengths: a 1, 1, 2 triangle, a 4, 5, 10 triangle, and a 3, 4, 5 triangle. I purposely do a little quiz with these side lengths to start because I heavily believe that making mistakes will make us learn more in the end. After this, I have students compare their drawings with their group members to see if their triangles look similar. I then hand out about 10 strands of spaghetti to each group (I found bags of spaghetti for 25 cents at FoodMaxx) as well as rulers. I tell them to measure and break these noodles to make a 1, 1, 2 triangle, a 4, 5, 10 triangle, and a 3, 4, 5 triangle. After a couple minutes, they will notice that the first two are impossible and the 3, 4, 5 triangle creates a right triangle (I do this purposely because Pythagorean Theorem is the next lesson). I then have students come up with 5 sets of side lengths that will not create a triangle and 5 sets of side lengths that will create a triangle. I would write a couple of these down and then ask the class what they notice about the sets that do not create a triangle and the sets that create a triangle. Boom. We have just discovered the Triangle Inequality.

12/22/17: A Reflection on Ditch That Homework

20543582_10155023689027098_7537156021307691409_o (1)

I read this book over the summer and talked with Alice Keeler about it at Starbucks. I wanted my students to read her book but she said that she would rather have students read Mathematical Mindsets by Jo Boaler (which is an awesome book) but I went against her anyway and gave students the option to read either Mathematical Mindsets or Ditch That Homework this past semester. The reason being that I want to show students that there are great local authors. After my students read the book, I had them meet with me during office hours so we can discuss what they’ve learned and see what we would take from the book into their future classroom. When I told them that Alice teaches at Fresno, their faces are literally like this: O_O. How cool is that?

I wrote about 15 pages of notes but I’ll highlight my favorite parts in this blog post. Here are my top 9 quotes from Ditch That Homework:

1. A few questions to consider before giving homework for your next lesson:

  • Does it increase a student’s love of learning?
  • Does it significantly increase learning?
  • Does it stimulate students’ interest in the subject and make them want to delve deeper?
  • Are students able to complete the assignment without help?
  • Is it differentiated for ability or interest?
  • If the students didn’t have to do it, would they WANT to do it anyway?
  • Is it fair to all students, especially those from poorer families and less-educated households?


  • I would take some of these questions out to make it more concise, but I love all of these questions. We should not feel obligated to give homework, and if we do assign homework, it needs to be meaningful. For me, the last one hit close to home. My parents had a 4th and 8th grade education and worked 12 hour days so I was basically raised by my great aunt who didn’t speak english. Though I was at a disadvantage, I got by fine, but just because I did doesn’t mean we expect others to.  

2. When the classroom is student-centered, teachers are free to provide the support that students crave.

  • We need to empower students. When we show students that we value their opinion, they are more open to ask questions (which is always a good thing!) and you are exposed to what they really know. For example, I had students cut up 8 congruent right triangles and had them arrange it in a specific way that proves the Pythagorean Theorem. I asked them how this proves the Pythagorean Theorem and I walked around to see what they come up with. I love these moments because I get to see and see how students think, (which I actually consider one of my hobbies). You lose these opportunities when we have a teacher-centered classroom. As much as we wish that students would understand the material if we just say it once, that is not the case. Students need/deserve one-on-one time.

3. Tip: Rather than focusing on what assignments you want students to do, consider providing students the learning objective. There are many ways to demonstrate understanding of a learning objective.

  • As much as I try to think of the best assignment, there will always be an assignment that will be “better” depending on what the student needs. I have been implementing options in my classroom, but I can definitely improve on this by giving students an option to create their own project. How powerful is that?

4. “I wasn’t seeing my students as people, as unique human beings. I was seeing them as soldiers that needed to fall in line.”

  • Earlier in my teaching career, I was so rigid in my expectations. I would make a big deal about cell phones, I would embarrass them if I saw them talking, I didn’t create a good and safe atmosphere. Our goal though, should be to prepare them to be leaders. Embrace them as the individuals they are, and the classroom will have a much brighter atmosphere. I am definitely not the king of classroom management, but we need to think about what we would want our classroom to be like if we were students again.

5. “During the time we spent together in class, I talked AT the students, not WITH them.”

  • Unfortunately when I was a student, a huge percentage of my college classes had instructors where they would talk AT the students. I don’t think anyone wants that (I mean, if they want to sleep, then maybe). If we want to value students, we need to have a conversation with them. Truly make it a student-centered classroom. Even in regular conversations, we would want to exchange dialogue right? It would be completely boring if one person just talks the entire time.

6. If you want assignments to reflect that kind of deep thinking, design them to be “back and forth assignments” rather than “one and done assignments” completing work and receiving a grade doesn’t do as much to encourage critical thinking as does reflecting and responding to feedback.

  • I was fortunate enough to work with Diana Herrington so I have had experience with “back and forth assignments.” This makes assignments much more meaningful and it shows that we really value learning. It also makes things more flexible; it’s OKAY to not understand it by the next day, if it takes you a week, that’s still good!

7. This is the culture of our classroom. Not only do my students expect feedback from me, they expect it from their peers as well. And peer feedback is so powerful. We’re a community of learners, and we help one another get better.

  • I need to focus on this one more next semester. I strongly believe in feedback but I need to realize that I am only one person. To empower students, I can have students give feedback to each other. This will also build classroom community.

8. Value learning over compliance.

  • When I was student-teaching, I would spend the first 3-5 minutes of the period looking at the students’ homework and stamping them to see if they did it. I honestly hated myself when I did it because someone could have spent an hour doing this homework and someone else could have been scribbling random work, wrote the answers from the back of the book, and they both would get the same credit. This quote sums it up for me. When I was stamping their homework, that says that I was valuing compliance over learning. I have been reflecting on this quote this semester in making sure that when I critique a student’s work, it’s not because of compliance.

9. What’s MOST valuable, though, is helping students discover and pursue their passions outside of class as a means of becoming better humans. If students are burdened with hours of homework, this kind of passion-producing, student-owned learning isn’t possible.

  • Students need time for their passions. When I was growing up, my passions were gymnastics, piano, soccer, and band. Looking back, I have no idea how I did it. How did I manage 7 hours of school and had the energy to do homework and follow my passions? Just because we went through it doesn’t mean that we should have our students do the same thing too. Students deserve to have a life outside of school. Students do not have the agency outside of school to choose what they want to do. If we want to create tomorrow’s leaders, we need to give them time to make their own choices and follow their passions.

Overall, I would recommend this book to any teacher. I love how this book is balanced between research and personal stories. About a dozen of my students read this book this past semester and they all loved it. Some are even passing the book along to other teachers. The emphasis should be on the students and the learning. If it’s not about those two things, think about ditch it.

Thank you so much Alice Keeler and Matt Miller for writing this book. You are effecting change on a topic that impacts many households across the nation.

12/21/17: Tips of the Day

If you’re in my class, every day starts out with a tip of the day. I first got the idea from my Dinosaurs Writing class (yes, it was a class dedicated to writing about dinosaurs, and yes, it was awesome) where the instructor would give us a tip of the day that had to do with writing, such as “Do NOT say ‘very unique,’ if it’s unique, it’s unique. It can’t be very unique.” These tips stuck with me and I thought it was a great attention-getter and it made the class more structured. Additionally, the classes I am teaching are supposed to be math content courses, but I thought that it would be a disservice to my students if I do not talk about pedagogy at all, so this would be the perfect way to sneak some pedagogy in there.

Here are some of my favorite tips of the day:
Math is the study of patterns

A lot of people confuse math with arithmetic. This is one of my first tips of the day that I give my students because we need to know what this subject really is about. Where do formulas come from? Well, we found patterns with specific numbers, and we were able to generalize. One student at the end wrote: Overall, I no longer fear or dread math. I’ve always liked patterns and trying to figure out what comes next so referring to math as the study of patterns has really helped me…I am now able to understand why math works and how to create a formula rather than trying to memorize formulas and when to use them.
“You learn 1,000 times more from your mistakes than your successes.” – Alice Keeler

Alice stated this about 4-5 years ago when I was taking her class and it stuck with me. It showed that we need to embrace our mistakes in order to learn. We are all going to make mistakes. It is not shameful at all.
When you teach, pretend that students can hear you but can’t see you.
I forgot where I heard this from, but I wanted to point out to students that we need to be precise in our language. When we are explaining how to do problems, we should replace “this” and “that” with specific words. For example, saying “subtract 2x from both sides to get 3x=6, then divide both sides by 3 to get x=2” is much more precise than “subtract this from both sides, then divide to get the answer.”
To be a good math teacher, you must know three things: 1. The content. 2. How to effectively teach the content. 3. The standards that you need to hit.
This was inspired by Tony Cotton, author of “Understanding and Teaching Primary Mathematics.” These three things aren’t the only things you need to know to become a good math teacher, but it forces students to know that it’s not just about the content. You could have the smartest person up in front but if they don’t know how to effectively teach the content, it’s pointless.
If you don’t believe in rounding an 89.9%, you are saying that you can accurately grade to the nearest 0.1%.
I had a chemistry teacher that would boast about this all the time and it was annoying. We are human. Do we completely understand the difference between a 94 and a 95 on a term paper? If we don’t, how would we know the difference between an 89.9% and a 90%?
You are going to have roughly 40 college instructors. What are you going to take from each of them?
I am huge on reflections. When students have the opportunity to see roughly 40 different styles of teaching, they should take note of that and start to develop who they want to be as a teacher.
Math should not be about speed.
A lot of my students have a fear of timed tests. It’s important to state this really early on to show them that they can be good at math, and speed is definitely not a factor. I care way more about conceptual understanding than speed.
Show, not tell.
I tell this to students so they can practice with their justification skills. Sure, they can tell me the Pythagorean Theorem or the product of two negative numbers is a positive number, but I want them to SHOW why these are true.
Design the class so you (the teacher) are learning too.
Having a student-centered classroom is still a relatively new concept for a lot of my students, but I want to show them the beauty of opening up the lesson so I am learning too. For example, 3 semesters ago, I wrote down the arithmetic sequence 3, 7, 11, 15, 19,… and told them to find the 100th term. I didn’t tell them the arithmetic sequence formula yet, so they relied on their problem solving skills. One student went up to the board and said that each number is one less than a multiple of 4, (4, 8, 12, 16, 20,…) so the answer is 4×100 – 1 = 399. I cannot believe it. I NEVER saw it that way before, and it really empowered the student. Another example was to find the area of a specific trapezoid. One student said that he saw the trapezoid as the bottom part of a triangle, but with the top part of the triangle cut off. I was in awe. Having student voice in the class was one of the best things I’ve done in the class because it really empowers students, showing them that they are completely capable.
Do not give formulas/procedures you do not completely understand
Math is not just about formulas/procedures. You can completely be successful in math without relying heavily on them. When I was student-teaching, my master teacher would say “don’t ask why, just flip the second and multiply” when dividing two fractions. Then a student asked why. The teacher said “don’t ask.” That stuck with me and I learned that I need to completely understand why these procedures work because I do not want to shoot down student curiosity. I want them to ask me why so I can have them explore the justification with me.

Your GPA does not determine how great of a teacher you can be.

When I was a student, I was super competitive. I took pride in my GPA. But now that I’m not a student anymore, I look back and notice that I cared way too much. Sure, you need a minimum GPA to get into a master’s program, but other than that, a 3.9 student isn’t automatically going to be a better teacher than a 2.9 student. When I told this to my students, they seemed relieved. By no means does it mean that they should just do the bare minimum to get a C in the course, it’s just that they need to focus on the learning, not the GPA.

These are just a few tips that I give my students and oftentimes I theme the entire day around that tip. I know that for a grade school teacher, that would mean around 180 tips, so maybe a tip of the week would be better suited if you want to do this. We all have a little bit of extra knowledge that students are missing out on, so maybe this would be the avenue to share that information with them.

Thank you for reading.

12/20/17: What I’ve Retained from CMC South

(I purposely delayed this post because I wanted to see what I retained.)

I went to my first conference, CMC Central, earlier this year, so CMC South was overwhelming, in a good way. Being surrounded by so many math educators felt incredible. I typed 27 pages full of notes from those two days and every sentence is gold. In reality though, you can only take in so much information and apply it to your practice, so here are my main takeaways from the speakers Chris Luzniak, Karim Ani, Jo Boaler, Fawn Nguyen, Robert Kaplinsky, Robert Berry, Tracy Zager, and Andrew Stadel.

Chris Luzniak: Chris talked about debates in the classroom, which I am familiar with, but I really liked his emphasis on sentence structure. Argument = Claim + Warrant. I have done debates before, but I have never done activities such as “which is the best way to solve this problem and why?” He also did a “Guess My Rule” which I’ve incorporated in one of my classes. The main takeaway though, was to take how open he was with the audience. Just the past month, I have felt more open to my students because of him.

Karim Ani: Karim’s talk was about finding real-world applications so we can practice making decisions based off mathematical reasoning. This one has stuck with me and made me feel completely incapable as a math instructor. I thought I knew what a real-world application was, but apparently I didn’t. I learned that a math concept is using the world to see math and a math application is using math to view the world, but every time I try to think of a real-world application, I still think that it’s a concept of math and not a real application. Using similar triangles to determine the angle at which to hit a golf ball and finding the equation of the parabolic shape a basketball makes when someone throws it are considered concepts, so I’m still stuck on this one unfortunately. He’s an awesome guy and makes me want to become a better math teacher, but I still need to do some research on this topic.

22859683_10155598294310708_1241199189522337496_o (1)

Jo Boaler: Having read Mathematical Mindsets, I knew I was going to enjoy this talk. I was already familiar with her work, but she really brought home the idea of giftedness being a negative impact in the long run. I still remember part of the video where they asked an elementary student how he would feel if his friends were labeled gifted and he wasn’t, and that really stuck with me. Categorizing students in itself damages mindsets. We really should be treating every student as if they were gifted. If we believe that every student has the ability to achieve math at a higher level, we need to not categorize.

Fawn Nguyen: Fawn was hands-down my favorite presenter. I love her personality and her humor. With my parents coming from Vietnam, I felt like I could relate to her just a little bit. I took notes of some of her quotes, “If they could think critically, it’ll be ideal. But on most days, I’ll take any kind of thinking.” “We are kidding ourselves when we give kids problems that only take a period. Are you kidding me? Do you think Mrs. Nguyen will give us a task that easy?”  I learned that we truly need to care about the problems that we assign. I also learned that “too high/too low” isn’t always the best, because I already know it’s not the answer, so what’s the point? Additionally, I learned that to never have students bored, I can include multiple assignments like a Problem of the Week, a task, problems from the textbook, etc. I also learned a new equation: Reflection + Practice = Less suck

LASTLY, she said something that not enough educators say: Surround yourself with people that will support you. Teaching is so hard, we don’t need people critical of us.

This semester, I focused on not caring about the negative voices and I realized people like Fawn even gets critical feedback even though I think she is amazing. It made me realize that no matter who you are, you cannot please everyone. I desperately wanted to go to her Grassroots workshop but it’s roughly a 5 hour drive and a lot of money, but I hope to see her talk again soon.

Robert Kaplinsky: I wanted to go to this talk to focus on the DOK levels of my problems. Also, it’s ROBERT KAPLINSKY. He showed us how to create higher DOK level questions by taking away certain parts of the question and adding a word/phrase like “highest sum, closest to 100.” We are not challenging our students enough if we just give them DOK 1 questions. We can still hit the standard but give them higher-level thinking questions, and it really shows the fluidity of math. I loved his quote “They are not thinkers, they are math zombies.” Overall, great talk.

Robert Berry: Right at the start, I knew I was going to like Robert Berry’s presentation. He made the entire room feel like family. I hope to make my classes feel the way Robert made us feel. His talk emphasized the importance of feeling safe in the classroom, using a video example of Shalunda Shackelford (who I wish was my Algebra 1 teacher!) as well as intersectionality. I loved his notice/wonder on a cell phone lock screen. We noticed and wondered so many things, and just from a lock screen! I have already used some of his ideas, emphasizing that my room is a safe space. I do agree that we show different sides of ourselves depending on our environment, and it is our goal to make that environment welcoming.

Tracy Zager: In Tracy’s talk, I learned that I should make students create their own questions. If we want students to be curious mathematicians, we need to teach students how to develop mathematical questions. I remember that she had pictures of mathematicians with worksheets, which was hilarious. But it totally made sense. Mathematicians back then were not motivated by packets. They asked their own questions, and used problem solving skills to find their answer. I also realized that KWL charts are ineffective. Students fill out these sheets, but then it doesn’t drive instruction. The teacher was going to do his/her original lesson plans anyways. Lastly, I will take away “riffing off solutions.” This is the idea that a student is not done once they find a solution. Maybe ask them to generalize, give them another scenario, a twist, etc.

Andrew Stadel: This talk reiterated that students are TIRED after 8 hours of learning, but I mean, come on, it’s ANDREW STADEL. I wouldn’t miss this talk for anything. I don’t think it was explicitly stated, but this really brought home the idea that there really shouldn’t be homework. I learned that to make math sticky, I need to make problems conceptual, make students curious, and there needs to be a personal connection to that problem. This talk also reminded me that it is important to bring back problems that students have seen a month or two ago to keep the content fresh in their minds. We can do this by practicing the 2-4-2 philosophy of giving 2 problems on current topics, 4 problems from what they have already learned, and 2 problems for higher order thinking. I also saw the cool Desmos activity of landing a plane, which I hope to use sometime soon!

Bonus: I also learned that Orange County teachers are AWESOME. I went to three talks with some of them and they are just wonderful to be around.

I hope to go to many more of these CMC conferences. Just being surrounded by math educators building each other up, it really reiterates that we are better together.

12/19/17: Ask me at least 2 questions

We need to stop asking “Do you have any questions?”. It’s not inviting, most of the time the teacher doesn’t give me enough time to think of a question, and I know a lot of people are too scared of asking questions in fear of sounding dumb.

It’s hard to get accurate feedback from students. All the students could be nodding their heads but that doesn’t mean that they completely understand what we just talked about. My partner told me that at his leadership retreat, he learned about questioning skills, and told me about “Ask me at least __ questions” and “What are your questions?” as alternatives to “Do you have any questions?”. With these alternatives, you are already assuming that they have questions and it doesn’t risk the student sounding dumb if they have a question. Through experience in the past 2 years, the latter question doesn’t seem as effective as the former, so I’ve stuck with the former.

In the beginning, the students seemed a little weirded out with the question, but as it became more normalized, students felt more comfortable. I started to get higher-level thinking questions, such as “What if we had three numbers?” when I introduced the Euclidean Algorithm to find the greatest common divisor, or “Why do we consider two bases in the trapezoidal area formula but not in the parallelogram area formula?”

This statement forces students to think of questions, and if they had a question to begin with, they feel better with asking since we are not moving on until the class asks 2 questions.

Side note: do NOT give in to silence. There is going to be awkward silence bit if you give in, it just shows students that all they have to do is not talk for 5 seconds and then you’ll move on. DO NOT GIVE IN. There were a couple times where I had to wait a minute until someone spoke up but it shows that you are serious. Even if they completely understand the topic, make them think of higher-level questions. Sure, some may argue that we wasted a minute of class time, but isn’t it worth it if it leads to a higher-level question that a student is curious of?

One other approach that I sometimes have students do as a replacement is to have them debrief in their groups for 1 minute. This gives them an opportunity to either go over the problem again, or ask each other questions that they are scared of asking in front of the entire class. During this time, I am walking around the room so students can pull me in and ask a question personally as well.

Overall, assume that students have questions (because they most likely do). “Ask me at least __ questions.” is way more inviting than “Do you have any questions?”.

So, with all this said, ask me at least 2 questions. I’ll wait. 🙂

12/18/17: A Reflection on Fall 2017

This semester, I have grown tremendously. I swapped about ⅓ to ½ of my previous lesson plans/projects because of what I learned from Twitter. Because of Twitter, I’ve implemented activities and sites such as: clothesline math, Which One Doesn’t Belong, Flipgrid, Estimation180, BreakoutEDU, fraction tiles, and much more.

As seen in a previous post, this semester, I’ve also focused on not caring about negative voices, and I was much happier. You can’t please everyone, and your self-worth is not based off the opinion of others. Trust your research, build relationships, give good timely feedback, and you’ll be fine.

The courses that I am teaching are supposed to be content-based, but I think we are taking away from these future educators if we don’t bring up Common Core, the 8 Mathematical Practices, or different types of pedagogies. I often talk about the 8 MPs, but next semester, I hope to bring in progressions and frameworks into my class.

As much as I have grown in the past couple years, I’m still not completely happy with the 3 courses that I’m teaching. It’s completely bad practice, but I do Math 10A and 10B in a point system, purely for convenience for both parties since we can easily calculate their grade. BUT, this enables students to be motivated by points, which I do not want. I really want to move to standards-based grading, but it’s completely unknown territory for me that I’d need to do more research on it. I like to build relationships with all 180+ students, but it’s extremely difficult to know each of them intimately enough that I can keep track of what standards they have each hit. I would love to do little portfolio sessions with each student so they have the opportunity to show off what they know, but I am against the thought of “It’s what you know in this x amount of time.”

As always, I could have been quicker with grades, but I literally grade EVERYTHING by hand for all 182 students. I only assign weekly homework for Math 100 and I believe that I already do very minimal assignments. I need to find some way to give students feedback without being exhausted. I do NOT want to have my students do MyMathLab. MyMathLab is expensive, and I would rather have students focus on conceptual understanding, not just trying to obtain an answer. I have helped many people on MyMathLab as a tutor and all they do is click on “View an Example” and just substituting their own numbers. As much as I want to help my students, I am only one person. I need to find some sort of balance.

The students that I had this semester were overall phenomenal. I really hit the idea of a growth-mindset hard and a lot of them took it to heart. Here are some of the comments I’ve received when asked about how they have grown throughout the semester:

  • I gained a lot of my confidence back after this class. I feel like once again I have the skills to be a great teacher after battling my anxiety disorder and wondering if I am fit to do this.
  • I really enjoyed being introduced to the idea of a growth mindset this semester. I have grown mathematically throughout the past couple months and feel that I am better equipped to teach math someday. I used to think math was always just a “right or wrong” answer, but now I know it is important to find multiple ways to do problems because everyone thinks differently. I love the idea of reflections and enjoyed being able to buy back some of my points, it made this semester/class less stressful. I never thought it would be possible to have math as my favorite class but it was!
  • I have grown mathematically by never giving up, constantly work hard, and always try to stay positive even when it seems impossible sometimes. I have made a lot of mistakes but I learned from them. I did not let a bad grade slow me down. I simply had to ask for help and take the time to work it out until I finally understood it. I admit some of the material I didn’t quite understand, but that doesn’t mean I can’t learn how to in the future. Because with a growth mindset, I will continue to grow.
  • I also learned that when I make a mistake, it’s okay. I used to think mistakes meant I wasn’t smart enough. Now I know that mistakes help me learn and grow. I feel more confident in my math abilities now than I did before.
  • Overall, I no longer fear or dread math. I’ve always liked patterns and trying to figure out what comes next so referring to math as the study of patterns has really helped me…I am now able to understand why math works and how to create a formula rather than trying to memorize formulas and when to use them. Thanks for being rad Howie, I actually enjoy the challenge instead of fearing it!

One wrote a little aside.

  • I thought it was really great you kept asking how my work was going or where I worked at. I think only 1 other teacher ever in my 4 ½ years at Fresno has ever asked me where I work or how is it. It really made me feel like I’m more than my ID #.

^^^This got me. I thought it was common to just ask students how they are, where they work, where they are from, but apparently not. It’s in these relationships where you get students. It starts with a simple question. You shouldn’t go into teaching just because you like the content. You need to be invested in your students as well.

Overall, I am very pleased with how the Fall 2017 courses went, but I can definitely be better. Working with Diana Herrington in the first years of teaching gave me a HUGE boost, but the thought of being even better than previous semesters is thrilling. Over the winter break, I am going to research more on standards-based grading to really show students that it’s not about the points, find ways to give feedback without overwhelming myself, and prepare them even better to become mathematical thinkers and educators of tomorrow’s leaders.

Thank you for reading.

12/14/17: Why I Love Fresno State


Honestly, it makes WAY more sense to work at a community college purely thinking monetarily: the benefits are better, there are actually tenure positions there, and I’d be making a lot more money (a LOT). Even though this is true, it’s honestly not even tempting because I love Fresno State. I love the students here, I love the department, and I love what this university stands for.

At Fresno State, roughly 70% of our students are first-generation college students, roughly 57% are an underrepresented minority, and roughly 63% are Pell Grant eligible. I love working with these students because I want to show them that they can be successful by telling them my story: My parents came here in 1980 after they lost in the Vietnam War. My mom has a 4th grade education and my dad has an 8th grade education. They were unable to help me with homework growing up not only because the skills weren’t there, but because they were working roughly 12 hours a day at a restaurant to make ends meet. Despite the struggles, my sister and I were able to graduate from college, and now she is a microbiologist in Tulare County and I’m teaching at a college. I want to show these students that you can break down barriers that you once thought were impenetrable.

Obviously, there are a lot of schools that work with these types of students as well, but that is only part of the reason why I love my school. I also love it because it’s my home. I graduated with a bachelor’s, credential, and master’s here. During that time, I was in the Fresno State Bulldog Marching Band and Wind Orchestra for four years. I even tutored Fresno State Athletes for 3 years, which really showed me that the athletic program really pushes for academics first. It may sound lame to some people that I would stay here, but I have pride in this school. This is not just a workplace for me; this is my home, and I hope to stay here for a long time.

Additionally, I love our math department. We are incredibly diverse, with faculty coming from Russia, South Korea, Hungary, Romania, Chile, China, Belgium, India, Sri Lanka, and the list goes on. We have events such as the Department of Math Day (where we celebrate the math department with talks, games, math jeopardy), Sonia Kovalevsky Day (where we promote math to 7th-12th grade girls), Math Field Day (a math contest for 4th-12th graders), and the Integration Bee (for high school and college students). The department, especially the department chair, makes sure that we are all thriving in our classrooms and it really shows that they care. I can’t ask for more from them.

Well…I could. I wish I had more than a semester-long contract and I wish I had a permanent office (I’m already in my 4th office in 4 years…). I also wish I had more funds to get more professional development without sacrificing my other budgets. Overall though, the goods definitely override the bads.

I know that there are wonderful departments, students, and schools just like ours out there, but I wouldn’t change my place of work for anything.

I love Fresno State.

12/13/17: Be You

When I first started teaching, I thought that you should have a professional life and your own life, and they have to be separate. Now, I ask, why? It is important to interweave the two to show students that you are human too. We are not boring teachers that are on the job 24/7. Additionally, if we want students to open up and feel comfortable in the classroom, so should the teacher.

There are people who will say that your personal life has nothing to do with their education, so why say it? I would tell them that the best teachers that I’ve had would be real humans with us, and I still remember some facts about them: One is obsessed with diet coke, one loves sons of anarchy and Guinness, one is obsessed with cats and has daughters who figure skate, one plays soccer, one sings and plays guitar, one has perfect pitch and sings, one plays World of Warcraft, I can go on and on. On the other hand, I’ve had some teachers who I do not even remember their name because there was no connection; they were bland and it seemed like they didn’t care about the students. If we don’t want our teachers talking about their personal lives ever, we might as well be taught by robots. Especially since I teach future teachers, I want to emphasize this to show that your personal life is not taboo.

So here is me in a nutshell:

25383247_10155722937550708_11904691_o (1)

I’m Howie. I have a wonderful fiancé Jim who I’ve been with for 7 years (today is our anniversary!). I love playing piano, watching gymnastics, Parks and Recreation, and Bob’s Burgers. I love math and all things band-related. I am definitely more of a cat-person than a dog-person. I continually want to be better at my craft. I love nature and my pipe dream is to create a vacuum that removes pollutants from the air.

For me, I want to show awareness and representation. There are plenty of people even in 2017 that will hate you just because you are gay. I want to show that we aren’t that different. I have had few people state that you shouldn’t bring up your orientation, but here is my response to that:

Very few straight people would think twice about whether they should mention their spouse, so why is mine any different? It’s not really an agenda, it’s just reality. Growing up, I wish I had someone to confide in. Maybe there are students that are too afraid to speak up, or are being bullied and have nowhere to go. I want to be that person that they can come to. I tell all my classes that our classroom/my office is a safe space. It’s okay to make mistakes, it’s okay to open up. But it’s really hard to do that when you are not yourself and show that you are human too.

So, be you. Students deserve it.

You are going to be hated

It is unrealistic to have *all* your students like you. Some of the best people I know/look up to have strong opponents of what they do, even though I have no idea why they are hated. For all I know, people can be hated just on the way they look, the way they talk, their sexual orientation, things we cannot control. For me, I have 180+ students at a time. Law of large numbers says that you are bound to have at least a couple who hate you no matter what you do.

Guess what?

You still teach. Still build relationships anyway. Show them that you are there for them unconditionally.

This semester, I focused on not caring about negative comments and I feel MUCH happier. My worth is not based off the opinions of others. Do I try my best making math fun and accessible to everyone? Absolutely. Do I still try to build relationships with them? Definitely, but there will always be negative comments. If it’s not constructive criticism, you can’t really do anything about it.

We meet people at different parts of our lives. Sometimes, that part is a growing area. Maybe it was our first year teaching, maybe we were trying something new, maybe we just weren’t feeling it that day, but our entire self shouldn’t be judged on that small period of time. I was a way different educator 4 years ago than I am today.

So to everyone reading this blog, educator or not: You are much more than the opinion of others. Remember why you went into the profession in the first place. If you’re chasing for people to like you, teaching is the wrong profession.

“You can’t please everyone, so you gotta please yourself.” – Ricky Nelson