Author Archives: howiehua

How I’ve grown in the past 5 years

This is my 5th year of teaching so I am relatively a new teacher, but I hope I am never done learning. Here are some ways I’ve grown throughout these 5 years:

Shift in homework – During my student teaching experience, the homework would be about 15 problems a night and I would go around the room and stamp it if they just did the homework. I honestly hated myself. Students probably spent 30 minutes to an hour on that homework, only for a 3 second glance and a stamp. That was when I knew that I was grading compliance, not mathematical ability. Now I know to only focus on 3-5 problems a week and make sure they really dive into those problems. I got this idea from Diana Herrington when we co-taught together. She would rather do fewer problems and spend a lot of time on those problems.

Formatively assessing multiple students – In my first semester of student teaching, one student would dominate the class with questions and solutions. I thought that she was a great student, but I focused a lot of my time on her rather than the other 35 students. Now knowing about equity in the classroom, I feel extremely bad that I didn’t give as much attention to others. Now I try my best to not have one student dominate the conversation by asking the “front tables” or “back tables” to answer, or randomly picking groups. Just because one student knows how to do it doesn’t mean that everyone knows.

Less emphasis on math tricks – I used to love and show math tricks to students. For example, I can square numbers ending in 5 in my head. For 65^2, you take 6 and multiply by the next number up (7) to get 42, and it’ll end in 25, so 65^2=4,225. Though this is cool, and this did make math fun for me when I learned about it in high school, I never taught students why. I won’t promise that I will get rid of tricks entirely, but I will definitely tell students why these tricks work and to emphasize that math is the study of patterns.

Hating technology in the classroom – While I was a math major thinking about my pedagogy, I thought technology in the classroom was unnecessary. I’ve been taught with just whiteboard and markers, so why do I need to teach differently? Well, I was totally wrong. It’s taking a few years, but I’m starting to feel comfortable with tech in the classroom. I think the problem was twofold: I wasn’t aware of the apps that were out there and I didn’t want it to feel forced. Some tech apps/tools that I found that truly enhance my lessons are: Desmos, Google slides, online geoboards, Kahoot, Flipgrid, just to name a few. The awesome thing about these tools is that they got students excited about math in a way that I couldn’t alone.

Not being as nit-picky – I think it stems from being in band for most of my life that I expect no one to be off-task because we are all working on the same goal. It’s been something that I’m still continually forcing myself to not care about, but if one person is off-task for a couple seconds, I need to let it go. For example, I am taking an Asian History class at Fresno State for fun, and I would go on Twitter just for a couple seconds at a time. It wasn’t a personal attack on the professor; I actually really like him. It just was that there was some free time in between topics. I shouldn’t embarrass a student especially if they already did what was asked of them. It’s also hard to engage students for the entire 50 minutes, so I need to let these things slide.

Emphasis on memorization – In my undergrad, I thought that to be successful in math, I just need to memorize formulas, theorems, and definitions and know how to apply them. That mentality got me through my undergrad, but it would be a disservice to math as a subject if I taught my students that that is all math is. Now I know that we shouldn’t test on memorization. Test them on big concepts. Check out one of my previous blogs on test anxiety for more information on how I go around memorization as a key to success.

Emphasis on speed – I loved timed tests when I was a kid. I love the competitive aspect. But as a teacher, it’s not about what you like; you need to cater to the students that you have. Being quick does not mean that you are smart.

Different approaches to lesson planning – My lesson plans in the beginning sucked. Let’s face it. I just looked at the book, wrote down definitions and necessary theorems, then did a couple examples with the class, then had students start their homework for the remainder of the time. Diana Herrington helped me see that math is creative and teaching is an art. How can we creatively teach this to where students can discover formulas? How can we be creative so students are making precise definitions rather than just writing something down? I’ll explain more of this in a later blog.

Changes in assessments – All I’ve had growing up were multiple choice and short answer tests, so when I had to give an assessment, these are the two that I go towards. However, I learned that feedback is extremely important as a teacher and multiple choice tests hardly allow for any feedback. I don’t know how they got B as their answer. How do I know if they just guessed or if they were torn between two answers? Check out my blog on Test Anxiety to see what kind of assessments I do now.

I can think of more but this blog is already long enough. Overall, even though I’m still new to the teaching profession, I have already learned so much, and it is really exciting to see how else I would change in the coming years. To new teachers: I highly recommend reflecting. Reflecting constantly is how we grow. The constant questioning of “Why am I teaching this specific way? Why am I giving this specific homework? Why am I doing this?” will help mold you to the teacher you want to be.

12/1/17 Flipgrid and Collaborative Google Slides

I understand how important it is for students to learn from each other. To empower students, it is important to show that students can learn from each other and not just the teacher. It has been shown over and over through testimonies that students love to be able to talk to each other in math class. Because my students are seated in groups of 4, they generally only know 3 other people, but I want my students to learn from everyone, not just 3 others. It is a disservice if students are not allowed to learn from more people, so I recently implemented Flipgrid and Collaborative Google Slides to create a community of learners.

I have tweeted about Flipgrid so much in the past 2 weeks that I’m pretty sure they are tired of hearing about it, BUT, I cannot give this app enough praise. Yes, there are a few students who feel uncomfortable in front of the camera, however, overall, the students love it. They love that they can redo their videos, they love that you can add emojis on your selfie, and they love that they can look back at how they can hear other ways of doing problems. I had my students do a couple Flipgrid videos for homework (and they needed to comment on other videos) and I overheard a student say “At first I was shy but then I wanted to comment on everyone’s!” How awesome is that?! A student who hardly talks in the classroom feels EMPOWERED and wants to have mathematical conversations with others. That comment alone is worth the subscription.

For me, I love the classroom community that is occurring. Students can finally interact with people across the room and critique and learn from each other. My mom also gave me the idea that I can use Flipgrid as a teacher by recording myself doing little examples so students can watch/review concepts whenever they want. AWESOME.

I learned about collaborative Google Slides from Alice Keeler (@alicekeeler) when I took her CI 149 class. I did this with my Math 10B and Math 100 class where there were deconstructing shapes to find the area of a polygon and they commented on other slides. I posted 36 slides, each of which had one of six shapes. I purposely put 6 of the same shape so students can verify with others and even compare if they deconstructed differently.Screen Shot 2017-12-01 at 7.43.42 PM

An added plus for using Google Slides is that I can see what students are doing all from my laptop. Though I like walking around asking students how they are doing, this is helpful because I can give quick feedback by leaving them a comment.

Some students preferred collaborative Google Slides over Flipgrid because they can quickly see what every student is doing and it’s not as “embarrassing”. However, some students preferred Flipgrid just because there is so much personality in their assignment; it truly feels like they own that assignment.

Overall, I love that both of these tools help create a classroom community. It helps students talk about math in a way where they are able to take their time developing their thoughts and answer when they are ready. Highly recommend.

Test Anxiety and what I do with it

A lot of people have test anxiety and it is completely understandable: you only have a certain amount of time to spill everything you know about a subject and whatever is on that piece of paper determines a big chunk of your grade. I can remember tests that I have taken where I would remember how to do a problem just a couple minutes after walking out of the classroom, which is a horrible feeling. I’m sorry that it took me 53 minutes to figure out the problems, not 50.

Because I teach future elementary school teachers who for the most part, believe that math is their weakest subject, they need to be carefully taught. I want to show them that they can be good at math, and to do that, we have to break down one of those barriers, which is test anxiety. With the help of Diana Herrington, we decided to do three things: either make assessments take-home projects or give students the first 5-7 minutes to talk about the test (with the tests in their hands) without pencils, and always let students buy back points after the tests.

Take-home assessments

Both parties like the idea of take-home tests. I give them 3-5 days to complete a project so they don’t have to feel anxious. With take-home tests, I can ask a little more from them since they have more time to think about it. Additionally, I can use this as an opportunity to extend what they know. Take-home assessments drive the point of “Here’s some information, what can you do with it?” I think it makes the assessments more meaningful. Why don’t we find the area/volume of actual objects rather than bubble in 25 multiple choice questions?

What I like most about take-home assessments is that it takes away the idea that memorization is key to being good at math. Even I used to think that during my bachelor’s. In high school, I was pretty peeved because my friend is GREAT at memorizing, and she would score the same if not better than me on tests. It irritated me because I felt like I understood the concepts better but she would just memorize formulas, which made me think: Does this test accurately assess what we actually know?

Giving 5-7 minutes to talk about the test

If I had to give a multiple choice/short answer test, I would pass out the tests and the students would discuss with their groups how to do the problems. Generally, I give students options (6 questions, choose 5 to answer). Even with multiple choice, there is still a justification portion. I have shared this with some other instructors but they seem hesitant because they see it as the “struggling” students getting help from the “smart” students. Here is my response to that:

Math should be conversational. In what job are you not allowed to ask others for help, or at least a little push? Even if they overhear all of the correct answers, they still need to justify and use precise vocabulary. Honestly, there have been some days where I would overhear their conversations during these 5-7 minutes and I would go to bed with a ridiculously huge smile on my face because these students who claimed to be bad at math are using deductive reasoning, precise mathematical language, and are HELPING each other (which by the way, the world needs more of). In my 5 semesters of doing this, I have never heard a complaint about this from students and more importantly, they explicitly say that it lowers their test anxiety.

In addition to these two ways to lower test anxiety, I also let my students know that they can buy back points after the test is done. This let’s them know that I value their learning even if it means that it took them a month to understand the concept. For revisions, they must reflect saying “I got this incorrect because…” and “I now know…”. Reflection is huge for me, because when they think about their mistakes, the less likely they are going to make that mistake again. Students explicitly appreciate this so much. As a teacher, I’m basically grading everything twice, but I honestly think it’s worth it to instill a growth mindset in these future teachers.

Overall, it is important to somehow reduce test anxiety because students are not performing at their highest if they are anxious. Are we accurately assessing what they know, or are we assessing how they perform in pressure situations?

11/28/17 Functions, Volume, and Optimization

I felt pretty good with the lessons that I did the past two days, so I thought I’d share what I’m doing in my classes. Because a lot of my students (who are future teachers) believe that math is one of their weaker subjects, I try my best to include fun, yet rich mathematical tasks so my students see that math is not scary, but rather, attainable and enjoyable.

Math 10A: What’s my Rule?

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In Math 10A, we are learning about functions, so I decided to have each group think of a rule, and other students would do a gallery walk and can only give 4 inputs, in which the docent would give the 4 outputs. Then, the students have to guess their rule. There was a lot of laughter shared. Surprisingly (or not so surprisingly), just getting students out of their chairs makes activities much more exciting.

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Math 10B: Finding volume

Power Solids are amazing. I had students make a conjecture of how many square pyramids fit into a square prism of the same base and height. A lot guessed 2 or 4, but hardly anyone said 3. After pouring rice from one solid to another, they found that 3 square pyramids fit into a square prism. We did the same for cones and cylinders, and triangular pyramids and triangular prisms with the same base and height, then we generalized to obtain the volume formulas. Discovering formulas is one of my favorite activities to do. I often see epiphanies and if you’re a teacher, you know that that is one of the best feelings ever.

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Math 100: Optimization

Alright, now this one is just fun. We did this in the 5 E’s style where I pretended that I was their boss at Coca-Cola and they are my interns. I want them to tell me which way to pack 12 cans of soda is more efficient in terms of space. This involved knowing the area of a rectangle, a circle, Pythagorean Theorem, and percentages. After we determined which model was the best, I then extended the problem to 20 cans and asked if the result would be the same.

One of my students commented that she loved this because it brings in a lot of prior knowledge. She said she never saw a clever way of using the Pythagorean Theorem but now she has.

I also love this because I can finally talk about limits. What if we had 1,000,000 cans? Does the space occupied by the cans tend to 100% if we keep increasing the amount of cans?

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Bonus:

Lastly, in office hours, I had a couple students talk to me about either Ditch that Homework by Alice Keeler and Matt Miller or Mathematical Mindsets by Jo Boaler. I LOVE students who take education seriously and are preparing themselves NOW. What surprises me about a lot of students is that they just take classes for the units, but it’s those students who really say “What can I take from this into my future classroom?” that makes teaching effortless.

 

11/27/17: Who run the world? GIRLS.

My four biggest influences in education are women: Diana Herrington, Alice Keeler, Jo Boaler, and Jenna Tague. They have shaped me into the educator that I am today and I cannot be grateful enough for everything that they have shared. This blog post will share what these female educators mean to me and the need to empower women in mathematics.

dHerrington

Diana Herrington and I worked together for two years developing curricula for Liberal Studies majors at Fresno State. She showed me that math is everywhere and that math is not DRY. She loved using technology in the classroom which was eye-opening at the time. Diana was one of the most innovative teachers I knew. Constantly using manipulatives, technology, items from Trash for Teachers, her selflessness knew no bounds. Without her, I would not have felt as comfortable teaching differently. She really solidified the idea that it’s important to go deep into a solution. Only do 3-5 problems.

Diana knew how to make people feel good. I remember I asked her how I did one day, and she said “You did better than me!” and that just took me aback. I thought to myself, “oh my gosh, THE Diana Herrington said that.” What constantly amazed me was that she took my suggestions as well. We were a TEAM. Even with her years of teaching experience, she was still open to suggestions, which I found inspiring.

Diana opened my eyes to new methods left and right; she was so great at that. I still use a lot of lessons that we’ve planned together and I will share those in a later blog. I think about her every time I teach Math 10A and Math 10B and I am so grateful I was partnered up with her.

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I met Alice Keeler in CI 101 Spring 2013. I was one of those students who didn’t think technology was necessary in the classroom (HA!). I was even writing my notes in a notebook even though it was in a computer lab. Alice opened a new world to me, a world where we need to use technology when it enhances the lesson but way more important than that, we use technology to enhance the relationships we have with our students. She is one of the teachers that truly cared about what you’re going to do with this information and she was so selfless about it. She shared everything she could. Not only that, I love that she does not settle. Teachers could so easily just repeat the same lessons and lessons over and over semester after semester but from what I’ve seen, she always adjusts to make her course even better, which is just awesome.

Alice is one of the few instructors that I have kept in touch with, and I am still learning from her. Just looking at all her blog posts on her website alicekeeler.com makes me want to be a better teacher. It made me realize that the best teachers share. Her ability to create is just amazing as well. Can’t find a way to make things easier? She creates programs to make it work. How cool is that?

Her teachings have been seen in my classroom quite often. I have told all of my students something she said to our class 4 years ago: You learn 1,000 times more from your mistakes than successes, and that has constantly been a theme in my classroom. Her mantra of relationships and feedback being the two most important things a teacher can give is constantly on my mind.

I can go on and on about how Alice changed my view of what a teacher should be but there are two more women that majorly inspired me.

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Diana gave me Jo Boaler’s book Mathematical Mindsets a couple years ago and I was just in awe. That book changed me. Personally, I LOVED speed, but I realized that math is not a competition. I used to teach cute little math tricks, but then realized that it’s all procedural; the students aren’t really understanding where it comes from. Math is not about getting answers quickly, math is about finding relationships. This book showed me that understanding that mistakes are important to learning. Because of this, Diana and I let students revise EVERYTHING. Students appreciated it so much and I think that because we teach future teachers, this idea is SO important. Because of Jo, I realized how important reflections are. Reflecting will make us not just better students or teachers, but better people.

Jenna_Tague

Lastly is Jenna Tague. She is a Professor at Fresno State and we collaborate often. What I love about her is that she is so knowledgeable when it comes to research. She showed me that it is important to look at research to verify teaching practices. She is one of the most patient people I know and one that I look up to when it comes to equity in the classroom. She made it mandatory for students to come to office hours in the first couple weeks to show that she is accessible and approachable. I took note of this myself this semester and I can tell you that my relationships with students this semester is much stronger because of it. Students are more willing to approach me when they need help and I honestly think it’s because of the relationships built in the mandatory office hours.

 

My teaching style is strongly influenced by these four women. This is why it is extremely important to empower women in mathematics. I don’t know the answer of exactly how to do that, but it starts with an equitable classroom and a growth mindset. Show every student that they are capable of achieving math at a higher level. Show students that math is not just about memorization, but rather, creativity. Show that math is applicable to their lives and help them. Show them women mathematicians. All we see are male mathematicians. Show them how Sonia Kovalevsky broke barriers by being the first woman to earn a PhD in Math. Show them that women can do it too.

 

11/26/17: Why am I a Teacher?

Welcome to my first blog post! Because this is a teacher blog, I might as well state why I wanted to teach. What’s my purpose?

In short, I decided to become a math teacher early in my college career because after seeing that the United States struggles as a nation in their mathematical abilities, I thought that this is the occupation where I would impact society the most.

Growing up, I really liked math. I’ve had the same math teacher all 4 years of high school (Mr. Trejo) and he just made math fun. Though my love of math stayed strong all my life, my thoughts for math drastically changed throughout the years. In K-12, math was a competition. I wanted to be the fastest and I wanted to have the highest scores. In college, math turned pretty dry, where I told myself that to be good in math, you just need to know three things: formulas, theorems, and definitions. That’s it. Just memorize those and you’re good. NOW, after a couple years of teaching and with the help of Diana Herrington, my co-teacher of 2 years, I realize that math is creative, math is exploratory, math is everywhere.

So even though I have loved math my whole life, the progression of what math meant/means to me is fascinating.

I hope to shift the mindsets of future elementary school teachers and show them that math is not just for the people who are good at memorizing. Math is for everyone. Like Jo Boaler states, everyone can achieve math at the highest level, and I hope I can lead my students there.