My Dear Fifth Graders,

This year has gone by fast, and it is time to say goodbye. Last year one of my fourth graders came to me and said “Mr. Lin, you inspired me!”. That is the most valuable comment I have ever received in my life. I hope I have inspired you at some point this year. Many teachers have told me I am spoiled to have this class my first year at Mesquite, and I totally agree. I enjoyed teaching you and seeing your growth. The joy I collected this year will last a lifetime. 

One thing I learned when I moved up to middle school is that change is inevitable. Middle school is going to be a big change for all of you. In fact, changes are everywhere as you grow up. They can be positive or negative, but what is important is how we react to them. What I did is to adapt and make the best of them. To be honest, I did not handle all the changes perfectly, but I am proud of myself because I tried my best. So always remember to adapt to the changes in your life and be a fighter. 

Please understand that what you learn today will change how you see the world and how you see your future. As you may have heard, being bilingual is going to open doors for you. You might not know what it really means now, but you will be surprised by what is behind those doors 10 years from now or even sooner.

My last advice to you is to encourage yourself to explore this world in every possible way that you can. Learn to embrace the discomfort of not knowing. Be friends with the mistakes you make, and learn from them. Please don’t hesitate to share your accomplishments with me in the future. I will always be proud of your accomplishments as I am today.

Love,

Mr. Lin

Choral Counting (数一数) is something that brings true joy into my classroom. Meanwhile, it is an under appreciated approach in upper grades. Children love to count and look for patterns. This urge is part of human nature, which creates a powerful classroom engagement. Moreover, it is a literacy-rich activity. The discussion followed by the counting offers an authentic context for students to use their language skills. This post is going to showcase two Choral Counting activities from my fifth-grade Mandarin Immersion classroom.

The first counting sequence is counting backwards by 7, starting at 200. The charm of Choral Counting comes from its variability. Depending on students’ need, teachers can conduct a counting on or counting down activity with whole number, fractions, even decimal fractions. This is the very first counting down activity we did. The reason for using 7 is that the atomicity of 7s fact is usually the last developed. The highlight of this counting is the discussion around why the number going down diagonally is 42 (in green) less than the previous number, and the number going down vertically is 35 (in blue) less than the previous number. After a turn and talk, students came to the conclusion that going down vertically is basically subtracting 7 five times from the original answer, which is 5 x 7=35. The pattern applies to the diagonal pattern as well; it is subtracting 7 six times which makes 42. What is even more amazing is that the pattern varies according to how the teacher arranges the layout of the recording. For example, instead of writing horizontally, the teacher can record it vertically. Another variation can be adjusting how many numbers to record each line. As a result, the same counting generates rich mathematical discourse.

The second counting sequence is counting up by 2/3, starting at 1/3. After some practice of counting whole numbers, my students were very curious about counting fractions. I dropped the ball when they first requested because I did not know how to record it. Should I write it as mixed numbers or improper fractions? This book saved me! One of the co-authors, Megan Franke, is also a co-author of the CGI series. The book offers many tools for teachers to plan the counting. The tricky part of a Choral Counting is how to conduct the follow-up discussion. The students will catch you off guard by throwing noticings at you, some of which you might have never thought of. Therefore, planning is crucial. In this case, students had a hard time figuring out the change is a fraction instead of a whole number. A student said it increases 10 (black pattern on the left), but actually, they meant it increases 10/3. What I love most about this talk is the diagonal pattern. Some students noticed it increases by 12/3, but some noticed it actually increases by 4. It is always fun for me to see students trying to convince each other. Following this noticing, another kid found the orange pattern on the right. The difference between the first-line number and the last-line one of the same column is 10.

If you want to try choral counting, I will recommend starting with counting up with whole numbers. Here is an example of counting up by 3, starting at 8. Once you and your student get familiar with the rules, you can try the different variations. This is a typical muti-entry activity for students to practice reasoning.

Stehouse has a planning tool for Choral Counting which helps you navigate the counts before doing it with the students. I usually print them out and write notes on them.

If you want a copy of the Chinese supporting poster you can click here to download. Have fun counting!

In the 2019 NCTM annual conference, NCTM announced that it is going to lunch a new book that is parallel to Catalyzing Change in High School Mathematics: Initiating Critical Conversations. I wrote down some notes about what could be some positive changes in elementary classrooms, and those notes become this post.

1.Math Instruction is speed-focused. Timed drill practice is still prevalent among districts. Some districts have allocated time (10-20 minutes) for drill practice every day. It is a waste of time and creates anxiety for both the teacher and students. No one will disagree we should encourage students to slow down and check their work, and we hear teachers say this to their students all the time. However, the way the instruction is designed is continuously delivering the message: Hurry up! There is no time for thinking. Just finish whatever you can. How can students slow down in such a setting? I have students who had a panic attack when we did the math fact dill. All of a sudden, she couldn’t breathe when we start the drill practice. This is a “high” kid who loves thinking deeply all the time.

2.“I do we do you do” model is overused in all the subject areas including Math. This model is effective in a very small part of language learning and almost ineffective in math learning. It delivers a message that math is no more than duplicating what the teacher is doing. In a classroom I observed, two of the “high” fifth-grade students couldn’t figure out the rule: when you have a whole number times multiple of ten problems, such as 12 times 10 to the power of 3. Just add the exponent number of 0 to the whole number. The students kept asking why. For those two, they refused to copy what teachers do without understanding the rationale behind it. The teacher moved on and had me pull these two students out for small talk. I am sure they are not the only ones that do not understand why but they are the only ones that speak up and asked for further explanation. Asking why is part of human nature. And that’s what we mean when we talk about humanizing math education.

3. The school system lacks a Teacher Support System for the NCTM math teaching practice. Not many schools offer a support system to set teachers up for success. Even the ones that have a support system may carry the outdated pedagogy. With this system in place, teachers, especially new teachers, are not able to implement the new pedagogy consistently. We all know how hard to make veteran teachers change how they teach. What is even more depressing is that new teachers who were trained for the new pedagogy go right back to the old school style when they have their classrooms.

4. “High performing” school is overlooked. I have attended a session led by the present of NCTM, Robert Berry, in the 2019 NCTM annual conference in San Diego. Dr. Berry presented us with three high school cases that showed tremendous improvement after adopting a systemic approach to change. These districts are the ones that were low performing in state standardized tests. Usually, we focus on the low performing districts when we think of changing. However, I want to argue that the “High performing” schools deserve the same focus. The equity issue can be even more severe in those districts. Even they are high performing in standardized tests(let’s say they have a 90% proficient rate), there is still a percentage of students who are left out in that data. So many factors could lead to this result. I don’t think we have looked far enough into these cases.

These thoughts are the results of my first-year teaching experience. It takes a village to educate a child, so it also takes a community to train a teacher. I would love to hear about your thoughts.

My name is Lufei Lin. Most of the time, I address myself as Lufi, so if you see the name Lufei or Lufi, they are all me. I teach for an Elementary Mandarin Immersion Program in Tucson Arizona (Fifth-grade in the 2018-2019 school year; fourth- and fifth-grade in the 2019-2020 school year). I got my Multiple Subject teaching credential in California, where this fantastic math journey started. Even though I live in the southern Arizona desert now, SoCal always has a special spot in my heart.

My dear dear mentor Dr. Cathery Yeh encouraged me to blog when I first started teaching. However, I did not feel like I was ready to write back then. As a new teacher, teaching was overwhelming. My mind was flooded with different feelings, but those feelings were all tangled. I couldn’t find a way to let them out.

Over the past week, Mathematics Education Trust of NCTM gave me a grant to attend the 2019 NCTM annual conference in San Diego. I got to meet my math superheroes! If you ran into me at the conference, you would probably find me acting like a high schooler stalking rock stars at different sessions. Going to these amazing sessions and meeting rock star math educators gave me a chance to reflect on my teaching practice. At one of the sessions, I met Megan Franke, the co-author of CGI book series. I stammered and told her how much I admire her work and how I have been trying to implement CGI in my Mandarin Immersion classroom. She encouraged me to write about my teaching because many bilingual programs are developing around the LA area. Any form of sharing is valuable. After the conference, I kept asking myself if I am ready to write some thoughts down. Right now, I m on the plane home starting this very first blog post. As an old Chinese saying “The long journey starts at your feet”(千里之行始于足下). I think I am ready.

This blog is my math playground. I want to share what I am doing during math block in my Mandarin Immersion classroom. I was trained as a CGI teacher. I love Choral Counting, Counting Collection, and Number Talk. Math modeling is my favorite thing to do with my students. How to build a discourse rich math classroom is on the top of my learning list. If you bring up equity issues in an elementary math classroom, I will ramble on and on and on. I hope that I will become a reflective teacher through writing. Besides, You will also find translated math resources for your Mandarin Immersion classroom at my blog.

I fully understand the challenges elementary school teachers face, especially in the bilingual setting, but let’s stop saying we are just teaching. I would like to quote Dr. Robert Berry, present of NCTM, to end this post—Teachers are change agents.

Let’s change the world one math problem at a time.