- How do I introduce myself?
- What are my rules and expectations this year?
- What difficult math problems do I want to introduce to show that productive struggle is meaningful?
- How do I cultivate a sense of community and teamwork?
- How do I get to know my students and build relations with them?
- What books do I need to finish reading so that I feel prepared to teach?
- Do I need to make any posters?
- What did I learn this summer that I must incorporate right away?
- When do I want to introduce Math Talk?
- How do I want to organize my lesson plans this year..electronic or paper?
- How do I use my Twitter and blog resources to help me be the most effective teacher?

The list goes on. If you are a first year teacher, you probably don’t really know what you need to do since you don’t have curriculum or tried-true first week lessons. But don’t worry. There are many people who have done the first week of school routine so many times that they blog and tweet about it. To name a few.

My Week 1 Math Posts By Sara VanDerWerf (Check her blog for other bloggers to read.)

Which comes first in the fall? Norms or tasks? By Tracy Zager

#MTBoS (Math Teacher Blog-o-Sphere)

And like all first year teachers, I am starting in a new building this fall and teaching a new course – Pre-Algebra (I taught it one year, 4 years ago.). I don’t know the norms of the school or my team. I don’t know the teaching sequence of Pre-Algebra. So this is my second list of things I need to accomplish.

- Does the school provide me with basic supplies like scissors, markers, and tape?
- How do I get the school to provide me with supplies or do I need to supply what’s not already there?
- Who do I go to for behavior and academic support for my students?
- How do I work with an already established team?
- What can I change in the sequence of teaching without undoing what my team has already done?
- How do I navigate teaching in multiple classrooms?
- How do I teach 85 minute math classes?
- How does the school address student test scores?

There are so many things to think about and sort out as a first year teacher, and it can all be overwhelming. Seek support. Seek out your team if you have one. Seek out the Twitter math teacher world. Seek out your friends from your cohort. Seek out your advisors and mentor teachers. You are not alone, trust me. Just ask any second year teacher, and they will say that it’s something you can survive and be good at.

Here is to you and your first year! And of course, congratulations to second year, third year, and newly tenure teachers!

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Summer is such an important part of the year for teachers. It’s time for us to rejuvenate and take time to take care of ourselves. Non-teachers may give us a hard time for not “working” all summer, but we know that it’s not what it seems. We may not have to report to anyone or clock in anywhere (unless you teach summer school or a summer program), but we are still teachers. If you are anything like me, you have your summer professional development lined up between everything else that you are doing during the summer. Along with summer professional development, you and I are catching up on latest instructional strategies and best practices through books and conversation we have with our colleagues. Summer may be here, but we don’t stop thinking about our students, our colleagues, and our work.

If you are looking for ways to refresh your teaching and professional self, here are some things I’m looking forward to.

**In-Person Professional Development:**

Sara Vanderwerf – Minneapolis, MN June 20, 21, 27, 28 – She is offering 4, possibly more, math professional development sessions on her time for a small fee (giftcards, cash…). This is as good as it gets if you couldn’t make it to Duluth for the spring conference.

Teachers of Color Coalition – St. Paul, MN August 9-11, 2017 – The Coalition to Increase Teachers of Color and American Indian Teachers in Minnesota unites individuals, organizations and communities concerned about the lack of racial, cultural, and linguistic diversity in the teaching force.

**Books:**

This is Not a Test. – Jose Vilson

The Mathematical Mindset – Jo Boaler

The Problem With Math is English. – Concepcion Molina

Building Powerful Numeracy for Middle and High School Students – Pam Weber Harris

Matherpiece – Greg Tang

*Most of these authors also have professional development all over the country.*

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I wanted to echo what I read in Sara’s article in the MCTM Math Bits this month. She speaks to many of us who feel the day to day isolation of teaching. We are not like many of our peers who lunch with, meet with, collaborate with, and sit next to their colleagues. We shut our doors (many of us do it for the sake of keep noise out) and teach children. We are lucky to talk to an adult for a minute between classes or passing by, let alone be able to spend 10 minutes of our lunch time with our colleagues.

This isolation is a reason why I am so excited to meet and network with math teachers in any situation. The connection I feel with other math teachers drives me to continue teaching with enthusiasm and to power through tough days. They are the ones who understand why I no longer teach FOIL, even though it’s what many of my non-math teacher friends remember from their high school math. They are the ones who get excited with me about new activities on Desmos. They are the ones who try to dissect why we “keep, change, flip” when dividing fractions. They are the ones who support my endeavors into using algebra tiles all year.

Where do you find people who continue to help you keep the excitement in teaching?Where do you find people who are not your PLC and are the ears you need? Where do you find people who understand what you do on a day to day basis?

Stay connected with through these events:

CONNECT Night Duluth – April 27th 7pm-9pm RSVP

CONNECT Math Mixer – Sept 2017 Time and Place are TBD

There will be more to come in the near future.

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Stephen Chrisomalis’s study is about Math Corps, a math program in Detroit, that help low achieving math students. Math Corps had a specific way of talking about math and using “mathematician” vocabulary. His study did not show a significant cognitive growth, but just the idea of math as it’s own language is powerful. Chrisomalis has inspired me to finally write what I have been thinking about lately. We use much language in our classrooms, but do we even take notice of what math language we are passing along? Are we helping students grow in their mathematical language along with their skills? Are we pass along tricks, rhymes, and chants, that don’t actually help with conceptual skills?

“Keep, change, flip.” “Cross multiply.” “Rise over run.” “Line up the decimal.” “FOIL.” “Three point five.” Eleven over nine.” “Cancel.” “Add on both sides of the equal sign.”

These are some of the things I hear my middle school student say as we move through concepts. I have a very hard time getting them to unsay it nor can I can get them to explain what it means. Many of those use the sayings no matter what concept they are learning. I want to tackle a couple of these because they are ones that I have stopped using or just mention briefly so that they can align their learning with their future math teachers.

“Keep, change, flip.” This one took me the longest time to understand. I was an inexperienced 6th grade math teacher who didn’t understand the concept. I just knew that it was something we did when dividing fractions. I asked around and finally got the answer as to why “keep, change, flip”. Even though I have the answer, I don’t use the phrase in my class ever. We talk about multiplying by the reciprocal but only after looking at many problems and coming up with the pattern. I don’t show them the work, but at least I have an understanding and don’t use the phrase anymore.

“Cross multiply.” If your students are like mine, they do this every time there are two fractions even if there is an addition sign between the two fractions.

- When comparing fractions or ratios, there are two things that I talk about with my students: 1) create like denominators or 2) make/imagine the pieces that you are drawing. This creates conceptual understanding instead of students thinking that there is a trick to comparing fractions.
- When solving proportions, use inverse operations. Teach and use algebraic skills. Remember, the fraction bar is the division operation.

“Rise over run.” Or even the slope formula are two thins I no long address in my class. The idea of rise over run makes sense on a graph, and slope formula is great for two points. I just find that too many students lose the conceptual connection it has with rate of change. Keeping to the concept of change in your dependent variable (y-values) compared to the change in your independent variable (x-values), students keep the connection between rate of change and slope. What I have discovered since making the change to talking about change in y over change in x, students have better linear graphing skills and better skills at finding the equation of a line. Even when it comes down to graphing linear functions, we don’t talk about using the y-intercept or (x_1 , y_1) and slope until they can see it in the function. I force students to use the x and y intercepts to graph and change in y over change in x to find slope. There is always that one or two students who see the connection and we no longer have to calculate but just graph.

“Line up the decimal.” When should you and when shouldn’t you? We should really be instilling in students place values. By the time they are middle school most students are able to decipher the places values greater than the units. But going to the right of the decimal gets hazy. Knowing place values, students are better able to work with decimals and operations. Also as we know, lining up place values is only for addition and subtraction, teaching them place values will teach conceptual understanding of when we multiply and divide decimal numbers.

“Three point five.” Eleven over nine.” Teach them and enforce place values. This enforces the fluency between decimals, fractions, and percents. Too many students see numbers like 40%, 5/8 and 0.4 as different numbers. Fluency and ability to move between the forms come from knowing and understanding place values.

“FOIL.” When multiplying two binomials, this works great, but what are students to do when there is a polynomial as one of the factors? FOIL gets confusing with polynomials, and students miss terms. Using the area model concept, students separate out each polynomial into its terms and multiply. This brings back the elementary concept of using the area model for multiplying multi-digit numbers and allows students to see the connection between elementary and algebraic concepts.

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The “new” trend in math discussions and the power behind it

Many teachers, including you perhaps, have heard about math talks. You may have heard bits and pieces or even tried it once or twice yourself. But what is a math talk really? How long should it be? What resources do I need? What questions do I ask? As teachers these are common questions we always ask so I wrote this article to help teachers new to math talks start implementing it in their classrooms. Below I will attempt to answer these questions as well as provide links and resources for you to try.

So what is a math talk? To put it simply it is an open ended discussion about a math topic or even just about one math problem with the class. But hidden underneath are some things you should always do in your math talk. One of the most important parts is that the goal of a math talk is to be more student led and the teacher takes a more facilitating role. Of course you cannot do this the first few or even first 10 times you do a math talk but it’s important to know that end goal. Another goal of math talks is for students to share and see strategies for solving problems from other students. They may even challenge one another’s thinking and a math talk provides a safe environment to do so. A math talk is a forum for students to focus on strategies and thinking and not just the answer. Sometimes I don’t even provide the answer to a problem when I do a math talk. I instead focus on how to find the answer.

How long should a math talk be and how do I do it? You may be surprised that a math talk can be as short as 5 minutes or as long as 10. It really shouldn’t go any further because then it starts turning into a mini lesson. Remember a math talk usually starts with just one problem or one question and that can be your focus or learning target for the whole lesson. In an elementary setting we still use TPR or (total physical response) strategies for helping students learn. For example, my students if they have something to say don’t raise their hands, they simply put a thumbs up in front of their chest. That way again for those students who need more think time they don’t see 7 hands shoot up and then they just rely on their fellow students. A thumb to the side means I am still thinking or I am not sure. A thumbs down means I don’t agree with what was just said or I have another way. It does NOT mean I don’t know. Erin L. Wagganer wrote a great article about math talks as well as some friendly strategies in the link below.

What types of questions should I ask in my math talk? Truthfully there aren’t a set of math questions to ask, but remember you want to build your math talk around a math problem or math strategy. Try to not build it around the answer unless your focus is finding many ways to an answer. Some questions I give my 1^{st} graders are as simple as “What do you notice first? What part do you look at first and why? Is there another way to do this?” For you more active energy teachers you can even say things like, “Help! I need to find a way to do this!” I love a good video example and I love this example below.

https://www.youtube.com/watch?v=62epCIFdRa0

The most important part though of a math talk is that you just keep practicing it. Seek out your instructional coach or principal for an outside pair of eyes for help but like any skill you need practice, confidence and patience. Any teacher can do a math talk but great teachers have practiced over and over and turned math talk into a razor sharp tool for successful math learning. Good luck out there.

My name is Bryan Bjorlin and I am a primary grade teacher. I currently teach 1st grade in Robbinsdale Public Schools but in the past I have taught kindergarten and preschool. I love to teach young students because I enjoy the challenge of building a strong academic, social and behavior foundation for life long learning.

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I’m not trying to put a negative light on those programs, websites or Apps or my district, but I have had a hard time with trying to incorporate them in a genuine way that promotes student learning. Then a few pre-serivce teachers told me about a new website called **goformative.com**. I was skeptical because it sounded like all the other websites and Apps I had used before, but I was so happy it proved me wrong. The website did much of what I had always hoped for.

Pros:

- free for anyone to use
- teachers need to create an account, but students don’t have to (Federal Laws prevent students 12 and under from creating any sort of log-in, email required account without parent permission.)
- all students need is the quickcode from the assignment you created to access it
- types of questions you can create – multiple choice, show your work (where students can write with their finger/stylus on the screen), short answer, true/false
- add content like image, text block, YouTube videos, Word documents
- see all student work at once and see live results as they work
- easy to use on an iPad

Cons:

- students can’t save and come back to their work unless they sign in
- using the student canvas, it’s not intuitive on how to erase work
- doesn’t have latex or equation editor
- can’t print the assignment for students if they don’t have a device

The list of cons have not deterred me from using the website over and over again. Students seem to like it, too. Using the website is like being able to work with all my students at once and addressing the students with most need because I see their mistake soon after they make it. The immediate and direct feedback has been very powerful and the most powerful aspect of this website.

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Relationship building is probably the number one thing that any veteran teacher would tell you when it comes to teaching. No matter the age or subject, the kind of relationship you have with students make a difference in their learning. This really is the best piece of advice and lesson I have learned. I love teaching math and talking about math, but it takes especial people like you and me to love math. Students, at any age, also need to “love” you before they can “love” math. They need you before they need the subject. I know that I am guilty of putting the subject before the students at times due to pressure from state test scores, my love of math, or even keeping pace with the other teachers. Just like you when you decided you wanted to be a math teacher, you didn’t do it for the love of the subject, but some teacher in your past inspired your love of math and your love to teach it.

Building a strong relationship with students is not easy and may not come naturally, but it’s such an essential part of being a teacher. But how do you do it and be genuine about it?

Weekly Reflections: This is my favorite way to get to know students. In one of my courses, I teach some of the lowest and behaviorally challenging 8th graders in my school. They are assigned homework every day even on test days, but every Friday, their assignment is to complete 3-5 questions about the week’s learning, the class, or themselves. They know that completion is all I ask for and that their responses will not affect their grades. With that stipulation, they are very honest when given the chance to reflect. When they write, I actually read it, which surprises students, because they think they are only doing it fulfill an assignment point. Through these weekly reflections, I learn more about their learning needs and wishes. I learn more about how they feel about themselves, their classmates, and me. I learn how to be a teacher that can and will meet their needs because they voice it. Some examples of more personal reflections I ask are:

- Why do you do homework?/Why do you NOT do homework?
- What do you think of Cornell Notes? (We always do notes in Cornell style.)
- What was the best part of your week?/What was the worst part of your week?
- Rate yourself from 0-4, how well did you understand this week’s lessons? Explain.
- What kind of teacher should Ms. Vang be so that you are successful this year?
- What kind of classroom should we have so that you are successful this year?
- What is one math goal you have this year?
- Describe how you feel about math.
- What are you looking forward to this weekend?
- What can Ms. Vang or the class improve on to help you learn better? If nothing, what is something you like about our class?
- What grade are you getting in this class? Do you think Ms. Vang is fair in her grading?
- What do you need to do in order to get better in this class? If you are doing well, what is something you want to keep doing so that your grade doesn’t drop?

Because of these questions, I feel that I building a strong trust and bond between my students and I. When they realize that I read them and use them to better our class, they feel that they are being heard and cared for. They acknowledge that I am trying my best to be the best teacher I can be for them. It’s my way to give voice to my students, and through it, I know that I’m being the teacher they need for success. I do have rules for when answering the question. I don’t accept “nothing” and “I don’t know” as answers. I know that students can answer the questions even if it’s artificial, but even those artificial answers become more real as the year goes by because they know I read it. I do have students who choose not to do the weekly reflections or forget to do them, but I don’t worry about it. I just continue to encourage everyone to complete them because it is homework and that I am doing it to help our class and especially me be better.

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As a secondary math teacher, I’m notorious for having blank walls. I have never really bought or made posters because I figured my students would make them as the year goes by. I didn’t even put up my classroom expectations/rules. I always assumed that since I verbalized what I expected, it was enough. But being a middle school teacher has changed that in me. Middle schoolers have such a hard time recalling or following instructions even when written. Now, I have a posters that I put up. They are colorful and have great messages. I even laminated them, making them a more permanent part of my teaching resources. My classroom looks great and not so empty. Then I made the assumption that my students would read them while they were in my room. But I was so wrong. My students don’t notice them or care about them. In the past whenever I pointed out my poster, my students would be shocked that I had a poster that showed them what I meant.

Last year, my coworker and I made a commitment to actually use them and point them out. She was the one who told me about an article (sorry I don’t know the reference) she read about the importance of actually talking about the poster. Why put up a poster and not talk about it? I didn’t realize that by not talking about them, I wasn’t telling my students why those ideas and messages were important to me and to being a mathematician.

As part of my commitment, I introduced the GROUPS poster after doing the 100 Numbers activity that @saravanderf used in her classroom (https://saravanderwerf.com/2015/12/07/100-numbers-to-get-students-talking/). Through the activity, I was able to show students how the acronym came into play. They understood it better and saw what GROUP looked like. I had taken pictures of their group work, and they didn’t even notice because they were so engrossed in the activity. Even that along helped illustrate group work for students.

With different activities that I do with my students will come the introduction of each poster. I do a lot of Math Talk (http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol22/Issue4/Creating-Math-Talk-Communities/) and inquiry activities/discourse, which lend themselves well to the Math Talk and STRONG Mathematicians posters. My students take Cornell Notes, which in itself needs some explanations because it’s such a specific way to take notes. Then I always like to give my students the chance to say “I don’t know” without saying “I don’t know”.

Next time you walk into a classroom, whether it be yours or not, ask yourself about the purpose of what you see hanging on the walls or from the ceilings. Everything in our classrooms have a purpose whether you talk about them or not.

Much of my poster inspirations have come from Pinterest.

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In my third year as a middle school teacher, I have days that beg me to question why I ever chose to become a middle school teacher. Grades in middle school do not matter, so grades are not any sort of incentive to do well. Middle school student brains are in a major developing phase, so they are constantly unable to control their voices or actions. They are more reactive than reflective. They still need me to be “mom” at times, which is a role I do not play well. They are still learning major school-life lessons like remembering to put their names on homework, learning how to work a locker lock, and listening, writing, and thinking at the same time.

I have a lot of nostalgic feelings about teaching high school students because of middle school students. I miss the conversations I had with high school students. I miss Algebra 2 and Geometry. I miss the 2pm end time. I miss being the teacher they turn to for a life talk. I miss watching students grow up from being young naive teenagers to young adults with whole futures ahead of them. All that nostalgia does go away though because like every memory, we always remember the good of the past and compare it to the negative of the present.

During the dark cold days of winter, I needed to remind myself of why I stuck around with being a middle school teacher. Being a high school teacher laid the grounds for me, but being a middle school teacher has changed me for the better.

Before, I never understood why middle school math was so difficult to learn or teach. After my first year as a middle school teacher, I took back every negative thought I had about middle school math. Teaching algebra came naturally, but teaching pre-algebra and math 6 have never felt so foreign. I frequently felt like an inadequate teacher. Trying to explain the logic behind dividing fractions or why the denominator changes with ratio addition but not with fraction addition still do not come as naturally as teaching how to factor a polynomial. To make up for my inexperience and natural inability for teaching middle school concepts, I read about math and teaching math. I surrounded myself with people and books, which supported my growth as a teacher. I could not be more appreciative of middle school math teachers. I feel like a better math teacher because of this middle school experience.

With the end of school year in sight, I have learned a few more things. The students themselves have really inspired me. Weeks ago, one of the most behaviorally difficult students came up to me and held me by the shoulders, telling me how much he actually joins math now. Another student, who was so scared to meet me during open house because I was her math teacher, told me that she loves math and couldn’t believe how much she didn’t enjoy it before. And of course, I got that letter that every teacher dreams of getting. The letter that tells you how much you have touched their lives and that they wouldn’t be where they are without you. These students remind me that I have a huge impact on them even if they are not quite ready to harness the impact teachers have on them. Lastly, I get to be the teacher who preps them for the “scary” world of high school.

Even though I never thought I would be middle school math teacher, I would not trade these last three years for three years as a high school teacher. The experiences and knowledge I have gained has made me the teacher I have always wanted to be. I may never feel confident teaching middle school concepts, but I know I will get better every year that I teach. Students may overwhelm me with their lack of control, but I know I am reaching them. I know they appreciate me and want to be their best when given the opportunity.

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March, 2014

Happy March! Although it is traditionally Minnesota’s snowiest month, I’m buoyed because I know that April is coming. Besides spring, I always look forward to April because it is Mathematics Awareness Month (MAM). Each April the Joint Policy Board for Mathematics (JPBM) sponsors MAM. The JPBM is a collaborative effort of the American Mathematical Society, the American Statistical Association, the Mathematics Association of American and the Society for Industrial and Applied Mathematics. They started MAM to increase the public’s understanding and appreciation for math. It actually started as Mathematics Awareness Week in 1986.

Every year the JPBM picks a theme, designs a cool poster, offers suggestions on activities, and has a list of resources. This year’s theme is Mathematics, Magic and Mystery. The theme comes from the title of a 1956 book by Martin Gardner. Each day during the month an activity will be made available that matches one of the images on the poster. Since the activities, videos, etc. aren’t available until April, I don’t know what they will be. Based on activities that have been featured in the past, they will probably be suitable for high school and college students and excellent interesting ones.

That certainly doesn’t mean that our K – 8 students shouldn’t participate. You can easily have a set of puzzles, poems, interesting problems, games, etc. that you give to your students, one each day during April. You can award the Math Awareness Crown to the students who solve the most correctly, with small prizes for those who get each day’s answer correct.

Enjoy MAM and use it to have fun with your students while they and their parents become more aware of and appreciative of math.

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