# Blog

WOW! Is there anything more rewarding than teaching first grade?!? To top it off—Singapore Math in first grade…priceless! It is mind-blowing to witness the level of mastery and critical thinking skills a six-year-old obtains through the curriculum!

A crucial component in teaching Singapore Math is the “math discussion.” Whether you are using Singapore Math or not, it would benefit your students a great deal to incorporate “math discussion” in your daily lessons. A large responsibility of a first-grade teacher is to guide the students to THINK and express their thought process. As we know by explaining their thought process, students learn how to evaluate their problem solving skills and identify errors in their work. Also, the students learn from listening to their peers answer thought provoking questions “in their language.”

In theory, it sounds great but having the students express their thinking orally was one of the biggest changes in my math lessons. When planning a lesson, a teacher should prepare questions ahead of time. Research shows that when instructors formulate questions “as they go,” the questions are not as thought-provoking as when teachers plan questions ahead of time. We all have our go to’s likely to include:

• How do you know that?

• Why do you think that answer is correct?

• What strategy did you use to get your answer?

• Did anyone solve this problem differently? How?

• Would this (name a different strategy) strategy work to solve this problem? Why/Why not?

• What similar problem did you solve before, and how can what you did then help with solving this problem?

• What would happen if we change this part of the problem to …?

• Can you draw a picture to show how you solved this problem?

Also, occasionally give a wrong answer and ask students why that answer is incorrect.

But we need to give time and thought about those questions that apply to an individual lesson.

At the beginning of first grade, when asking students how they knew an answer to a question, they would usually state, “I don’t know” or “I got that from my head.” It was like pulling teeth to get them to explain their thought process. I found that modeling the thought process worked best by using Think Alouds, especially when introducing a new concept. I recommend using a trigger word such as JUSTIFY that when a student hears, they automatically go in their reasoning. Eventually, the students catch on, so much so, that they want to explain every time they give an answer. They also carry into other subject areas, explaining how they knew the answers to questions. Once you begin implementing “math discussion” in your math instruction, you will be amazed at the reasoning that your students will demonstrate.

There is no arguing against the fact that men outnumber women in math related fields. Do you know how your girls think about gender and math? How they see their identity as a girl and/or as a mathematician. To gain some more insight I decided to ask a number of my female sixth grade students how they see gender play out at our school. These were their answers…

“It doesn’t matter if you’re a boy or a girl. Anyone can be good at math.”

“I think girls are better at math because they try harder and concentrate more on their future.”

“Well usually boys like math and girls like reading because girls are better at reading.”

“Girls are better at everything!”

“Girls are better…yeah, I think girls are better students in sixth grade”

“I don’t know. I don’t think there’s a difference.”

“Well the smartest kid at math at our school is a girl, so I think girls are better.”

I was happily surprised that only one of the girls I interviewed said that they thought boys were better at math. Maybe this has to do with eleven and twelve year old being rather self-absorbed and always thinking they’re in the right, therefore their gender being the best. Maybe it’s because in elementary schools girls tend to be seen as the better-behaved or more studious gender. I’d like to think that it’s because they have has strong female teachers . But either way it brings up a new question for me – at what point does the shift happen where we find more men in high education mathematics class and in the math related job force? While we continue to build up intelligent problem solving young ladies, I hope that you are encouraged by some of the statements my students made. I love seeing them be confident and proud of being a girl, and being someone who loves math!

From high achieving students to the kids who really struggle in our math classroom, they are all focused on one thing – the answer! Think about it, student who get good grades are continually reinforced to keep working hard when they see that they are getting the correct answers. While students keep getting that wrong answer (usually without understanding at all why it’s wrong) continue to get more and more frustrated and often lead to just giving up. And can we blame them for putting so much of a focus on the answers? Yes we ask them to show work on homework and tests, we praise effort and hard work in the classroom, but how are they graded? How have they been graded for the past six years? What do their parents really care about? In fact, what do entrance exams for honors classes or colleges look for?

At times it seems absolutely impossible to fight the beast of grades. I see the efforts of many schools trying to open up their view of grades and recording progress, but as a society we still put a lot of value on getting the correct answers – no matter how you get them.

To try and open up the minds of my students I have been including some classwork where students work backwards. I present them with a problem and then give them the answer outright. It was hilarious to see how my kiddos responded the first time I tried it. It was as if they thought I was helping them cheat! The great thing about giving students the answer is that I think it helps turn the problem into a puzzle. They know the problem (a box of mixed-up jigsaw pieces) and they know the answer they need to arrive at (the beautiful picture on the front of the puzzle box), so now the fun is in figuring out how to put the pieces together just right. I hope I didn’t lose you with that analogy! My point is that when students don’t have to worry about what the answer is they are freed up to experiment with the process. That experimentation is what leads to a deeper understanding of the problem.

This is just one example of a way to prioritize teaching problem solving skills. To take the focus off of being right or wrong, and put it on the beauty that is found when students persists, learning from their mistakes, and work out a viable solution to a problem.

How many of you 6^{th} grade math teachers have already fought the good fight with ratios and rates? Ha! We are halfway through our ratio unit and I’m happy to say that the headaches are on the decline (for both the students and myself)! This year I had a new idea to integrate art into my ratio unit with a color-mixing lesson.

I used this lesson to introduce the concept of equivalent ratios. My students already knew how to find equivalent fractions, but I felt like the deeper understanding just wasn’t quite there. Before we even began using the ratio vocabulary I told my students that we were going to paint color wheels (a quick internet search will lead you to many examples of a color wheel). We discussed primary and secondary colors and then practiced mixing paints. Here I set out a challenged for students in one group to make the same shade of light yellow, we called it sun yellow. We talked about how adding too much white would make it too light, and not enough would make it too dark. The trick was that they were all making different amounts.

Before I even said the word ratio or equivalent students were able to explain those concepts in their own words. I heard things like “I need more white for all this yellow!” They were connecting the dots and understanding that a ratio is a comparison of two things (in this case yellow and white paint) and that you can make the same shade of yellow in bigger or smaller quantities you just have to account for the change. It was an overall success of a lesson. Of course my students weren’t as excited to exit this activity and move over to “mathy” equivalent ratio word problems, but this remained a great experience for us to spring back on as a class if anyone got confused about equivalent ratios.

It seems that report cards and parent conferences bring out the stress in everyone. This year I’ve noticed that I have a lot of students who are really worrying about their first trimester report card. Couple that stress of a looming grade with all the assessments we’ve had to complete and there is a definite need for some anxiety reducing activities in the classroom.

This year I have had the pleasure of coaching a girls running program for our 4^{th} – 6^{th} graders. One of the practices focused on meditation and teaching girls how to relax and why it’s important to de-stress and live a balanced life. I thought this lesson was very powerful for our running team and I think it would be an awesome addition to any math classroom. Who wouldn’t benefit from learning some relaxation techniques and then getting space to practice!

Here are a couple of quick things you can do to help teach age appropriate meditation and relaxation.

- Breathing – have students close their eyes and practice focusing on their breathing, counting how long then inhale and exhale.
- Visualization – have students close their eyes and them visual their stressors as papers. Have them visualize balling up each stress and throwing it in an imaginary trashcan.
- Body Awareness – lead students through thinking about different parts of their body. Start with their toes and end at the fingertips, guiding them through a process of focusing on each body part and how it feels.

I’d love to hear what other mediation and relaxation techniques you might know of that would work with students. I can’t wait to start using these on a regular basis with my kiddos. I am planning to start it this next week and I’m really interested in seeing if there is a shift in my classroom climate. To see how spending a little time helping my kids relax might change their attitude towards math, and hopefully even help their test scores. I saw it make a huge shift in my running team and I’m willing to bet it will be similar in class.

This year I have some highly excitable and energetic young learners. It feels like we spent a great deal of time at the beginning just learning how to sit and stay in our seats and not run from one place to another—even inside the classroom! It felt like there was a lot of “no” and “don’t” coming from me and to be honest; that can be incredibly exhausting. Instead of trying to beat them-I joined them. We get really silly during math in my classroom. We play games. We move around. We explore. We talk to each other. My kiddos need to move. Instead of spending a great deal of time working through our workbooks we act out what we are learning about.

Manipulatives are a great way to exercise those fine motor skills we are helping to develop in kindergarten, but let’s not forget the importance of gross motor skills and physical activity! It has been proven time and time again that we all learn best when we are actively engaged. Physical Education is one of the easiest and best ways I integrate math content. Even if it is just simple exercises we count *everything*! We might do a set of five arm curls and then I’ll say “Ok class, what is *one more* than 5?” They will yell out “6!” and then we will do six arms curls. Sometimes I’ll just write a number on a small white board and they have to do that many jumping jacks, lunges, etc. As the year progresses we might have a conversation that goes like this, “If we did three squats and then we did three big arm circles, how many exercises did we do *all together*?” Another fun thing we like to do is make a human ten frame! Our meeting area rug has a grid of thirty squares so it lends itself quite easily to this task. I will write a number on the board and then the kids will have to show me that number on the carpet “ten frame” using their bodies. It’s great because they get to move around, they need to talk with one another and negotiate and navigate their physical space all while being actively engaged in the math content. Acting out math problems is another favorite especially when the kids get to be silly and perform for their classmates. We know that kids learn best when they are doing and the little ones learn especially well when they are moving, so why not combine the two and see the benefits?

#### There has been a lot of talk recently on fixed and growth mindset and how they relate to young learners in particular. Mindset and it’s importance is not something new or revolutionary but rather the in depth examination of its power has caused educators and parents to pause and really be cognizant of not only their own mindset but the young and burgeoning mindsets of their students and children, whom they influence daily. While recently reading an article by Stanford Professor of Mathematics Education, Jo Boaler I was struck by how important it is to send positive messages to your students in order to foster a growth mindset. In Kindergarten I hear “I can’t” a lot. It makes me sad because I think about how young they are and how they might already have these beliefs that they cannot do something. In our classroom we talk about how the only way you “can’t” do something is if you do not try. If you make a mistake it’s proof that you are learning. Mistakes are important. Mistakes need to happen. If everything were easy all the time it would be boring! This strikes close to home because I grew up thinking I was bad at math. No one ever told me I was, it just seemed so easy for others and I was struggling all the time. I just got it in my brain that I was “not good” at math and that I would never be good at it. Full disclosure, I still struggle with this but teaching math to young children has helped me move closer to a growth mindset on my math capabilities. Educators must celebrate even seemingly small achievements with their students. This can make such a difference. These are small things we probably already do throughout are day but just making a point to do this can bolster a child’s confidence to keep trying, not give up and be proud of themselves. Reminding children of how smart they are and how much they have already learning and accomplished is crucial to their growth mindset. If a child tells me they “can’t do math” I remind them that use to not be able to talk, feed themselves and walk, but they can do all that now because they tried and they practiced. I know that sounds silly but it really works. They have clear examples from their lives of things they couldn’t do before and now they can. We hold a powerful position in the lives and minds of our students. We are their cheerleaders and their advocates- the messages we send must be positive and genuine in order for real learning to take place.

One of my biggest pieces of advice is something we all know but maybe aren’t doing as well as we could. Keep parents in the loop! I have written about this before but I cannot express it enough how much better the school year will be if you have established and healthy lines of communication with the parents of your students. I need to let you in on a not-so-secret-secret: LOTS OF PEOPLE ARE SCARED OF MATH! You may even be one of them. As teachers we all know that we are required to “wear many hats” as the expression goes. It is one thing to help with the anxiety of a child learning something new, but we also can’t forget about the parents. Common core is like a swear word in some parental circles and I have discovered that this is largely due to the fact that there is a lot of misinformation out there. As a teacher you can help rectify this. You can be the source of correct information! One thing I am planning on doing this year is holding a parent workshop with my grade level to specifically go over math standards with the parents and give them real strategies they can do at home to help improve their child’s math skills. The beauty of common core is that it’s so mindful of making sure kids know why they are learning something and how they can and will use it in real life. Busy parents can incorporate math in many ways at home they just sometimes need to be showed how. Simple things like setting the table (counting how many plates there are, etc.) or going on “Number Hunts” are quick, fun ways to work on math that go beyond traditional homework. Knowledge is power and by working hard to inform the parents of your students you empower them and reduce anxiety they might harbor around math and in turn they become better teachers to their children. It’s a win-win-win!

As I write this we are about to start our fourth week of the new school year. It’s always an exciting (and hectic) time for any grade but in kindergarten it can be downright crazy! A thing I did over the summer and something that I blogged about that really has proven successful was getting all my math manipulative organized and stored in way that is accessible to the kids. These first few weeks are all about getting our routines down, lots and lots and lots of behavior management and just overall getting used to being in school. The kids in the beginning undoubtedly see all the math manipulatives as toys. Instead of immediately pushing against this idea by explaining what we can and will use them for, I let them approach them as such. During the first few days of school when we practiced our centers I would have manipulatives at each center. As the kids got used to rotating and the attention signal and all that other stuff they had time to freely explore the manipulatives without direction or explicit instructions from me. For the record, the manipulatives they were exploring were: counting links, unifix cubes, dominoes, counting bears, pattern blocks and number magnets. This gave each child time to use and handle all these new “toys” and allowed me to make observation about this new group of little people I will be spending the majority of my day with. Naturally the children counted, sorted, made up stories and built with them. All the things we will eventually do with them in a more formal and purposeful way. All the things we want them to do as it relates to the common core as well. By allowing them to approach the manipulatives each within their chosen way, while also being able to see how their peers chose to use them we are simply capitalizing on what young children do innately without the need for explicit direction from the teacher. Obviously the direct teaching will follow but in these early days of our new kindergarten classroom it is so important to allow for exploration and discovery. Lastly, something else I discovered by allowing the students this time with the manipulatives was that it removed their stigma in a way. What I mean by that is in past years they were taken out during math and put away when we were done and not readily accessible to the children and therefore the kids didn’t really have ownership of them. Having this early exposure in the beginning will also save time when it gets down to lessons where the children need to be using them and not “playing” with them. It really is a great investment of your time as a teacher and for your students to allow them the exploration they so readily need and desire in their new classroom!

As math instructors aren’t we always just walking that fine line between fluency and conceptual understanding? We know that the answer lies in both. Our students need to have fact fluency, but that fluency is only meaningful if they can problem solve. We know this, we teach this, we preach this – but you won’t believe how I saw this play out with a new student in my class.

During the first couple weeks of school I like to work problems out with each of my students during independent work time. I like to talk to them and watch them work so I can hopefully get a better understanding of how they process math. And I have to say that I saw something this year that I have never seen before from a sixth grade student. We are studying decimal operations right now and the problem I’m about to show you was a decimal division problem.

Here’s the problem. (See Step 1)

So he realized that the first step was the move the decimal in the divisor and then dividend. Then he knew to see how many times 4 goes into 11. Here is where it gets so interesting! He applied a division strategy of drawing a picture and representing the division with circles. He drew 11 circles and then grouped them into groups of 4. He realized that he could only make 2 complete groups of 4 in 11, so he put a 2 above the 11. Here’s a picture of his work. (See Step 2)

Next he knew that he needed to multiply 4 times 2. Let’s stop for a quick second, this should be a fluent memorized fact, right? Not here! Instead the student drew 2 sets of 4 tallies and counted that there were 8 tallies together. Here’s another picture of this step. (See Step 3)

By this point I was completely mesmerized. He has a great conceptual knowledge of the meaning of multiplication and division, but this process is so slow! He continued working the problem this way and got the right answer, but I swear it took close to twenty minutes! This was such an eye opening experience and further cemented the fact that we have to prioritize our students building fluency for their own efficiency. Have you ever seen anything like this? I was amazed, impressed, and absolutely shocked – and I sent him home with some flashcards.