The benefits of patience…and dragons

I keep telling this story to colleagues and several times it’s been suggested that I write it up, so here it goes…

Over the past few weeks I’ve been in several classrooms across my campus doing Number Talks in grades K-3. I can safely say that I have learned way more about number talks in the past 2 weeks than I did in all of my reading/researching for the past 6 months, and have seen the benefits of patience in many ways. My takeaways have included:

  1. Never wear sparkly sandals in a Kinder classroom, unless your goal is distraction.
  2. Always be prepared for students to come up with ways of solving that you have not come up with yourself, and realize that’s a good thing!
  3. Patience will be rewarded, even though it’s painful to sit and wait…there are major payoffs.
  4. Consistency across grade levels is not only helpful, it’s classroom changing, and I’m predicting, school changing, in regards to how our students perceive and learn mathematics.

The third take away was evident in almost every number talk I gave from Kinder up to 3rd grade. In several classrooms, I was introducing number talks for the first time, so students were somewhat apprehensive, therefore, the wait time was crucial. I had to give time for them to see I really did want to hear from them, and I was not going to give any answers or even “hints” to what the correct answer or strategy was. As soon as a few brave souls shared their strategies and the class saw that this really was a low stress, fun way to share their thinking, there was no problem getting volunteers for subsequent problems.

The fourth takeaway about consistency across grade levels stems from an experience in one of our 5th grade classrooms. I can’t take credit for doing the number talk because the teacher was already comfortable conducting them, so she started week 1 of this school year! And according to her, “It was obvious which students had experienced number talks last year and which students were new to our school.” The students who participated in number talks at the end of the previous school year were able to begin

5thnumbertalk
Forgive me, this is a terrible photo, and didn’t even capture the final work, I’ll do better next time.

this year seamlessly. She mentioned that students were already identifying strategies and were able to solve and justify their answers in a variety of ways. So, how does this effect the students were have never participated in a number talk? Apparently, they were able to jump right in after seeing and hearing their classmates model the processes, and the entire class was able to tackle some decent sized multiplication problems the first week of school!

 

So, to round things out, let’s look back at takeaway #1, it’s about sparkly shoes and kindergarten. ūüôā I now know that my sparkly sandals, while being super cute and fashionable, are way too good at their job which is to get noticed and adored, while I’m trying to teach/model a lesson in Kinder! (there really was a kid, or two, face down, belly on the floor inspecting my sparkle while I’m
trying to conduct my number talk) So, while I’m conducting the number talk, I used all the tools I could muster from my “teacher bag” to redirect and get these students focused on the task at hand. After promising to let one of the distracted students share if he would just pry his eyes from my sandals and look at my dot cards it came time to follow through on my promise, so I called him up and I asked, “Henry, how many dots did you see?” to which his response

kinder-dragon-number-talk

Do you see the dragon?
 

was…”I saw a DRAGON, and it was huge, and it was coming at me, and it opened it’s huge mouth, and it grabbed me, and I was in his mouth,” (pause, so around this point I was starting to get a little worried and was not so sure this patience thing was going to pay off, un-pause) “and I looked up in his mouth and I saw…1, 2, 3, 4 TEETH! That’s how I saw 4!” The End

 

 

“Curiouser and curiouser!”

Alice’s words from Lewis Carroll’s Alice’s Adventures in Wonderland¬†were definitely running through my head as I was presenting a Number Talk in Mrs. Bammel’s Kindergarten classroom this week! When I chose the word “curiosity” from Tracy Seger’s call to action¬†#ShadowCon15, I chose it because the word curious makes me think about fun, learning something new, or the beginning of a new adventure, and who doesn’t want all that when they’re working with math? Of course, there is a flip side to the idea of curiosity, the side of anxiety about what we might find when we are curious or the fear of the unknown that may be exposed. So, I admit I did feel a mixture of all of these emotions as I began my talk.

We started with simple arrangements of two dots as I was also introducing the idea and structure of a number talk for the first time. Once students caught on to the idea that I was going to ask them to explain their reasoning and might even ask them to come up and show their reasoning, or even touch the card to explain, I had no lack of participants!

However, in order to spur their curiosity on, I finally had to move to more interesting dot images of three dots. I admit I was thrown off when a kid stated, “It’s just going to be two every time!”, but I had to remind myself that it was a good thing that they wanted more challenge and variety. They were curious about where we were going with this.

As we moved into more interesting dot images, students were beginning to make some connections, I actually had a student say, “I saw these 2 and 1 more”, which made me do a happy dance in my head! And as we continued, I tried to highlight those moments without discouraging the array of curious answers students were presenting. In the end, I was left excited and looking forward to seeing where this group of Kindergartners will get in number talks by the end of this year. I was also left with a few takeaways for myself in the roll of facilitator of number talks.

  • Takeaway 1: Begin number talks with a curious stance about how students will see and connect to the images/numbers.
  • Takeaway 2: Be prepared for the unknown and sometimes a little off the wall responses that students may bring to the discussion, like, “I see 3 trillion!!”. Still not quite sure how to facilitate that one…
  • Takeaway 3: Work on balance between allowing enough students to share that we see a variety of thinking, but not so many that we lose focus on what we are doing.

For Alice, her curiouser and curiouser moment was a result of so much surprise she couldn’t even speak good English and there were definitely some surprises in my Kinder Number Talk, but as I looked at those surprises through the lens of curiosity I was actually pleasantly surprised rather than dumbfounded. I realized the students and I were learning in a fun and engaging way with numbers and to me, that’s a good day!

My Take on 3rd Grade, Unit 1

Unit 1 for our Round Rock 3rd graders is titled, “Summarizing and Analyzing Data Using a Variety of Old and New Data Displays” which is very much reflective of the Focus TEKS for this unit.

Collect and Display Data:
3.8A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals; and – R RC4

Solve Problems Using Data:
3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 [with 1- and 2-digit numbers only in this unit] using strategies based on place value, properties of operations, and the relationship between addition and subtraction; – R RC2
3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 [with 1- and 2-digit numbers only in this unit] using pictorial models, number lines, and equations; – R RC2
3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals. – S RC4

On a personal note, I love that this unit has been moved to the beginning of the year! Students always enjoy collecting data about themselves, their families, and their friends, and this unit should lend itself to some great conversations that will allow students and teachers to begin making those valuable connections between their lives. Of course, it’s also awesome that teachers will be able to pull these skills in repeatedly during science throughout the year. Great suggestion, teachers!!

The most important ideas I would want my students to get out of this unit are

  • Data can be collected and analyzed many different ways
  • There are different types of data that require different types of graphs
  • Collecting and organizing data into graphic representations can help us efficiently solve problems.

I would start the unit by previewing graphs students have previously seen and used in 1st and 2nd grade, then allow a few days for students to collect some different types of data and create graphs using that data, utilizing frequency tables as a collection tool each time. Then I would have students use the data they already collected and turn it into a dot plot, after modeling what this is and how I could use it for my own data. I would hope that some of the students’ data would lend itself to using dot plots while others may not. This situation could give us a great platform for discourse and a discussion about how we decide which graph to use for a particular set of data.

Along the way and throughout the data collection and analyzing using graphs, I would ask students to think about what they wonder when they look at other students’ graphs and slip in some computation problems about some of our class graphs each day. I’m thinking I would create a bank of questions to pull from including both one- and two-step addition and subtraction problems and some open-ended thought provoking problems such as

  • Which graph will best represent the data I collected? Why?
  • Is my data easier to read in a pictograph or a dot plot? Why?
  • How could I justify why I chose a bar graph to represent my data?

Hopefully, by beginning to ask some of these questions early in the unit, as we move through the unit, students will begin to use the same questions and really start to see why we summarize data using multiple categories, and also have a lot of fun along the way!!

 

About to burst!!

Ok, so this is not a required blog post for my Math Rocks cohort, but I am so excited about something I just created that I’m going to burst if I don’t share it!

I just made my very first screencast-o-matic video!!!

This may not be a big deal to a lot of people, but for me it is huge. I learned about this resource at a tech training given by our district ITS’s (Instructional Technology Specialists) last semester but hadn’t seen a need for it yet. Well, given the right opportunity, just look what can be created!

My need came from a problem. My campus principal wanted me to present a Math Unit Planning Kick Off for our campus, but the Monday she wanted this to happen was the same day I had a required training. Uh oh… After we talked through it and foudn that there was no flexibility with when this information should be presented, we decided she would just present it for me and I gave her some main points to cover. Well, that just wasn’t good enough for me. I knew there had to be a better way for me to give information to my campus without actually being present and making sure everything I would want to cover would get covered, that’s where screencast-0-matic comes in!!

At first I was going to just record myself talking on the webcam but I really needed to show teachers what I was talking about on a computer screen. Luckily, I can do both with this program. I used a scripted recording and was able to fairly easily create the video in about 2 hours, granted it was my first time, I’m pretty sure it will go faster next time I make a video.

So, I guess the proof is in the pudding, so here’s my video. Feel free to leave constructive feedback on how I could improve my process in the future and let my new learning encourage you to try something new instead of giving up the next time you encounter a problem or obstacle.

Click here to see my video.

Strategies, Algorithms, and Multiplication, oh my!

After watching Graham Fletcher’s ShadowCon 2016 video about telling a math story and getting back to the standards as our basis for what math to teach in the first place, I was drawn to some of what we may see as the most basic skills to be taught in elementary. Multiplication, its just multiplication, right? You just memorize your facts and use them over and over, right? Nope and nope, actually there’s an amazing depth to learning multiplication. I found that students are starting to represent multiplication situations in 2nd grade, then they take those experiences into 3rd grade where it becomes an exploratory wonderland of arrays, skip counting, hopping on number lines, mental math, mathematical properties, and so many more as shown in TEKS 3(4)(E)! The standards then begin to include multiplying ¬†two-digit by one-digit numbers using these strategies and/or algorithms they have made sense of while playing with multiplication as seen below.

3(4)(G) Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy.

The student is expected to use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.

When we start teaching kids about multiplication in this wonderland, they will be able to discover what strategies, or even algorithms when appropriate, ¬†make sense to them and help them multiply¬†“flexibly, accurately, and efficiently‚ÄĚ (National Research Council, 2001, p. 121) which is an essential piece of¬†procedural fluency. And these students can then take those strategies and algorithms with them into 4th, 5th, and middle grades where they will be able to make sense of math operations even when they include fractions and decimals. No matter what the math is, we must remember that the strategies and algorithms are not what we are teaching, they are what our students are discovering for themselves!

Here we boldly go…

I have been given the privilege of joining a group of learners in my district that is exploring math in elementary called “Math Rocks”! This is my first post on my first blog which is why I chose my favorite quote for my tagline:

“Without change there would be no butterflies.” -Unknown

I realize this journey will be challenging and exciting, may involve changing some thinking on my part, and I can’t wait to grow alongside my peers! I have to confess, I’m also super excited that we are going to be exploring MATH! I have always enjoyed math, mostly because I’m a rule follower and as a kid I was taught to follow certain rules and I would get the right answers. I love getting the right answer!! Luckily, I’ve been involved in some amazing professional development both inside and outside of my school district which has taught me that there is actually more to math than just following rules, and working with students for 14 years has shown me there is definitely more to math than the “right” answers. The more I learn, the more intrigued I become about how¬†interesting and mystical math really is. (yes, I realize this makes me a huge math dork, and I’m ok with that)

So, in conclusion, I would like to publicly declare my goal for this Math Rocks cohort. To Boldly Go, where no man has gone before in the name of Math…actually several people have gone before, but it’s my first time, and I love me some Star Trek. But I do plan to go boldly and realize there may be moments of discomfort and frustration but it will all be worth it in the end. I look forward to the enhancing, changing, and transforming of my own ideas and practices in the name of Math!