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This summer I began a journey with our Round Rock ISD cohort: MathRocks. In our first session, we told to pick a word to describe our focus for our math instruction and learning this year.
My word: Discovery. I selected this word for a couple of reasons: 1.)I wanted to DISCOVER new ways of teaching math and 2.) The word, “discovery,” contains an element of risk, and I wanted to challenge myself by being a risk-taker in math.
S0 the question is: Did I DISCOVER what I hoping to during this journey? What did I DISCOVER?
I absolutely accomplished my of goal of discovery. Throughout this process, I have learned so many new ways to teach math that are engaging and most importantly, meaningful to my students. Through number talks, notice/wonder discussions, open-middle problems, Estimation180, and 3 Act math lessons, I truly feel that I have gained a wealth of knowledge.
My goal for next year is to incorporate at least one “3 Act math lesson” throughout every unit. I love how these types of lessons make math REAL to the students. Students are able to see WHY math is important, not just in 4th grade, but in LIFE!
I feel like I was a risk-taker and tried everything I learned, but I look forward to next year, implementing these strategies and lessons from DAY 1!!
I gave my students an open-middle problem that involved multiplication because that is an area where I would like to focus. When my students first saw the problem, many of them were puzzled. Questions were being asked left and right.
As a class, we discussed the problem and directions- only digits 1-4 could be used ONCE in the problem to create the LARGEST product possible. Almost all students immediately placed the four in the tens’ place of the top number. As I walked around, students were certain that they had found the largest possible product. I encouraged students to try other combinations- some began right away to guess and check other solutions. Some didn’t want to try anything else because they were confident they had done it.
When we came together as a class, I called on a student to come and explain his solution. He correctly placed the digits 2-4 to make the largest product, but he had trouble explaining his reasoning for placing the digits in certain locations. I then called on other students who agreed with his solution to add on to his explanation. With some questioning and probing, we were finally able to have a whole class consensus as to why his solution made the largest product.
I wrapped up the lesson by asking the students what they thought about this type of problem, compared to others we’ve done this year. Many students stated that this was fun– “It was like a puzzle!”
I will definitely be trying more problems like this to stretch my students thinking!
First things first… I am a self- diagnosed control freak and perfectionist, so beginning number talks was a scary adventure because I couldn’t plan for every possible scenario or outcome. That being said, once I started doing number talks, the fear I had has slowly subsided, and I’m so excited about the learning and conversations that my students have when we do number talks.
For my most recent number talk, I chose the subtraction problem 63-28. My students and I had been doing a lot of work with dot images, so I decided it was time to move into equations. I specifically wanted to start with subtraction because I have a large number of my 4th graders still using their fingers to subtract or using the algorithm and ending up with the wrong answer. When I planned this number talk, you’ll see on my plan that I was envisioning my students having a wealth of other strategies BESIDES the algorithm. I didn’t even put the algorithm on my plan because I thought, “well, they won’t have paper and pencil, so they won’t be able to that in their heads.” I WAS WRONG! (I’ll get into that a little later.)
Here’s my plan:
When I planned out this number talk, I was really hoping that my students would use methods like count on, friendly numbers, etc. I hadn’t realized how attached my students were to the standard algorithm…for many that is their security blanket, regardless of whether or not it gets them the correct answer! I brainstormed possible strategies and clarifying questions that I could ask during the number talk. The section on my plan where it says, “reflection/what might you do next?” is blank because I really wasn’t sure where I would need to go since this was our first subtraction number talk. Now that we’ve had this number talk, our direction is very clear!
To start, I reviewed our number talks hand symbols with an anchor chart I created ( I found it on Pinterest).
Made by: TeacherCreature
I also reviewed the talk moves, and let the students know that we have become really good at “adding-on” to others’ comments, but that I wanted us to focus on “re-voicing” what others said in our number talk today. We discussed what “re-voicing” meant. I projected the problem on the board, and almost in an instant, saw students’ hands whip out like guns out of holsters in a shoot off! Not only did they think this number talks was a race, but they immediately relied on their trusty fingers to do all the counting!
Many students started showing a “thumbs up” signal when they had a strategy and an answer. Once all students were given adequate wait time, I called on those willing to share their answer. We had two answers: 45 and 35. I then asked if anyone would like to defend one of these answers. One of my higher students immediately raised her hand and said, “I would like to defend 35.” So then she proceeded to tell/explain how she used the standard algorithm in her head…crossing out the tens, regrouping…. My heart sank, but I continued on, documenting her strategy, honoring it, and quickly asking, ” Does anybody else have a different strategy?”
Another very competent student raised his hand, and explained that he started at 28 and wanted to count up to 63 to find his answer. HALLELUJAH!! I then asked if a number line would be an appropriate way for me to record his thinking. He agreed, and began telling his strategy. He did an amazing job of describing how he added to 2 to get to 30, then added 30 to get to 60, and then added 60 and 3 to get 35??? I honored his explanation, but quickly began racking my brain for clarifying questions. I was hoping that by writing it on the board and him seeing it, he would catch his mistake. Other students were looking confused, and I could tell they wanted to help him. I asked my questions, and at first, he stuck to his original thinking, but after more questioning, he realized his mistake. I crossed out his original thinking and recorded his revision.
Another student who had given the answer of 45, raised his hand and said, “I want to change my answer.” YAY!! He then was able to explain how he used a form of regrouping (not the standard algorithm) to check his original answer and realized he was 10 off.
My final student who shared is not as confident in math, so I was very excited that he was willing to contribute. He began by subtracting the numbers in the 10’s place, but then when he said, “I subtracted 3 minus 8,” he stopped because he knew he wasn’t going to get the right answer. I gave him wait time, but I could see him getting frustrated, so I told him to continue to think, and I would come back. When I came back to him, he then explained that he subtracted the tens (60-20) and got 40. Then he subtracted 40-3 to get 37. Then he explained he subtracted 37-2 and got 35. I asked a clarifying question, Where did the 2 come from? How did you get that for your next step?” Again, he struggled and started to turn red, so I moved on as to not embarrass him.
To wrap up the number talk, I wanted students to focus on the strategy of the student who counted up from 28 to 63. So I asked a few students to re-voice his strategy. The students seemed to understand it, but it wasn’t a comfortable strategy for them…YET!!
After this number talk, I realized that my students need more practice with mental math strategies for subtraction (counting up and using friendly numbers). So, I’ve decided to stick with this for a while. I am going to use problem strings from the book, Number Talks: Helping Children Build Mental Math and Computational Strategies, to focus on the use of friendly numbers. I would like to see ALL my students be able to verbalize a strategy such as, “I added 2 to 28 to make it 30. Then I added 33 to get to 63. I knew I had to add those 2 back to my final answer, so I added 33+2 and got 35 as the difference between 28 and 63.” I know with more practice, WE WILL GET THERE!!
What are my goals for myself as a math teacher this year? LESS CONTROL….This is going to be a tough one, but I am really going to strive to be more the facilitator and guide, and not so much the “Know it all” for my students. Last year was my first year in fourth grade, so it was a big learning year for me. On top of that, the TEKS changed, and therefore some of it was new for my colleges as well. As a result, I feel my instruction was more controlled than normal because I wanted it to be as predictable as possible since so many other parts were unknown! Now that I feel slightly more comfortable with the curriculum, I really want to focus my math instruction on inquiry and discovery. I know this will be very powerful for my students.
For my students, I would like to see them take more ownership of their math journey. We are beginning the Leader in Me program at my school, and I think this is the perfect opportunity to teach students how to analyze their own data and progress. I would love for my students to see themselves as the driving force behind their learning: really understanding their strengths, challenges, and areas of growth.
Time! Time will always be the challenge when it comes to obtaining my goals, either for myself or my students. It never fails, I start the year pumped up and ready to go…then reality sets in: grading, BAS testing, conferences, the list goes on and on and on. One change that I am hoping with help me overcome this challenge is that I will be planning math this year for our team. I think this will allow me to use more of my time focusing on my math goals, but also to share what I’m learning with my team. I’m looking forward to a very exciting and successful new year!
Till next time….
My name is Maggie Payne. How I got into teaching? Well, that journey began before I was five years old. From a very young age, I knew that it was my destiny to become a teacher. Not only did I have so much wisdom to impart upon the world (said with great sarcasm), I also was organized, driven and shall we say a demanding child. Not that teachers are demanding or need to be, but at the age of five it was a required skill set in order to get my students (older siblings and cousins) to go along with my teacher charade. All of my practice paid off, and I graduated from Texas State University. I began my teaching career, and I have loved every moment! The day to day challenges, surprises, and successes make me smile and want to continue on this journey. Hopefully, I’ll have much more to share in the years to come! Stay tuned…