It’s been interesting to see the growth in students this year in using Number Talks. Right now, the team is trying to encourage students to subitize and decompose numbers into its parts with ease. With this in mind, we are using ten frames to show numbers in several ways. For this segment, we have shown the number 6 in a ten frame and have now shown the same quantity in a different manner. This will be done a couple of more times with the number 6, though not necessarily in consecutive days. The first student to speak looked at what I had written about there being less dots this week than last week (I was out sick earlier this week), then as he read his statement, he said, “No, wait” and raised his hand to revise his statement. Last week the top row was full with one dot on the bottom row. Some students are still wanting to get creative with the math sentence, such as “13 – 7 = 6.” I usually ask them if that’s what they notice about the image and they will shake their heads and continue looking. Some students are eager to show 1 finger that they have a method, willing to stop there, while other students immediately have 5 or 6 fingers held to their chests to compete with how many methods they have found to explain the math image. However, they are growing. The students now know to expand on what they see with a math sentence. Perhaps this isn’t something I should ask? If a student notices 4 and 2, I’ll ask the student to come up to the board to show exactly how he/she saw 4 and 2 and explain how this would be described in a math sentence. Though, one student did look at the ten frame from a geometry perspective, I didn’t consider it a frustration since it’s one of our current spiral review objectives :).
I’d like to move towards the students talking to one another, asking questions, expanding or supporting one another’s statements. However, right now there is interest in different perspectives and aha moments in spotting a new way to view numbers. Also, some students aren’t sold on participating yet. I’m hoping this will come with time. Lovin’ it.
* Add 10 minutes to the yellow as our time moves beyond 1 hour and 5 (as noted) to the blue. Students return to my room after Recess and Specials back to back. They tend to be hungry and thirsty, leading to my decision to switch my snack to the afternoon, rather than the typical morning snack. Between this and a water break, I noticed some waste of learning time. Ouch! We also begin our Math block with Conceptual Review rather than ending with review. If the review went with a new game and I hadn’t taught it the day before, I gave a quick model – again wasting time so begins ideas to improve my math block. I will return to morning snack, plus model the game/review prior to the math block, either in the morning before 8 or the day before. I also noticed that Conceptual Review has time that can be given to Guided Practice, but I really need to maximize the block I’m going to shorten. Because I went to a Kathy Richardson workshop this past summer, I will blend review time, inserting her program with the goal of strengthening number sense. I’ve not used her games yet. According to our Kindergarten and First grade teams, this program is excellent without being lengthy.
New goals – reduce wasted time and giving more time to Guided Practice. Within this increase learning in Conceptual Review by incorporating a fun, effective program.
As I looked at my clock, keeping in mind Andrew Stadel’s advice to make the 20% of what we use help out 80% of what we need, I tried to think of my year end goals for my students and I fall back to number sense. Since Kathy Richardson is designed for this and doesn’t veer away from my goal of bringing curiosity into the room, then this should help as I move my students in a better direction for learning, with time well spent versus time used up.
For this year, I’ve decided to work on adding a more curious perspective into my math lessons because let’s face it, I was taught a traditional way of doing math so I have to watch hogging the math lesson at the front of the room. Also, if math is more fun and students’ sense of wonder is activated, more connections can be made. This week, we were beginning our journey to understanding how to decompose numbers up to 99 in more than 1 way with an ability to add/subtract 10 or 1. In Origo, there is an extra practice suggested where students roll two dice: one labeled with words twenty through seventy and the other labeled four through nine. The idea is to score points when you roll a greater number than your partner. I wanted to use these dice throughout the unit so I decided to created drawing cards +10, -10, +1, and -1. I also wanted the students to practice building numbers with unifix cubes before moving to drawing base 10 representations and using standard form. The idea was that students would think about the number rolled, exploring how to build the number with a partner (each with on set, but working collaboratively and checking one another), then drawing one of the cards to rebuild the number. The game, RollnBuild and Draw, is a hit! The kids love it, however, it did not necessarily run smoothly. I discovered I need to model with this class much more than I modeled last year so I’ll need to plan for time to play as a class, before modeling a couple of times, then working with a small group. During a longer investigation, I often work with a group at the kidney table to serve as a close support system, which means I can’t hear the conversations going on around the room. Perhaps I can create a recording sheet so I can see their thinking on paper. I also discovered this class will need more practice to play with integrity – so again more whole class practice as we discuss more what it should look like when playing with a partner. I plan to move towards the students creating numbers for one another, then build the number in more than one way. Beyond that, I’m trying to ask more questions of the students to get them thinking and more curious within the direct teach portion as well. My hope is to integrate exploration and investigation to inspire the students’ curiosity of how numbers work together.
After watching a short video by Annie Fetter, math educator at Drexel University, called “The Hurrier I Go, The Behinder I Get,” our cohort was asked to look deeply at our unit rationale and TEKS. In addition, we looked through the vocabulary, worked through big ideas of student expectations, and essential questions. Throughout I jotted notes, reflecting on what I feel I should prioritize. With the Unit Title “Applying 2-Digit Place Value Concepts and Descriptions.”
So what do I feel is most important? What I really feel is the goal of this unit is to continue the students’ journey to understanding numbers beyond its standard form, a symbol. We’re asking the students to understand to look at numbers as representing the idea of distance and quantity. Later we’ll add the ideas of time and speed. We’re helping the students to understand what the number represents. One part of this goal is the relationships between numbers in base 10 – individual units that can combine in a set pattern or proportion to groups or units of a number, unitizing. In looking at relationships, a student can compare, realizing a greater quantity or distance. In adding bars and graphs to the unit, the student is given a a real world application of using these concepts, as well as learning to reason through information, then finding an efficient method to problem-solve.
So given the 3 bold phrases which are my priorities for this unit, how do I get there?
1) The beginning of our math block will start with conversation about numbers in various ways. I plan to start small, allowing students to talk about smaller numbers/images/expressions so they can build the number sense to understand the concept of numbers. Our team has decided to have
at least 3 number talks a week
, asking students to look at computational fluency, then look at word problems twice a week using a number talk, which may or may not include computational fluency. Many of these will be problems they can work through mentally, though some may require some concrete manipulation. District instruction shows that this takes about 10 minutes.
2) In our core time, there will be approximately 40 minutes of time given to
exploration, collaboration, and discussion
3) After this, the students will be given time to review what they have learned through
. We’ve used a lot of Fundamental games in the past two years. This year we will add games from Developing Number Concepts by Kathy Richardson. The link will take you to her 3rd book which has a focus on place value.
*Spiral review may be included within a number talk, at the end of a number talk, during conversation in the core block, or during game review. It depends on where there’s a relevant fit to what is being planned.
This year I move back into an inclusion class. It was beneficial to listen to the video about focusing on the purpose of teaching math, rather than fitting standards into a calendar.
“Becoming a Better Storyteller” is the name of a video with Graham Fletcher, math education specialist, speaking about how presentation of math matters. He explains that math is a story, and like any story that is “read” aloud, the listener can be interested or wish to escape. Within this idea, he discusses the content we are teaching. As we work day to day, are we intentionally matching our curriculum to state standards?
Interested, even intimidated, I checked the state standards for second grade math. I found a few TEKS which gave me food for thought. One, was the word estimation in 2.1C (Texas Y’all): (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. You see, I’ve been told a couple of times that estimation is not a current standard for second grade, so it wasn’t included in my lessons this past year. We talked about what is reasonable when problem-solving so I hit the idea indirectly, but here it is: estimation as an appropriate tool that 2nd graders need. What does this mean for me? Well, estimation will be a purposeful part of my year.
Another TEK wasn’t exactly surprising, but the language shows I need to teach at a deeper level. Listen to this: 2.1G (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. In our grade level teams, we talk throughout the year about facilitating experiences to give students the skills to explain their thinking using correct vocabulary, but it’s the words justify and argue that I find appealing. Here’s a great avenue to teach respectful discourse, team work, to defend or revise your ideas when there is disagreement. What a strong concept! I hope to highlight this TEK within our team discussions to deepen the relevance of our number talks. I highly encourage anyone reading this to listen to the linked video, then take a closer look at your state standards. It’s an eye opener that can only help you as an educator.
Number Talks PD
I’ve gone through a little professional development for Number Talks, but today we spent 6 hours diving into understanding its components, analyzing and discussing a common routine from which to work as a district group, and practicing structure from planning through implementation to reflection. Walking away, I felt a better understanding of how a Number Talk should look. The leaders, Brian Bushart and Regina Payne, explained how the purpose of these conversations isn’t to improve concept comprehension, though there are aha moments within, but instead to gain computational fluency. How did I miss this essential attribute? Yet, during the demos and student (teacher) practice, I could see how deeply learning occurs through such a seemingly simple discussion. In practice, students can understand how to apply subitizing, relationships, patterns, and realize how to efficiently solve problems in a reasonable manner.
Questions asked by the teacher seemed intuitive: how did you think about this, does this look like an earlier expression, does anyone have a different strategy? Yet listening to how to model the student’s thinking was new to me. The idea is to listen to the students as they are talking to their partners about how they came to their answer. From this, the teacher may selectively invite specific students to present efficient, varied strategies, focus on one or two strategies, including answers that are not correct, to both honor the thinking and the student, as well as allow the students to learn from one another. The teacher gains important information about individual students while the children are truly thinking about numbers, learning how to explain their ideas, and how to speak in a collaborative, constructive, respectful manner. What a treasure from only 10 – 15 minutes of routine class time.
We were introduced to the book which provided much of the background to this idea: Making Number Talks Matter by Cathy Humphreys. It is one route you can go to learn more about Number Talks independently, but I recommend a personal workshop in your district if possible. There was better clarity to watch it in action and discuss the steps of a number talk.
You can discover more about all things elementary math from Brian Stockus at his blog: Teaching to the Beat of a Different Drummer. On Twitter, you can find him @bstockus
Regina Payne’s blog can be found here: Regina Rocks: A Mathematical Journey to Change the World. I’m not sure if her twitter account is for public viewing, but I’ll keep you posted.
Check their blogs out – it’s worth exploration. Oh, and today’s tech site of exploration: desmos.com. In the classroom activities, you can create math questions for students to answer and explain their thinking after they enter a join code, then display the answers as a group anonymously for discussion. Most applications seem to be for fourth grade and up, but a tech savvy teacher could play to create an activity for lower grades. Try it – can’t beat free, it’s the best in teacher collaboration.
Math Rocks Long Term Professional Development
Each year I determine a focus for the upcoming year for personal development. This year it will be math. Why math and why Math Rocks (a district year long program)? One reason is I wish to increase exploration and discussion in my classroom during math time. Growing up in a traditional classroom, this doesn’t come naturally to me. Although I try to purposefully include these factors within my lessons, I know that learning from experts and peers will be a valuable experience!
Today was our first day. Wow, I’ve gained so much already. We joined Twitter for professional use; I added a separate account to keep my personal interactions separate from work. Should you be interested, feel free to check me out at @acheelove2learn. We received two websites which I look forward to trying in the classroom:
These two tools should provide an excellent way to get the students to think and talk about their thinking.
What am I hoping to gain from this program? I hope to develop new strategies through peer collaboration, stretch my thinking about how numbers work in order to provide deeper learning within my room, and gain new perspectives. This will be an exciting year as I learn so my students can learn. I’m looking forward to learning more how to use number talks that yields strong growth in concept comprehension.
One assignment given is to suggest one way my classroom is distinctively mine. My answer is the continuous celebration of each student as an individual we build in our room. Celebrations are posted on the board for effort, compassion, risk-taking, and persistence. Students give cheers to one another or write notes of specific praise/encouragement as we help one another be our best. I believe my students truly feel this in our classroom. It is a safe, of zone of encouragement. Certainly that is my daily goal, but students seem happy within our room.
New Classroom Gerbils
The students will each provide one name for each gerbil. Each student will receive 5 counters to choose 5 favorite names for the brown gerbil and 5 favorite names for the black gerbil. We will graph the results then vote on the top 4 names for each. In the event of a tie, we will vote on the top 5.
Teaching 3rd grade, I feel there are two main goals: solidify number sense and read, read, read. The math can feel a little frustrating if number sense hasn’t been gained as the curriculum moves along. I bring in games, review, small groups, more games, and more review. I still feel some frustration with wishing I could just focus on number sense for the small fries who desperately need to focus on the basics. However, I work as hard as I can to reach and teach.
Motivating students to read is my candy. I use several avenues. If students have an interest, I find matching books in multiple genres. They learn quickly that they can write a desired book, author, or topic on a post-it and I will try to fulfill that request.
Read Across America
I use “Read Across America,” an idea inspired by my team when I was student teaching, with my personal twist. The original plan gave the students prizes when a Reading Log page was completed, plus showed a graph of how many pages each student finishes. Every 4 pages, a state was colored on a United States map. There was a competition between the classes to see who could color the most states within the year. No one is competing with my class, which means it needed an additional driving force. When a student has 4 stars on the graph, he or she colors in any state. Then I purchase a matching state book for our classroom library, plus a book set within this state, hopefully with a focus on that student’s interests. These two books receive a dedication sticker to the student and reside in his/her personal book box before going into the library. My goal here is to leave a strong impression that reading truly does take you places – always a Seuss fan!
Bluebonnet Book Club
My favorite program right now is the Bluebonnet Nominee Club. Each year in Texas, 3rd through 5th graders at registered institutions, receive an opportunity to read (or hear read aloud) a minimum of 5 of the 20 Bluebonnet Nominee books in order to vote for the personal favorite in January. After reading each book, they must complete a form which proves the book was read. The Texas Bluebonnet Award is presented to the author of the winning book.
In my school, the librarian presented the 20 nominees to classes. She has a graph within the library for each class. My students were excited about the books which gave me an idea. I offered for each student in my class to choose their top 3 books they wished to read, then write me a letter explaining why I should buy their top chosen book to add to our classroom library. I promised to buy 5, but ended up purchasing 9 of the 20 books. I created a “Bluebonnet Book Club” with images of each book where students received their names above each book read with a summary submission form completed. Between the school library and mine, most of my students have a Bluebonnet book in their book box at all times. Many ask for a new one, once a form has been submitted.
I love the enthusiasm and interest this program is bringing to my room. Students are enjoying sharing their opinions of each book read. I’ve just bought 5 more Bluebonnet books to keep the interest fresh.
We also have a pair of vultures nesting on top of our school roof. The students have taken a huge interest in vultures. I’ve bought Vulture View and two other books about vultures to present to the students once Bluebonnet enthusiasm wanes. One of the books is by Sandra Markle, a favorite author of mine. I’ve made several Animoto Book Trailers which are assessible on this blog, but haven’t needed to use them yet. I need to build my collection of videos for the spring.
If you’re not moving or sleeping, consider reading. Pick up a book :).
After spending the past two summers as a full time student, I thought I would enjoy the extra free time with my children. Of course I do, spending wonderful moments with family and friends, but I find a little too much free time on my hands. During that time, I’ve worked on future bulletin boards, extension games, reading strategies, organizational papers such as transportation home in Excel or creating “Absent Folders”, plus independent professional development through my readings. I really do not like being idle. Because of this, I searched Google for online courses to claim some of my time productively. I found Singapore Math Model Drawing for Grades 1-6. I’m pretty excited. This sounds like a really useful class to provide another tool students can use. Any visual I can provide that gives children access to the relational nature of math will be beneficial in the second step of cocrete:pictorial (or concrete repesentational, but that’s a mouthful): abstract. With word problems, it’s the organization of the material which can often be difficult. I think if I can provide a consistent method which can be used throughout various types of word problems such as the bar method, then perhaps it will ease some of the organizational issues. Both districts in which I worked sometimes used a similar concept of Singapore, using the example of a tape diagram. It’s a 6 week class which begins in a couple of weeks; I’ll post again at the end of the course. In the meantime, I’ll enjoy family trips to Schlitterbahn, card games, trail walks, and continued professional preparation. Today, I’ll seal the stool I painted ages ago and begin another one. Next summer, I need to teach summer school or begin my graduate classes.