Strategies in Number Talks

In kindergarten, we use a variety of dot arrangements for Number Talks. We started with under 5 dots in the beginning of the year, and after few months in, we are under ten. From the beginning, I observed various strategies and the most popular strategy has been to find a smaller number inside a larger one and count the rest. Other strategies are grouping smaller numbers in a large group, and quickly and mentally counting the arrangement by ones.

As time has passed, students are making faster and faster calculations and they are quicker at finding smaller numbers in a large arrangement. For example, in an 8 dot arrangement some students will quickly see 4 and 4 dots, while others will see 5 and 3 or 6 and 2. This type of grouping has evolved as we are working with bigger numbers and it is especially relevant now that we are working in a Unit with addition. Their explanations of their thinking have also evolved with time. Students not only see 4 and 4 dots, now they are more specific in explaining their dots location with a more sophisticated language. I see 4 dots in the center and other 4 dots around the center. I see five on the top and 3 on the bottom. I see six in the left side and 2 other dots in the right side.

Of course I still have a little group that is working with numbers under five and we are meeting daily to work on larger numbers and to use more specific language to explain their thinking. 

Building Community in Number Talks.

Community building is an important area in classroom management, and more so in kindergarten. In kindergarten, most of the students haven’t yet been exposed to a large group of children. When school starts the first thing we teach are expectations which include several guidelines on behavior within class discussions. We come up with steps to follow in community circle and we practice these and review as often as needed. We also create a social contract with agreements on how we will treat each other in class. Still, it is difficult for students to understand that others’ input is just as important in a discussion as theirs. We learn this and practice almost everyday during Number Talks. 

Number Talks start with the question ¿Cuántos hay? How many are there? Students have learned that they are not to shout out the answer but show that they know it with a thumbs up. These took a lot of practice in the beginning and by now everyone follows it (every now and then eager students still shout out the number). By now, students know to wait to be called to respond and if they aren’t called they get a chance to agree or disagree showing a thumbs up or thumbs down. This part can be tricky without guidelines that show respect to other students’ thoughts and opinions. Why is it important to show respect if others are wrong?

In our school, my class is known as Los Amigos de Ms. San Miguel. We learn that we are a community of friends and we are learners that learn at our own pace. During social studies, we talk about feelings and how we need to show respect even if we do not agree with another friend. We sing songs about our classroom community to create a sense of belonging and we earn points as a class for behaviors that show love, respect and kindness to other students. We also have created hand signals that recall the agreements in our social contract such as a heart signal with both hands, fingers touching, for love. During our Number Talks we refer to these guidelines and our social contract using the hand signals, when needed.

Because students have being involved in the process of creating the social contract, having been involved in listing the guidelines that show respect between each other, this is very meaningful to them. Furthermore, because they also created hand signals to recall the items listed in the social contract, they have become experts in identifying moments when the hand signals are needed. Just last week, a student showed his hand heart to another student during a Number Talk, when this friend had made fun of a wrong answer. The first student reminded him that we do not make fun of others because we are loving friends. We are, los Amigos amorosos, loving friends 😉



Kinder Chats abt Numbers :)

In Kinder, our Number Talks are growing steady. After starting this about a month ago, I am feeling a lot more confident. The routine is set and my little ones get very excited to share their thinking and their thinking surprises me every day. They are learning to use more than one strategy, they are learning to agree or disagree with respect, and more importantly (and this is a bonus with Number Talks),  kindergarteners are learning to quietly draw their thumbs up sign instead of shouting their answers.

In this month, I have used dots and ten frames starting with quantities below five and slowly growing up to ten. While a group of students can easily do quantities over ten we still need to reinforce, refine their five-ness knowledge (as demonstrated in the pics).

Recording students thinking is the part that I am least confident. Are students really making mathematical connections or lucky guesses? Are they learning strategies from their classmates? Are students growing in number knowledge? I tend to be almost over optimistic of the growth my students make (I like to think cup half full) but I also don’t want to miss the need to strengthen their basic mathematical skills (that keeps me up sometimes). So we keep going back to five-ness and try a different, new arrangement, or a different mode. Soon, we will be adding rekenrecks (I should have done this already, I know) to add to our repertoire of Number Talk tools and increase our five-ness talks.

I am very excited to see how will number chats be at the end of this year. How their mathematical skills will grow and how far will they go to express mathematical thinking.. till then lets keep talking about numbers!

Hickory Dickory …

Time.. I agree with Andrew Stadel from It’s definitely a dirty/hot topic at school. Teachers, are constantly  running out of time, and we are consistently trying to maximize our instruction minutes. The 80/20  design principle makes sense and I also would like to and need to redesign my classroom clock.. but how?

Yes, we are always looking to maximize learning and improve the art of teaching. Most of the time, however, it is a very difficult task to fit it all in a limited period of time. Below are the ideal and the current clocks for my math block and you will notice that my issue with time starts at 7:45 am!

Math that early in the morning is a new system in our kindergarten schedule. It is a positive thing, because I feel students are most motivated early in the morning. My class has been enjoying math and working productively. But, to have all the 70 minutes required for math, it has to start right at 7:45!

Moving on to the actual math block, Kinder is no place for long talks (so the issue other classes have with long lectures is non existent, already). The challenge here is to keep students engaged long enough for a good practice. In kinder we have  “Mini Lessons”, we have to add movement, music, brainbreaks, and many times, we even have to add a whole different lesson to keep students motivated in learning their numbers.

Even though starting with math at 7:45 squeezes my morning routine, I believe, it is always possible to improve and maximize our instruction time. It is all about organization and it is a challenging endeavor.. Time is, after all, a four letter word filled with timeless challenges!

Making music that lasts..

I heard Brian Bushart’s talk “Make Your Own Kind of Music” and Tracy Zager’s “Braking the Cycle” and other talks from the 2016 NCTM Annual Meeting and Exposition. The talks reminded me of my own children’s memories in elementary and middle schools (my son is in tenth grade and my daughter in 8th). Both have very fond memories of few of their teachers. Over the years, I have wanted to find out what made my children talk more fondly of certain teachers. Why do they keep few school memories alive? 

Today I introduced my class to Number Talks. To be honest, I haven’t done this properly in the past. This year, I wanted to start off as it should be, so I took extra time to plan and prepare (I was at this for last two weeks!). First, I did some research at the ARRC and the resources listed under Number Talks. I read the TEKS over and over for Unit 1 “Introducing Number Concepts to 5” and marked this one: 

Focus TEKS K.2D recognize instantly the quantity of a small group of objects [up to 5 in this unit] in organized and random arrangements.

I prepared several dot cards in random arrangements representing 4. Students were very excited and attentive (it helps that math is first in our schedule). The first arrangement was 4 dots in a row. The first student said he counted the dots, another one shared that he just knew there were four dots. The second arrangement was 4 dots arranged as in a dice, and their eager responses were similar to the first, except for one. This student said she saw 2 and 2 dots and she knew 2 plus 2 is four (I tried to remain very calm and neutral but I wanted to shout, YAY!!!) That paved the way for the next. The arrangement was 3 dots in a row with one on top and students responses got more descriptive, “I saw 3 pls 1”, “I see 2 in the middle and 2 on the sides”. As simple as that, the first Number Talks started in my class; and it’s only the beginning.

When school started last week, my children came home very excited about their new teachers. I noticed that their conversations have motivation in common. I think I found my answer; it’s inspiration. My kiddos memories are about the inspirational moments they got from these teachers. So, I agree with Brian’s talk. If we only repeat our lessons, like in a known pattern, or a scripted dialogue,  we will not cause a change in our audience. When we MAKE our own music, we’ll motivate and inspire our students, enough to last throughout their school years and beyond. This is the mantra that will guide my lesson planning this year!

Unit 1-Intro to number concepts (to 5)

This is day two of the Unit. The TEKS are K.2 A-E with a focus on representing, counting numbers 1 to 5 (to 5, for the sake of the unit) through number recognition, generating sets, and subitizing.

First of all, this is a new year for Dual Language Kindergarten teachers. This year we will be teaching math in Spanish, for the first time. I cannot express, enough, how excited about this, I am! Why? No, is not because I am a native Spanish speaker and, by default, I am more comfortable teaching in Spanish. It is because, I believe, MATH learning occurs naturally in a person’s native language. This means, that young ELL students will feel more successful at math, counting, representing numbers etc, if they can do this in their native language.

School has started and the Unit 1 is already being unfolded. We have gone over procedures to use the number tracks, and the manipulatives and we have already begun using Unifix blocks to count to 5.

On our first day at school, (yesterday) while we organized our classroom and learned procedures, we filled our small pencil boxes to store our 5 crayons (students could pick any color they like but they could only pick 5) and the promise is to give them 5 more every start of the week until we get to 20 (lets see if they can keep track of how many weeks it took to get the 20). We “organized” a box of Unifix blocks in groups of 5, “because we wanted them to fit in the blocks bin”. Students had a blast getting their hands messy with shaving cream, writing numbers to 5.. and at the end of the day we stacked chairs on stacks of five; because 5 is a reasonable pile of chairs and stacking more is unsafe (or so I made them believe).

Tomorrow, we’ll introduce number talk, use dots and five frames and we will be doing dot subitizing too. And because Wells Branch is now an Art Integration Academy, we will be creating bracelets of 5 and do more number art!

I am very very excited about this year at WBE AIA and our new Dual Language model!



ReStudying K TEKS

K(1)(B) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

This SE describes the traditional problem-solving process used in mathematics and science. Students are expected to use this process in a grade appropriate manner when solving problems that can be considered difficult relative to mathematic maturity.

This is the number one TEK. It is where it all starts. It requires gentle but efficient modeling, plus tons of application variety, and tons of practice time. It needs to be relevant to the day to day world of our students. This TEK is logical, it’s easy to read it and understand it, but teaching it can be tricky, especially in kindergarten. I love that the people behind the ARRC, work hard to provide us, with ideas that we can use in the classroom.

In this K. 1B, students are to use a problem solving model with more than 3 critical components. Analyze given information -students could generate their own questions, or their own view of the problem. The way I start problem solving in my classroom (as taught to me by sweet Mrs. Cordon, in my first year in kinder) is by using a variety of numberless problems that students can relate to. Once we have students generating their own questions, we are off to a good start. Formulate a plan or strategy- this is generally when things can fall apart. Teachers should allow students to find their own way through. At the same time, having all students actively and purposefully working towards a solution, is not an easy task. If many students are not able to generate a plan or come up with a strategy then the problem needs to be readjust to fit their ability and when modeling, this is were the focus can be strengthened. The next critical component has to do with the solution: determine the solution, justify it and evaluate the problem. I love observing how students think of very creative ways to find a solution (I have been surprised, more than once). There will be students who find answers faster than others, and will be very happy to share. Just keep in mind, that if a student could not find a solution it is not the end of the world. With more practice, and more variety, it will happen.

So as Graham Fletcher  puts it , this is definitely the one math “story” that needs to be told over and over in a variety of tales. And each time needs to be retold in such an engaging manner that we do not have students running for the restroom (or raising their hand for it 😉

Math Rocks, Really!

I signed up for Math Rocks because I want (I urgently need) to improve my Math block of our daily schedule, and make it more efficient and relevant for my class. I have heard very good things about this training from colleagues.  I can’t wait to apply what I am learning to assist my students in loving numbers and make of our Math a rocking time.