Number Sense Routines Book Study: Chapter 2

I am linking up again with Little Minds at Work for a book study on Number Sense Routines by Jessica Shumway.

This is my second attempt to post this entry from my phone. I wrote an entire post that was not saved and had to rewrite the entire thing! Ugh! Please forgive any mistakes for that reason.

I also want to apologize for the delay in writing my reflection on the second chapter. I was out of town last week on a road trip around south Florida and only had a day and a half before leaving for my next trip. I am now on my way to visit one of my closest teaching friends from the Philippines in her home state of Minnesota. I'm taking advantage of my downtime at the airport while on my layover to catch up!

Chapter 2 Improving Number Sense 

Routines That Are Not Routinized  

In this chapter, Jessica Shumway says that most teachers already begin their math blocks with some kind of warm-up, and her goal is to help those teachers refine their warm-up to expand students' number sense. She writes, "These number sense routines are not 'auto pilot' activities, but opportunities for meaningful practice." This statement really hit home with me because my current warm-up is what I call my Calendar time, and about half way through the first semester, I am already terribly bored of the monotony. I did switch it up a little throughout the year, but with subtle changes such as singing a different song for the days of the week and using a different counting strategy (count the numbers on the calendar by 1s, 5s, 10s) and so on. For the most part, the day-to-day routine was very much the same. It was my thought that having a predictable routine was what was best for my students which is sort of right. Predictability helps students feel more comfortable and willing to share, but there should be different routines instead of the same activities every day because students need multiple opportunities to develop number sense. The routines need to be fluid and flexible as well so that they are responsive to the students. To be a "responsive" routine, they should be responsive to students' discussions, understandings, and learning needs.

All routines should do the following:

• Provide daily number sense activities. 

• Include discussion about numbers and their relationships.

• Respond to students' current understandings.

• Build on students' existing number sense.

• Encourage students to play with numbers and enrich their mathematical thinking.

• Help students make connections to big ideas in mathematics.

Also, number sense routines should get all of the students actively involved as they review old concepts and practice new ideas. With my current set up, I have a Calendar Helper that runs the daily warm-up/calendar. This person is obviously involved, and I can count on a handful of other students to always participate, but then the rest of the class checks out during portions of the calendar routine. Who can blame them? If they aren't being challenged then they will not pay attention and instead will act out. And this isn't helping anyone! I can only assume they were bored but maybe the reality is that they were not participating because they did not know the answers to the questions being asked. A warm-up consisting of number sense routines is the perfect time to assess students. I definitely knew that the students that regularly participated had a strong grasp of the concepts being reviewed, but what about those that did not respond? I had no way of telling if the students had a clear understanding if they were not always involved. 

It is important to note that number sense routines do not always need to be related to the current math content being taught. What is important is that students build number sense and use their number sense. 

Part II of the book discusses the routines that Shumway has found to be the most effective in helping students build number sense. I look forward to gaining new tools to spice up my warm-up time! 

Number Sense Routines Book Study: Chapter 1

I am linking up with Little Minds at Work for a book study on Number Sense Routines by Jessica Shumway.

The first chapter answers the question, "What is number sense?" In the past when I have thought about number sense, I have considered it the first step in children learning how to add and to subtract. After reading this chapter I realized that number sense is so much more complex than that. As Shumway wrote, "There are many layers to it, and it is rooted within all strands of mathematics." Students with a strong number sense demonstrate all of the following understandings and skills:

• A sense of what numbers mean.
• An ability to look at the world in terms of quantity and number.
• An ability to make comparisons among quantities.
• Flexibility, automaticity, and fluidity with numbers.
• An ability to perform mental math.
• Flexibility with problems.
• Automatic use of math information.
• An ability to determine reasonableness of an answer.
• An ability to decide on a strategy based on the numbers in a problem.

One of the things that stood out to me in this chapter was Figure 1.3 Components of Number Sense. This web shows that number senses involves big ideas, strategies, skills, models, tools, and language. Once again, this helped show me that number sense is not only children knowing how to compute fluently, but also being able to use the appropriate language and tools to do so. Too many time I have asked my students, "How did you find your answer?" only to be told, "I just thought about it in my head." If my students had a strong sense of numbers, they would have been able to explain their reasoning and thought process.

I also loved, loved, loved Box 1.1 Early Number Sense Learning Trajectory. As a Kindergarten teacher, this is so helpful for me to understand so that I can better support my students' mathematical development. This box includes information on subitizing, magnitude, counting, one-to-one correspondence, cardinality, hierarchical inclusion, part/whole relationships, compensation, and unitizing. To be honest, when I first saw this box I started to think I was in trouble because I was not familiar with half of the terms! Once I read the explanations I felt a lot better because I realized I DO know this stuff, and I have seen this progression in my students throughout the year. I just did not know the proper terminology. I loved that these clear descriptions were included because I believe it is important that I know as much as possible about number sense development to be able to plan developmentally appropriate lessons for my students. 

Tara from Little Minds at Work asked some questions to go along with Chapter 1.

1. What is your current comfort level with teaching number sense?

As a newer teacher, I think my current comfort level with teaching number sense is on the lower side. I have taught two different grade levels and both years I was unsure of where my students would be at the beginning of the year and where they should end up at the end of the year. As the year progressed, I would get to know my students' mathematical skills, but I did not always know what to do to help those that were struggling in their development of number sense.

2. What have you already started in your classroom to build number sense?
At the beginning of the year, I did a lot of subitizing activities with dot cards. I usually used the dot cards while lining up or transitioning to another activity. I also did a daily calendar where we practiced counting (at first rote counting and then later counting with one-to-one correspondence) and place value (when we counted our days in school). The same way I used the dot cards at the beginning of the year, I started to use flash cards towards the end of the year to improve students' mental math with addition and subtracting. 

3. What have you considered adding to your classroom that will give your students that much needed "multiple exposures" component? 
I plan on expanding my subitizing activities to use other tools instead of only using dot cards. Some ideas I have are ten frames and pictures of objects or fingers (I had some students towards the end of the year that were still counting each individual finger on their hands instead of automatically knowing that one hand had five fingers). I would like to do these activities daily and continue throughout the year, not only at the beginning. In my math stations, I would like to include a variety of number sense activities that the students can continuously work on every day. I also plan on extending my calendar time to include more number sense activities including a number of the day and estimation jar. Hopefully with all of these and other additions, I will no longer be told, "I just thought about it in my head" when I asked for a student's explanation of an answer!

I will leave you with my favorite quote from the chapter: Only if children come to believe that there are always multiple ways to solve problems, and that they, personally, are capable of discovering some of these ways, will they be likely to exercise - and thereby develop - number sense.