# Number Sense

## Introduction

As each student enters the 4th grade from different backgrounds, the mathematics that they each have been taught is similar. Each student was taught the 3rd grade Common Core Standards the year before. And as a 4th grader, the expectation is to be taught the 4th Grade Common Core Standards. The 4th Grade Common Core standards place a lot of emphasis on number sense. Each child’s number sense is of a varying degree when they enter 4th grade. Research has shown that every student is capable of learning and acquiring number sense when given a supportive environment with a number sense intervention (Yang, 2003). Number sense is not measured by puzzles and games, but by numbers representing quantities, spoken number names, and number inherent relationships to each other (Connell, 2012). In the 4th grade number sense is highly emphasized throughout the year. It is apparent through testing, observation, and small groups which student can grasp a number and which ones cannot. Number sense does not just assess that a student can memorize a number or a fact, but that they can explain how a problem should be solved and why they solved it that way. For example, one reason students can’t solve problems because many students don’t understand that numbers are flexible. However, numbers can be broken apart and put back together and help them with problem solving. If 4th grade students were instructed daily on number sense concepts, such as the idea that numbers can be broken apart and put back together, how would this improve their strategies for problem solving?

## Findings

Findings/Conclusions from the first IKAN assessment:

· Only 9 students were able to write the fractions for one half and one fifth.

· Only 1 student got the two ordering fractions questions correct.

· Word form for fractions was not a skill that students had retained from third grade.

· The students were taught how to order fractions and many of them used the strategy of finding a common denominator. Since these assessments are timed, the students do not have enough time to change the denominators.

· Areas to focus on for the second IKAN assessment: writing fractions and ordering fractions

· The strategies to teach for ordering fractions are using a common numerator, comparing to a half, and comparing to one. Also, when comparing fractions, it is essential to understand that the larger the numerator, the smaller the fraction.

Findings/Conclusions from the second IKAN assessment:

· Eleven students increased from no stage or stage 4 to a stage 4, stage 5, or stage 7.

· The first time the students took the assessment, no student was higher than a stage 4. Now 8 students have increased past a stage 4.

· Three students went down a stage and one student stayed the same.

· Thirteen of the twenty three students are at a stage 4 or higher.

· Six of the ten students that are not at a level are special education students.

· The two questions for stage 4 last week asked the students to write a fraction for one quarter and one third. I think the students would have understood if the question had said one-fourth. The academic language used in this problem was confusing to the students.

· Areas to focus on for the third IKAN assessment: writing fractions, ordering fractions, comparing fractions with a common numerator, comparing to a half, and comparing to a whole

• Two students left the study because they are no longer in my classroom.

Findings/Conclusions from the third IKAN assessment:

· Nine students increase from no stage, stage 4, and stage 5 to a stage 4, stage 5, stage 6 or stage 7.

· Only one student went down a stage, but four students stayed the same.

· Fifteen of the 21 students are at a stage 4 or higher.

· Four of the six students that are not at a level are special education students.

· Two of the students who started the fraction number talk with my class are no longer in my class.

· Areas to focus on for the fourth IKAN assessment: writing fractions, changing a mixed number to an improper fraction and recognizing equivalent fractions

Findings/Conclusions from the fourth IKAN assessment:

· Eleven students increase from no stage, stage 4, and stage 5 to a stage 4, stage 5, stage 6, stage 7, or stage 8.

· Three students went down a stage, and five students stayed the same.

· Ninteen of the 21 students are at a stage 4 or higher.

· One of the two students that are not at a level is special education students with no motivation.

· Two of the students who started the fraction number talk with my class are no longer in my class.

Overall the growth the students showed from the first IKAN assessment to the final IKAN assessment is tremendous. I think many of the students have put forth great effort in learning new strategies and working hard. There is not one particular group that has shown significant improvement over another. Whether the student is ESOL, Special Education, EIP, or not flagged for an academic need, there has been improvement across the class. There are still six students who are not at a level. These students vary in academic need.

In finding a student's knowledge stage using the IKAN assessment and teaching fraction Number Talks daily, I have seen significant growth in the students problem solving ability. Having a structured program and assessment tool to use definitely helped identify student's weaknesses and strengths. I will contonue to use Number Talks in my classroom and incorporate it into all topics. Students need to be encouraged to think critically and have peers to discuss problems with. Number Talks allows these two aspects to take place in the classroom.

## References

Connell, Mike. (2012). Number Sense: What it is, why it’s important, and how it develops.