Teachers over the years have invested numerous hours into helping their young learners establish firm math foundations and “make friends with numbers” in turn which will develop what teachers today refer to as number sense.
Judy Hornigold, from Math’s No Problem, describes number sense as emerging understanding that refers to a “child’s fluidity and flexibility with numbers and what numbers mean as well as an ability to perform mental mathematics and to look at the world and make comparisons”.
Dr. Keith Devlin, a mathematician at Stanford University in Palo Alto, California, unpacked a study conducted on 180 seventh-graders on math skills needed to function as adults. Results showed that the students who scored lower than their peers when tested on core math skills needed to function as adults were also the same students who scored the lowest in number sense and fluency as a first grader. Furthermore, it was revealed that 1 out of 5 adults in the United States lack the math competency of a middle school student.
Schools know that to be considered a great school, high-quality instruction must be evident in the classrooms. For math, high-quality instruction means setting a strong math foundation at a young age in order for students to successfully comprehend higher level math concepts as they advance in their education. With that in mind, Christian Life School has taken steps to implement additional training for our elementary teachers through courses focusing on number sense.
THE FOUNDATIONS OF NUMBER SENSE AND FLUENCY
Building a strong number sense commonly starts with foundation skills like these:
- Object counting to cardinality: Object counting is the process of rote counting in order to find the number of objects in a set. Cardinality refers to the actual count or number of items in a set. For example, counting the number of eggs left in the egg carton (1, 2, 3…through 7) and being able to identify there are 7 eggs left in the carton.
- Subitizing: The ability to instantly identify the number of objects in a small group without counting them. For example, recognizing the pattern used on a pair of dice for the number 5 and knowing the number without counting the dots.
- Part-part-whole: Children use part-part-whole thinking when they are asked to show problems in different ways such as addition and subtraction problems. For example, 7 is thought of as 5 and 2, 3 and 4, etc.
- Ten-frames usage: Ten–frames are used to develop a strong sense of groups of ten which is key in developing math skills. A basic ten-frame is a grid of two by five rectangular frames. This device is used to illustrate numbers less than or equal to ten. Ten-frames were developed by Van de Walle and Bobis after their research that highlighted the importance of understanding numbers in groups of ten and the importance of visualizing the numbers in a variety of ways.
IMPLEMENTING NUMBER SENSE AND FLUENCY WITH IXL
The goal of teachers today is to build students that are mathematical thinkers and not just calculators. Great schools recognize this and strategically implement technology into their instruction. A helpful factor in building a firm and comprehensive math foundation is for students to have a strong technology tool that can assist the teachers. A powerful program such as IXL supports our students and teachers in this way. This tool is able to support students on skills that need more practice in a consistent and organized manner. It also provides students with suggested areas to work on for those students needing an extra challenge which provides wonderful differentiated instruction. There are three key areas of strength with this program:
- IXL offers personalized skill recommendations for each student, based on what the student has been practicing, their diagnostic test, and teacher established recommendations
- Supplying enrichment opportunities that fit each student’s profile and skill set
- Suggesting areas for extra practice scaffolding prior knowledge needed in order to master concepts
- Provides immediate feedback on skills being practiced and adjusts the difficulty level as needed
- Pinpoints students’ overall working grades levels and their levels on key strands
- Groups students with similar levels and shows the most common skill recommendations for each group
- Students will receive immediate feedback
- Students will be given insight on their own growth
- Helps the teacher to instruct more effectively by knowing what areas need to be retaught or went to advance students on to another concept
NUMBER SENSE AND FLUENCY IN THE CLASSROOM
Christian Life School believes that high-quality instruction, partnered with best practice strategies used by teachers, combined with strategically implementing technology with tools such as IXL, will set students up for success. Excellent learning starts with instruction from teachers who have a clear picture of what skills are needed for a firm mathematical foundation. Daily, our staff combines their training along with our curriculum to build firm math foundations in our students. While participating in the number sense course, our elementary teachers have drilled down to add to their instructional repertoire in areas such as:
- Child cognitive development
- Early numeracy
- Number relationships
- Deeper understanding of Number Sense
On a regular basis, Christian Life School students can practice the new concept that the teacher presented during class, and review areas not yet mastered. The IXL program then provides the teacher with a detailed report of the progress that a student has made.
Combining best practice teaching that builds solid number sense foundations supported by purposeful technology will produce maximum learning in students. Strategies such as these provide a comprehensive approach to building number sense and fluency with our students.
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