Handwriting of Numerals
So what about handwriting of numerals? You may be very familiar with the research and the importance of writing letters and words by hand as it pertains to literacy. Just like students who struggle with letter formation, students who struggle with handwriting of numerals must also devote working memory to the act of forming numbers, leaving them with less working memory to devote to higher-level cognitive tasks such as addition, subtraction, multiplication, and division and the application of those operations for word problems and other mathematical tasks. If students cannot efficiently form numerals, they cannot calculate efficiently. If the student cannot write numerals automatically, speed of performing written math tasks could be very slow and math assignments may not be completed on time or accurately.
Numeral writing is one process that affects written calculation in mathematics for our students. It is one process of many, that good mathematicians have. Students also need to be able to orally produce numbers, store numbers, do quantitative operations, code written numerals into working memory quickly and accurately, name and write numerals, and retrieve math facts with accuracy and speed among other processes.
So numeral writing is just one very important component for students to be successful in mathematics. The accurate, efficient ability to write numerals by hand is considered a gateway skill along with oral counting and number identification to support the development of concepts aligned with number sense and overall math proficiency.
Berninger, V. W., Wolf, B. J., & Berninger, V. W. (2016). Teaching students with dyslexia, dysgraphia, OWL LD, and dyscalculia: Lessons from science and teaching. Baltimore, MD: Paul H. Brookes Publishing.
Codding, R. S., Volpe, R. J., & Poncy, B. C. (2017). Effective math interventions: A guide to improving whole-number knowledge. New York: The Guilford Press.
McCloskey, George (2016, September). Process Assessment of the Learner-Second Edition (PAL-II) Math Battery (Presentation slides)
The Instructional Hierarchy
Acquisition
In the acquisition stage of the instructional hierarchy, a student has begun to learn how to write numerals correctly but is not yet accurate or fluent in the skill. The goal in this phase is to improve accuracy, making sure that students are forming the numerals correctly. You will notice that as students progress in this stage, errors go down and the number of correct responses go up. In this stage, teachers actively demonstrate how to form the numbers correctly using models of correct numeral formation. Teachers use ‘think-aloud’ strategies while modeling how to write the numbers using wording about formation and directionality. Students get feedback about how they are doing and receive praise and encouragement for their effort and accuracy.
Becht, L. C. (2005). The sensible pencil: A handwriting program. Birmingham, AL: ACT Learning, LLC.
Berninger, V. W., & Richards, T. L. (2007). Brain literacy for educators and psychologists. Amsterdam: Elsevier.
Berninger, V. W., & Wolf, B. J. (2009). Teaching students with dyslexia and dysgraphia: Lessons from teaching and science. Baltimore: Paul H. Brookes Publishing.
Berninger, V.W. (2012, May-June). Strengthening the Mind's Eye. Principal, v91 n5 p28-31.
Berninger, V. W., Wolf, B. J., & Berninger, V. W. (2016). Teaching students with dyslexia, dysgraphia, OWL LD, and dyscalculia: Lessons from science and teaching. Baltimore, MD: Paul H. Brookes Publishing.
Graham, S., MacArthur, C. A., & Fitzgerald, J. (2018). Best practices in writing instruction. New York: The Guilford Press.
The Instructional Hierarchy
Fluency
In the fluency stage, students are able to write numerals accurately and legibly but work slowly. The goal of this phase is to increase the student's speed of responding. It is this accurate speed of responding writing by hand that helps to free up working memory to attend to higher-level cognitive tasks of computation and the application of those operations and procedures to word problems and other mathematical tasks. If students cannot efficiently form numerals, they cannot calculate efficiently. If the child cannot write numerals automatically, speed of performing written math tasks could be very slow and math assignments may not be completed on time or accurately.
The teacher structures learning activities to give students opportunities for active (observable) practice of writing numerals with direct repetition. Students get feedback on fluency and accuracy of performance and receive praise and encouragement for increased fluency. Fluency routines fall on a continuum of support from a teacher. These fluency practice routines are not independent practice; teachers guide the practice at each step. Generally, fluency practice can take the form of a 3-7 minute warm-up and do not replace the direct, explicit instruction that comes prior in acquisition lessons.
(Chart used with permission, Dr. Amanda VanDerHeyden)
Berninger, V. W., & Wolf, B. J. (2009). Teaching students with dyslexia and dysgraphia: Lessons from teaching and science. Baltimore: Paul H. Brookes Publishing.
Berninger, V. W., Wolf, B. J., & Berninger, V. W. (2015). Teaching students with dyslexia, dysgraphia, OWL LD, and dyscalculia: Lessons from science and teaching. Baltimore, MD: Paul H. Brookes Publishing.
McCloskey, George (2016, September). Process Assessment of the Learner-Second Edition (PAL-II) Math Battery (Presentation slides)
Trace, Copy, Cover, Compare (TCCC)
TCCC is a modification of the evidenced-based practice, Cover, Copy, Compare. In this routine, teachers scaffold students' transition from acquisition of writing numerals to fluency of writing numerals by modeling how to trace and write the numerals. Students trace the numeral with their finger and pencil, make the numerals with the model, and then cover the models and write the numeral using their mind’s eye to reproduce the number. Students also practice other numbers that they have been writing in previous fluency lessons.
Ready Set Go! and Treasure Hunt
Another example of an instructional warm-up routine is called Ready Set Go! This fluency building routine is helping students practice writing numerals in an automatic way. You will notice that this warm up fluency routine is less scaffolded than Trace, Copy, Cover Compare. Ready, Set, Go! is used after acquisition lessons have been taught and for students who are already accurate.
In another instructional warm-up, Treasure Hunt, students and teachers practice writing numerals from dictation. Number names play an important role in number retrieval from memory. Students should be asked to write numerals from dictated names without a visual model when ready. Ask students to write each of the 10 numerals, 0-9, in random numeric order, from dictation.
The Instructional Hierarchy
Generalization Stage
In the generalization stage, the student is accurate and fluent in writing numerals but does not typically use it in different situations or settings. The goal of this stage is to for the student to use the skill in the widest possible range of mathematical work. Teachers give academic tasks that require that the student use the handwriting of numerals regularly in assignments.
Students receive encouragement, praise, reinforcement for using the skill in new settings and get periodic opportunities to review and practice target skills to ensure maintenance.
Teachers can use activities that focus on students writing the missing number in a sequence, ex. 3, _, 5 or 6, 7, _, 9. In addition, to help with generalization, the teacher can ask students to write the numeral(s) that come before and after other numerals. Examples, What number comes after 7? What number comes before 5?
Berninger, V. W., & Wolf, B. J. (2009). Teaching students with dyslexia and dysgraphia: Lessons from teaching and science. Baltimore: Paul H. Brookes Publishing.
Berninger, V. W., Wolf, B. J., & Berninger, V. W. (2015). Teaching students with dyslexia, dysgraphia, OWL LD, and dyscalculia: Lessons from science and teaching. Baltimore, MD: Paul H. Brookes Publishing.