Description

Teaching objective: The aim of this e-book is to train students of mixed ability (low, typical, high) to perform fluently additions and subtractions up to 20 mentally. 

Content: This is a student's book containing strategies that are hierarchically structured in terms of pre-requisite mathematical skills as well as level of difficulty. 

Supplementary materials:Each strategy makes use of specific supplementary materials (e.g. Montessori number cards) found in the appendix, as well as using everyday authentic materials (e.g. coins, rulers, playing cards). The visual and kinesthetic activities through the use of the tangible materials as well as the embodied activities (e.g. use of fingers and toes), contained in this book, aim at understanding the relevant mathematical concepts as well as reducing the required cognitive load. As a result, students are better able to maintain in their memory the steps of the mathematical procedures that each strategy contains. 

Αnimation videos:The book is accompanied by videos in which the differentiated strategies are presented in a detailed and entertaining way through animations, making use of the corresponding supplementary materials. Thus, the student can follow and understand each strategy without having to read instructions or have the supplementary materials used. 

Structure: Each strategy is a separate module which includes: a) a short introduction (description, the supplementary materials to be used, the accompanying animation videos), b) solved characteristic examples, c) numerous worksheets of increasing difficulty, d) automatization activities, e) revision/evaluation activities. After the modules, there are specially designed activities which aim to train students to choose the optimal (easiest/ fastest /economical) addition or subtraction strategy depending on the size of the numbers used each time in order to stimulate their metacognitive skills. Finally, review assessment sheets are included which contain addition and subtraction activities that can be performed using one or more of the set of strategies presented in this book. The worksheets can be completed in digital or paper format.

Rationale: Performing mental addition and subtraction up to 20 is considered a very important skill, as students are required to overcome the first decade (10). This can be achieved at an initial stage by using forward counting in the case of addition (e.g. 14+4 = 15, 16, 17, 18) and by counting backwards in subtraction (e.g. 11-9 = 10, 9, 8, 7, 6, 5, 4, 3, 2). However, performing addition and subtraction in this way (often supported by the use of fingers) is time-consuming and very tedious for the brain, and moreover it is not appropriate for larger numbers. This book presents more advanced or superior strategies which contain less cognitive load so that they can be performed more quickly and, with training, can be both automatized and applied to operations with larger numbers. 

Audience :The different teaching approaches mentioned above are expected to meet the needs of students of mixed abilities or differently students who have different mathematical cognitive profiles enabling each student to choose the way that best suits them by compensating for their potential difficulties which may be due to either deficient learning or innate difficulties (dyslexia, dyscalculia, ADHD, autistic spectrum, borderline intelligence, etc.). On the other hand, it is also addressed to students with standard or high mathematical skills, who are looking for more advanced strategies to perform mental calculations with accuracy and speed.

Age group: This book is primarily aimed at grade 1 pupils, as the strategies contained in the e-book are related to the relevant material in the school curriculum. However, it can also be used by pupils in older grades who have difficulty in performing mental operations with numbers up to 20 (e.g. they insist on counting strategies using their fingers) or who have not automatized them. 

Acknowledgment: Several of the strategies and ideas presented in this book are derived from the RekenTrapperS teaching method developed by Anny Cooreman at Eureka Leuven School in Belgium and have been successfully implemented since 2000 as the exclusive teaching method at this school and have been adopted by other educational institutions. Dr. Giannis Karagiannakis has been collaborated as a research associate at the Eureka Leuven school and has shared with Anny Cooreman good practices in teaching mathematics.

References

Cooreman, A. & Bringmans, M. (2004).  Rekenen Remediëren: droom of haalbare kaart?Antwerpen: Uitgeverij De Boeck, 147 en 153. 

Cooreman, A. (2015). Rekentrappers 3HR module 2 Getalkaarten, buren en strategisch rekenen tot 1000. EurekaExpert, 5-7, 9, 17.

Karagiannakis, G. (2018). Οι αριθμοί πέρα απ’ τους κανόνες: Προλαβαίνοντας τις δυσκολίες στα Μαθηματικά. Αθήνα: Πεδίο.

Nöel, M-P. & Karagiannakis, G. (2022). Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics: Perspectives from Cognitive Neuroscience. London: Taylor & Francis Ltd.