The renowned educator Bruner (1966) suggested that there are three key elements in the design of effective teaching tasks, which are “Learning Expressions”, “Economy”, and “Effectiveness”. If we take these three elements as a framework and put them on a timeline, it is a good way to describe the trajectory of the work of the Central Group of Mathematics and the JDM program over the years.
Phase I (2014-2017) Development of the Foundation Module
Our students in elementary schools and junior high schools show relatively high average achievement in international mathematics assessments, but low interest and confidence, and do not find mathematics useful. Many students believe that learning mathematics is a matter of memorizing formulas and endless calculating only for exams. In order to change their cognition, JDM has set the principles of “making it fun and meaningful and give opportunities to express one’s own ideas” for designing learning activities. In order to promote meaningful learning in mathematics, the activities are designed to have a foundation for learning before the students learning the conecpt themselves, hence the name “Math Foundations Module”. Many teachers, mathematics instructors, and especially members of the Central Committee worked together to develop 175 mathematics foundational modules in 2014-2017, covering most of the mathematical concepts in the textbook units of elementary and junior high schools.
In order to make the development of the foundational modules more smooth, a “Mathematics Foundational Module Designer Training Workshop” was held from 2016-2018, hoping that through systematic training, the modules would be more complete.
Phase II (2017-2019) Development of foundation modules for the classroom
The time set for each activity of the mathematics foundation module is 90 minutes, which can be effectively used during winter and summer vacations and outside of school hours. However, since students are more receptive to the foundation activities, they naturally want to integrate them into the formal school curriculum. Given the limitation of the teaching hours of each module in the formal mathematics class, the task of developing a lesson plan for transforming the foundational activities into a “foundational classroom project” was to be developed at this stage. This was accomplished through a design workshop and a rigorous review process for nearly 100 classroom-based lesson plans.
In order to promote the modules to all primary and junior high school teachers, after the modules are designed, the modules will be selected for promotion and a video will be made for the reference of all primary and junior high school teachers.
From 2018 to 2019, we developed mathematics modules and held training workshops for classroom module designers.
Phase III (2020-2021) Development of Literacy Teaching Module
During the filming of the Foundation Advancement classroom video, people can feel the pressure of teaching literacy in the 2019 syllabus on site. Therefore, in addition to continuing the principles of the original lesson plan design, it became a further challenge to guide the teachers in the field to make minimal adjustments in order to promote students’ literacy development. As a result, JDM further revised and simplified four principles that are closer to the 2019 syllabus of literacy teaching: stimulating thinking, diagnostic learning, emotional sharing, and language evolution, as the principles for the development of the “Mathematics Foundations of Literacy Package”.
In addition, in order to support the development of the mathematics literacy package, a 21st century mathematics literacy teaching video was produced in 2021, which includes the eight thinking skills of PISA 2022 for the reference of all elementary and middle school teachers.
Phase IV (2022~) Development of Literacy Micro-courses
Development of Literacy Micro-courses
Based on the number of teachers participating in the workshops and their feedback in recent years, it can be found that the participation of teachers at the middle school level is lower than that of teachers at the elementary school level, which means that teachers at the middle school level are still under the pressure of teaching progress. The micro-courses are a series of mini-activities (4-6, 5-15 minutes each) that are integrated into formal classroom teaching to achieve the goal of developing students’ 21st century thinking skills. The purpose of the mini-activities is to make teachers willing to perform these activities under less pressure, and then gradually infiltrate into their daily teaching and develop a habit of teaching literacy.
Establishing a database of literacy assessment questions
Under the examination system of Taiwan, teachers are still most concerned about the results, which means that literacy teaching and literacy assessment need to be promoted at the same time. Thus, it is necessary to gradually build and improve a database of literacy assessment questions in the future plan. Based on the 2021 years of experience, the eight 21st century skills will be used as the framework for mathematical literacy, and the assessment questions will be developed accordingly. The assessment questions can be presented in groups of right and wrong, multiple-choice, short-answer, and expository questions, with the timing and mode of use indicated at the end of the questions so that users know how to use the questions at different times in the same situation.
Independent exploration experiment activities
Under the influence of the epidemic, the importance and necessity of online learning and teaching has increased, and even after the epidemic has passed, online learning will still be needed. On the other hand, the Mathematics Foundations Module developed in this project focuses on collaborative learning by students in physical groups, but is not conducive to providing a learning environment for students to explore independently online. Therefore, the goal of this activity is to develop experimental activities based on the Math Foundations Module, combined with multimedia learning tools, for students to explore independently. Teachers can also integrate this activity into distance learning and conduct mathematical experiments through online tutorials.
Teacher Training at Easy Thinking
Schools in remote rural areas and the ones lacking math expertise are the focus of this program. If a school makes an application, a professional instructor will be provided to conduct six hands-on workshops in a school year according to the school’s individual needs. Also, through the hands-on workshops, effective teaching and assessment cases will emerge. We will also provide a school-based math curriculum with local characteristics.