- Workshop A: Design Strategies of Conceptualizing Procedural Tasks
Presenter: Alex Friedlander (Weizmann Institute of Science)
- Workshop B: The Development of a Project-Based Learning Textbook in Mathematics: Theory and Practice
Presenter:Chunxia Qi (Bejing Normal University)
- Workshop C: PreTeXt Authoring Workshop
Presenter: Rob Beezer (University of Puget Sound)
Workshop A: Design Strategies of Conceptualizing Procedural Tasks
The learning of algebraic procedures (for example, simplifying expressions and solving equations) is frequently pursued through ample and repetitive practice of the relevant algorithm. This practice usually requires lower-level thinking skills, such as memorization and replication of the steps involved in the performance of a particular procedure.
I claim that a considerable part of the practice-oriented tasks can, and should be based on higherlevel thinking skills, that are usually associated with processes of problem solving (Friedlander & Arcavi, 2012, 2017)
The Integrated Mathematics project based the learning of algebraic procedures on both standard algorithmic exercises, and tasks that require the following higher-order requirements: global comprehension, representing, divergent thinking, reversed thinking, generating examples, monitoring one’s own and others’ work, generalizing, and justifying.
The proposed workshop will have the following structure:
First, I intend to present and analyze several examples of procedural tasks from the Integrated Mathematics textbooks that involve some of the higher-order requirements mentioned above.
Next, I intend to present standard algorithmic procedural tasks, and ask the participants to apply the above-mentioned principles to design conceptually oriented procedural tasks. Some of the created tasks will be presented and discussed. The figure bellow illustrates the workshop’s intended products. The examples of conceptually-oriented tasks are taken from the Integrated Mathematics (Grade 8 Part B) textbook.
Figure: Examples of adding higher-order cognitive requirements to procedural tasks.
Friedlander, A., & Arcavi, A. (2012). Practicing Algebraic Skills: A conceptual approach. Mathematics Teacher, 105(8), 608-614.
Friedlander, A., & Arcavi, A. (2017). Tasks and Competencies in the Teaching and Learning of Algebra. Reston, Virginia: National Council of Teachers of Mathematics. Figure. Examples of adding higher-order cognitive requirements to procedural tasks.
Workshop B: The development of Project-Based Learning textbook in Mathematics: Theory and Practice
In the last decade, project-based learning (PBL) has been increasingly applied in discipline education; However, there is really few PBL application research has been applied in mathematics education. Therefore, our team have continuously conducted theoretical and practical researches on PBL application and developed PBL textbook during the past five years.
Our theoretical research mainly explored how to apply PBL philosophy in mathematics textbook and its possible effect. Firstly, we clarified the standards for implementation and evaluation of PBL textbook; Secondly, we concluded the learning model of PBL textbook; Thirdly, we clarified the application path, influence effect and challenges of PBL textbook; Fourthly we standardized the general path of project-based textbook design.
Practically, we mainly explored the textbook development and instruction of PBL. First of all, we clarified the functions and roles, general layout, as well as design principles of project-based textbook in mathematics, which provided a unified standard for the follow-up systematic design. Secondly, based on the current curriculum standards and textbooks, we systematically developed project-based mathematics textbook in middle school which has the following features: 1) design project theme based on key concepts; 2) Take the task implementation as the overt plot while the knowledge development as the covert plot; 3) Pay attention to the authenticity of situation that allowed students to immersed in; 4) Focus on the mathematical learning process and gain more experience during mathematics activity. Thirdly, we prompted a series of research to apply mathematics PBL textbook at the experiment schools. And we concluded that the PBL textbook was a very good fit for middle school students’ cognitive style and could meet their learning requirements. Moreover, it had significant positive impact not only on the development of students’ mathematical abilities in problem solving, exploring and innovation, but also on some non-intellectual perspectives, such as their learning attitudes and interests in mathematics.
As a result, we propose the following suggestions for the functions and implementation of PBL textbook in mathematics:
On one hand, PBL textbook could be used as an auxiliary form of learning material. It could be used as a mean to intervene mathematical learning process of gifted students or low learners.< br/> On the other hand, in PBL textbook development, the relationship between knowledge learning and project activities, as well as the contextualization and mathematicization of learning content should be considered. Meanwhile, it is also necessary to deal with the contradiction between PBL and standardized test, and the relationship between PBL and traditional instruction in mathematics; moreover, teacher training such, as knowledge accumulation, belief, and etc. should be strengthen.
Workshop C: PreTeXt Authoring Workshop
PreTeXt  is an authoring and publishing system, used primarily (but not exclusively) to create and dis-tribute undergraduate mathematics textbooks. There are presently about fifty textbooks authored with Pre-TeXt, mostly published with open licenses. A key part of the design is that authors create source material ina very structured form. This allows us to replicate that structure within the electronic versions produced–inways invisible to the reader, but such that it is possible to very accurately observe how a reader interacts withtheir book. See  for more details.This will be a very hands-on workshop. Participants will need to bring their Internet-connected laptopequipped with a recent Chrome or Firefox web browser. Then, each participant will author a small text-book, and by the end of the workshop simultaneously produce an online version and a print version of theirbook.Even if you do not have plans to write a textbook, or do not even know anybody else who does, this workshopwill give you a concrete introduction to the value derived by authoring scholary documents in a structuredway, and the implications for collecting data about textbook use.
 K.L. O’Halloran, R.A. Beezer, D.W. Farmer, A New Generation of Mathematics Textbook Research and De-velopment. ZDM Mathematics Education, Special Issue: Recent Advances in Mathematics Textbook Researchand Development. Gert Schubring & Lianghuo Fan (eds.), 50(2), June 2018.