Designing creative electronic books for mathematical creativity
The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n 610467 - project M C Squared. This publication reflects only the authors views and Union is not liable for any use that may be made of the information contained therein.
Eirini Geraniou UCL Institute of Education (email@example.com)Christian Bokhove University of Southampton (firstname.lastname@example.org) Manolis Mavrikis UCL Knowledge Lab (email@example.com)
Saturday, 12th of November 2016Designing creative electronic books for mathematical creativity
Overview5 mins Introduce the MC2 project and its aims10 mins Introduce MC-squared platform, the different functionalities, tools, such as widgets15 mins Present the list of current c-books and focus on 3 c-books8 mins Show some data2 mins Share Key messagesDiscussion
AimsDesign and develop a new genre of authorable e-book, which we call 'the c-book' (c for creative)Creative Mathematical Thinking (CMT)
Initiate a Community of Interest (CoI)A community of interest consists of several stakeholders from various Communities of Practice.England, Spain, Greece, FranceWithin these, teachers who co-design and use resources for teaching, can contribute to their own professional development.Social Creativity
UK CoI: learning analytics and feedback(e.g. Fischer, 2001; Wenger, 1998; Jaworski, 2006)
MC Squared PlatformJAVA/HTML5 disclaimer C-books available Widget list
At the end, we can demo the platform:https://is.gd/bsrlm_brighton and login as guest
The environment stores student work. Separate schools can have several classes.This is the edit mode of the environment : this c-book is about planetsc-books can have several pages: each circle indicates a page. Other options are available as wellC-book pages can have random elements, like random values.Pages consist of widgets, which can range from simple text to simulations (here: Cinderella). Some widgets can give automatic feedback.http://www.mc2-project.eu
CreativitySocial creativity (SC) in the design of CMT resources (c-book units)
(b) Creative mathematical thinking (CMT) has been drawn on Guilfords (1950) model of fluency (the ability to generate a number of solutions to a problem), flexibility (the ability to create different solutions), originality (the ability to generate new and unique solutions), and elaboration (the ability to redefine a problem).
Trying to operationalize creativityGeometry example(object=quadrilaterals)Algebra example(object=expression)Create a certain object with a widget that can produce these objects. If certain is not included then (originality)Create a (certain) quadrilateralCreate a (certain) numberWe should be able to ask the widget what classes/types have been produced (fluency)From the 9 types of quadrilaterals 3 were made by the student: square, rhombus and trapezium.Different numbers or expressions were madeWe should be able to ask the widget how these classes/types were produced (flexibility)The square and rhombus were made once. The trapezium in two distinct ways.The numbers/expressions were made in very distinct waysIf the outputs are numbers they can be compared over a group of students (originality)Student was only one who made a rhombus. / Teacher submitted non original answers.Student was only one who made this expression. / Teacher submitted non original answers.Explain what you created and how you created them in your own words (elaboration)Student supplies an elaboration on the types and processes of quadrilateral making.Student supplies elaboration on the types and processes of making numbers/expressions.
Feedback as cue for creativity
Also feedback for more open tasks
Case Study Reflections c-bookWe considered CMT as (i) the construction of math ideas or objects, in accordance to constructionism that sees CMT being expressed through exploration, modification and creation of digital artefacts
(ii) Fluency (as many answers as possible) and Flexibility (different solutions/strategies for the same problem)
(iii) novelty/originality (new/unusual/unexpected ways of applying mathematical knowledge in posing and solving problems). (Daskolia & Kynigos, 2012; Papadopoulos et al. 2015; 2016) as a thinking process in a mathematical activity in order to produce a product (e.g. a solution to a mathematical problem).
Case Study - Aimsexplore the potential of the Reflection digital book and of automated feedback and reflection
focus on building bridges to the maths involved (and may be hidden) in digital resources. Bridging activities = short tasks or questions used to intervene and encourage students to reflect upon mathematical concepts and problem-solving strategies they use throughout a sequence of activities (or simple interactions) with a digital tool.
Such activities could take various forms from questions or prompts within the digital tool to paper-based worksheets or verbal teachers interventions.
Case StudyMETHODOLOGICAL TOOL: design experiment (Collins et al., 2004; Cobb et al., 2003). SAMPLE: 21 Grade-7 students and their class teacher 2 lessons in the schools computer lab. DIFFERENT ROLES: Researchers as participant observers Teacher as COI member to design the Reflections c-book, offered assistance in technical issues and ensured that all students were on task and answered the bridging activities DATA:logged answers in the MC2 platform, voice recordings of students elaborations on their interaction/answers and a student evaluation questionnaire
Case Study Reflections c-book
(A F) Excerpts from the Reflection c-book and (G) a sample solution of (F)
QuestionnaireA Likert multiple-choice questionnaire consisting of questions such as: (1) How satisfied were you after completing the c-book activities? (2) How easy to use do you think the c-book is?(3) How free did you feel to experiment with the c-book and try out your ideas? (4) I feel I understand Reflection now. Another two questions (5 and 6) gave them options to pick on their thoughts on the c-book and their preferred features. The questionnaire finished with three more questions to request suggestions from students.
Findings (Students)Language. Moving from informal terminology (the other shape moves, we have to flip the shape or count how many down from the mirror line) to using mathematical terms (the reflected church or the reflection line). Superficial responses. if you move the green shape, the orange shape moves with it.They seemed to have noticed that the 2 shapes (green and orange F) are linked, but only 2 were able to articulate that they maintain the same distance from the Reflection line. Bridging activities revealed students solving strategies and their CMT. Competition task. 3 different strategies: (i) counting boxes across and down, (ii) tilt the head so that the reflection line becomes vertical and then find the reflected image and (iii) imagine using tracing paper on the screen to find the reflected image.
QUESTIONSRESULTS(Q4) I feel I understand Reflection now. 85% (18/21) responded on with an answer above 4 in the Likert scale(Q5)-(Q6) Students thoughts on the c-book and their preferred features. 43% (9/21) said that it included problems that they would not have tried to solve.
60% (13/21) answered that it helped them see the idea of reflection in different ways.
3 students made comments that showed that they appreciate the advantages of digital technologies:the digital book help[s] because you could have actually test[ed] out your ideas and improve if its wrong or notStudents SuggestionsThey recognized the dynamicity of such resources and how seeing the immediate feedback on their actions helps them validate an answer or solution.
Findings (Teacher)Teachers keenness to use Digital Technologies was re-enforced throughauthoring activities, designing bridging activities and participating in the creation of the Reflection c-bookReflection c-book was further developedThe most notable improvement was breaking down the bridging questions to smaller questions with guidance, and using the feedback affordances to encourage the CMT aspect of flexibility in terms of the strategies. KEY MESSAGEThe c-book technology can be integrated in the mathematics classroom and promote a positive learning experience through the use of playful activities for students, matched with carefully designed bridging activities, followed by constructionist activities that allow deeper exploration of the subject matter.
ConclusionsOperationalising creativity: challengingAdded value of technology: more than the sum of the partsAuthoringWidgets with different featuresFeedbackStoring student dataDifferent people can work together in participatory design (Community of Interest) with c-books acting as boundary objectsCreative and interactive activities made by designers (creative process authoring)Collaboration within CoI between designers, teachers and computer scientists.Interactivity: feedback designMore than one widget factories usedAll student data storedSum is more than the parts
MC Squared PlatformJAVA/HTML5 disclaimerC-books availableWidget list
To demo the platform, go to:https://is.gd/bsrlm_brighton and login as guest
Thank youEirini Geranioue.firstname.lastname@example.org