eLearning Mathematics – key points from the research.

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In an attempt to get a better grounding in the challenges facing the implementation of eLearning in schools, I have done much reading. Most of it has resonated with my own experiences both in the classroom and in the wider school community. In particular, I have been interested in the specific challenges that Mathematics teachers face in embracing technological advances which, at first glance, seem to have very little to offer their teaching.

The following points are ideas/outcomes/realities that appear to me to be universal in relation to implementing eLearning components into the Mathematics curriculum:

1. Implementing technology-rich mathematical tasks into the classroom is difficult.

While technology has potential to improve the teaching and learning of mathematics, research indicates that teachers struggle in their efforts to implement technology-rich mathematical tasks in their classrooms. Effective technology integration in mathematics requires teachers to be able to apply their classroom knowledge related to mathematics content, pedagogies, educational technologies and the interplay between those aspects of knowledge.

Schools that have successfully overcome this challenge have, typically, had three aspects that I could identify as similar:

– ICT Leaders were not Administrators but Classroom Teachers with a fractional time allowance for the responsibility role. This structure allowed the role to ‘straddle’ the Admin/Teacher divide, resulting in in-class demonstrations of effective ICT use for other teachers to observe and model.

– ICT Leaders identified early adopters who, although not necessarily technologically literate, were keen to try new things. These individuals exuded a positive attitude toward the change process, assisting in implementation. These early adopters also participated in internal Professional Development opportunities, offered to all Mathematics teachers to assist in overcoming the challenges of the change.

– ICT leaders also removed editing rights to current intranet systems and mandated authentication to new models or systems. For example, all Mathematics staff were required to ensure students had – and used – logins to the Mathletics site, whilst traditional paper homework books were no longer on the student book list.

2. Web-based homework outperforms paper-based homework.

In mathematics, homework offers an important opportunity for students to practice the procedural aspect of computation, particularly in the middle years when fundamental concepts are being taught. Student motivation to attempt, complete or extend upon this homework is, however, a consistent challenge for Mathematics teachers. Whilst there are many methods for addressing the challenge (Flipped Classrooms are just one example) of homework, research into web-based homework (WBH) has been shown that students were more likely to attempt and to receive higher homework grades with WBH than with Pen-Paper Homework (PPH).

In addition to this, studies indicated  that when students were divided based on incoming math skill level, the analysis showed that low-skilled students who used online homework exhibited significantly higher mathematical achievement than low-skilled students who used textbook homework. In another study, students who were given WBH often took the opportunity to complete 2nd, even 3rd attempts. Students who completed traditional methods rarely attempted the task for a second time and never for a third.

Within the WBH group of a third study, while male  students gained  more  confidence  than females,  females expressed  stronger opinions  on the fact  that  instant scores  and feedback  helped  them  overcome  difficulties  in  mathematics  problem -solving.  Though some  limitations  still  exist  with written  explanations  and  partial  credits,  in  comparison  with the  traditional  assessment,  the  web-based  assessment  and practice  tool  in  this  study  substantially  helped  students  build motivation  and  elevates  the  meaning  of  learning  and  doing mathematics with the use of web-based  technology.

3. Technology itself does not improve student outcomes.

A common belief – and excuse for not embracing technology in the classroom – is that it has no direct impact on student outcomes in standardized testing regimes. This belief is actually supported by research such as Bonham, Deardorff & Beichner (2003), Cole & Todd (2003) and Smith & Ferguson (2005).

Interestingly, however, each of these studies also identified that the integration of new technologies, web-based homework (with its’ associated feedback – see point 4) and online delivery methods increased student motivation to complete tasks both in and out of class. In particular, it was noted by Tzu-Hua Wang in his research that the use of dynamic web-based technologies – technologies that provided instantaneous, graduated, feedback with adaptive question sequences – resulted in students who were most lacking in mathematical problem-solving knowledge achieving significantly improved results.

Until the standardized testing regime that students currently experience at all levels of their education evolves, Mathematics Teachers are going to grapple with the dual challenges of a cohort that require greater involvement of technology to motivate them and an assessment program that requires 20th Century competencies. To overcome these challenges, teachers will need to develop learning tasks that incorporate the ‘best of both worlds’.

4. Technology-based delivery provides more regular, and timely, feedback on performance.

Regular, timely feedback is fundamental. John Hattie, in his meta-analysis of over 800 research studies, found that feedback had the greatest effect size on student academic outcomes. In mathematics, this comes as no surprise. Students flourish when they are able to experience success in their work. Mathematics that is delivered in a web-based format allows for this type of functionality and can provide the richest growth to students’ understandings.

5. Students are more willing/able to self-direct learning and adapt mathematical strategies online.

Mathematics is a unique subject area in that it encompasses abstract thinking, requires sequential development of concepts, has a need for instructor modelling of problem-solving, has many visual-spatial components and has a unique set of symbols and notation. All of these areas are relevant to Mathematics Teachers whether they are online or offline.

As discussed by Gordon-Smith, Torres-Ayala & Heindel, eLearning instructional design in Mathematics requires that all of the above areas be addressed. Only in very recent years have students and teachers of Mathematics had the ability to develop and access technology that can do these things. The results are – in my honest opinion – truly revolutionary. Khan Academy, Purplemath, Microsoft Mathematics 4.0, Maths Online are all resources that have been developed to specifically cover the unique areas of Mathematics content. These resources allow students to broaden the ‘experts’ that they utilize in understanding a concept. No longer is the teacher the only ‘Sage on Stage’ – much of the information that the student requires can be accessed on YouTube – when and where they need it.

As technology advances in its’ ability to do more, students are demonstrating a greater willingness (or ability?) to diversify the strategies that they use to problem-solve mathematical problems. This ability is seen in regular video game usage. The idea that students attention spans are adversely affected by the use of video games flies in the face of the evidence – parents around the globe will support this! – of students playing online games for hours on end. This type of engagement, even in the situation of repeated ‘failure’, shows students adapting their strategies to achieve a desirable end result. In part this works because, as these authors attest, students feel that they are not being judged on their responses, nor are there real world consequences.

 

These points are by no means comprehensive in their detail but rather, they identify and articulate the key challenges facing all educators who are looking to integrate eLearning components into their Mathematics teaching.

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