Mathematical Proficiency

The mathematics curriculum during elementary school in Sweden has many components, but there is a strong emphasis on concepts of numbers and operations with numbers. From an international perspective, mathematics knowledge is defined as something more complex than concept of numbers and operations with numbers. Kilpatrick et al. (2001) argue for five strands which together build students’ mathematical proficiency. The five strands provide a framework for discussing the knowledge, skills, abilities, and beliefs that constitute mathematical proficiency. In their report they discuss,

1. Conceptual understanding is about comprehension of mathematical concepts, operations, and relationships. Students with conceptual understanding know more than isolated facts and methods. Items measuring conceptual understanding are for instance: “Your number is 123.45. Change the hundreds and the tenths. What is your new number?

2. Procedural fluency refers to skills in carrying out procedures flexibly, accurately, efficiently, and appropriately. Students need to be efficient in performing basic computations with whole numbers (e.g., 6+7, 17–9, 8×4) without always having to refer to tables or other aids.

3. Strategic competence is the ability to formulate, represent, and solve mathematical problems. Kilpatrick et al. (2001, p.126) give the following example of item testing strategic competence: “A cycle shop has a total of 36 bicycles and tricycles in stock. Collectively there are 80 wheels. How many bikes and how many tricycles are there?”

4. Adaptive reasoning refers to the capacity for logical thought, reflection, explanation, and justification. Kilpatrick et al. (2001) gives the following example where students can use their adaptive reasoning. “Through a carefully constructed sequence of activities about adding and removing marbles from a bag containing many marbles, second graders can reason that 5+(–6)=–1. In the context of cutting short bows from a 12-meter package of ribbon and using physical models to calculate that 12 divided by 1/3 is 36, fifth graders can reason that 12 divided by 2/3 cannot be 72 because that would mean getting more bows from a package when the individual bow is larger, which does not make sense” (p.130).

5. “Productive disposition is the habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy” (Kilpatrick et al., 2001, p.5). Items measuring productive disposition are for instance: “How confident are you in the following situations? When you count 8-1=___+3 (completely confident, confident, fairly confident, not at al confident).”

Teaching Approaches Affecting Student Learning

The influence of the learning environment upon knowledge development has received relatively little attention in the field of mathematics teaching and learning (Boaler, 1999; Samuelsson, 2008). Even so, teachers often expect researchers to provide that kind of knowledge in mathematics didactics.

What happens in the classroom has an impact on students’ opportunity to learn. The activities in the classroom, the repeated actions in which students and teachers engage as they learn are important because they constitute the knowledge that is produced (Cobb, 1998). There is some evidence that different teaching styles can have different impacts on student achievement (Aitkin & Zukovsky, 1994) and that the choice of teaching approaches can make an important difference in a student’s learning (Wentzel, 2002). The synthesis of meta-analysis and reviews of Teddlie and Reynolds (2000) gives evidence for positive relationships between achievement and varied classroom settings. Case (1996) argues that a variation of teaching methods is important because different teaching methods draw attention to different competencies in mathematics (e.g. Boaler, 2002; Samuelsson, 2008). Thus, the mode of teaching method in mathematics seems to be important for students’ development of mathematical proficiency.

There are very few studies focusing on how different teaching methods affect students’ calculation and conceptual understanding as well as self-regulated learning skills, but there are several studies that focus on closely related areas.

For learning in general, Granström (2006) shows that different teaching approaches in classrooms influence the outcomes for students in different ways. Settings where students are allowed and encouraged to cooperate with classmates and teachers give the students more opportunities to understand and succeed. Similarly, Oppendekker and Van Damme (2006) stress that good teaching involves communication and building relationships with students. Boaler (1999, 2002) reports that practices such as working through textbook exercises or discussing and using mathematical ideas were important vehicles for the development of flexible mathematical knowledge. One outcome of Boaler’s research was that students who had worked in textbooks performed well in similar textbook situations. However, these students found it difficult to use mathematics in open, applied or discussion-based situations. The students who had learned mathematics through group-based projects were more able to apply their knowledge in a range of situations. Boaler’s research gives evidence for the theory that context constructs the knowledge that is produced.

In a review of successful teaching of mathematics, Reynolds and Muijs (1999) discuss American as well as British research. A result of their review is that effective teaching is signified by a high number of opportunities to learn. Opportunity to learn is related to factors such as length of school day and year, and the amount of hours of mathematics classes. It is also related to the quality of classroom management, especially time-on-task. According to research in the area, achievement is improved when teachers create classrooms that include (a) substantial emphasis on academic instruction and students’ engagement in academic tasks (Brophy & Good, 1986; Griffin & Barnes, 1986; Lampert, 1988; Cooney, 1994), (b) whole-class instruction (Reynolds & Muijs, 1999), (c) effective question-answer and individual practices (Brophy, 1986; Brophy & Good, 1986; Borich, 1996), (d) minimal disruptive behaviour (Evertsson et al., 1980; Brophy & Good, 1986; Lampert, 1988; Secada, 1992), (e) high teacher expectations (Borich, 1996; Clarke, 1997), and (f) substantial feedback to students (Brophy, 1986; Brophy & Good, 1986; Borich, 1996). Aspects of successful teaching are found in a traditional classroom (lecturing and drill) with one big exception- in successful teaching, teachers are actively asking a lot of questions and students are involved in a class discussion. With the addition of active discussion, students are kept involved in the lesson and the teacher has a chance to continually monitor students’ understanding of the concept being taught.

On the other hand, negative relationships have also been found between teachers who spend a high proportion of time communicating with pupils individually and students’ achievement (Mortimer et al., 1988; OfSTED, 1996). Students’ mathematics performances were low when they practiced too much repetitive number work individually (OfSTED, 1996). A traditional direct-instruction/active teaching model seems to be more effective than a teaching model that focuses on independent work.

Another teaching model discussed in the literature is the one dependent on cooperative, small-group work. The advantage of problem-solving in small groups lies in the scaffolding process whereby students help each other advance in the Zone of Proximal Development (Vygotsky, 1934/1986). Giving and receiving help and explanations may widen students’ thinking skills, and verbalising can help students structure their thoughts (Leiken & Zaslavsky, 1997). The exchange of ideas may encourage students to engage in higher-order thinking (Becker & Selter, 1996). Students who work in small groups are developing an understanding of themselves and learning that others have both strengths and weaknesses. Programmes that have attempted problem-solving in small groups as a teaching method report good results, such as improved conceptual understanding and higher scores on problem-solving tasks (Goods & Gailbraith, 1996; Leiken & Zaslavsky, 1997).

Samuelsson (2008) used a split-plot factorial design with group (i.e., traditional, independent work, and problem-solving) as a between-subject factor and time (i.e., before and after a 10 week intervention) as a within-subject factor. In that design, traditional approach means that teacher explained methods and procedures from the chalk board at the start of the lessons, and the students then practice with textbook questions. Independent work means that students work individually on problems from a textbook without a teacher’s introduction to the lesson; teachers just helped students who asked for it. Problem solving means that students were introduced to different ideas and problems that could be investigated and solved using a range of mathematical methods. Students worked in groups of four, and they discussed and negotiated arithmetic issues with each other and with the teacher, both in groups and in whole-class discussions. There were a total of seven dependent variables in the study. There were three measures of mathematics abilities; that is, a total score of mathematics ability, calculation, and conceptual understanding. Measures related to self-regulated learning skills such as internal and instrumental motivation, self-concept, and anxiety were also used as dependent variables. The results showed that there are no significant interaction effects between group and time according to total arithmetic ability and calculation. However, differences in students’ progress in conceptual understanding may be explained by the teaching method. Traditional work as well as problem-solving seems to have more positive effects on students’ development of conceptual understanding than independent work does.

To develop aspects of self-regulated learning skills, teachers, according to Samuelsson (2008), would be advised to use traditional work or problem-solving. Problem solving appears to be more effective in developing students’ interest and enjoyment of mathematics than does traditional work or independent work. Also traditional work and problem-solving are more effective than independent work for students’ self-concept.

Thus, different teaching methods also seem to influence students’ self-regulated learning skills (interest, view of the subject’s importance, self-perception, and attribution) (Boaler, 2002). Students who were expected to cram for examinations describe their attitudes in passive and negative terms. Those who were invited to contribute with ideas and methods describe their attitudes in active and positive terms that were inconsistent with the identities they had previously developed in mathematics (Boaler, 2002). A negative attitude towards mathematics can be influenced, for instance, by too much individual practice (Tobias, 1987) as well as by teachers who reveal students’ inabilities. Students who do well in school (Chapman & Tunmer, 1997) demonstrate appropriate task-focused behaviour (Onatsu-Arvillomi & Nurmi, 2002), and they have positive learning strategies. If the students are reluctant in learning situations and avoid challenges, they normally show low achievement (Midgley & Urdan, 1995; Zuckerman, Kieffer, & Knee, 1998).

As a result, the choice of teaching method not only affects mathematics achievement but also students’ self-regulated learning skills.

Why develop e-learning?

Many organizations and institutions are using e-learning because it can be as effective as traditional training at a lower cost.

Developing e-learning is more expensive than preparing classroom materials and training the trainers, especially if multimedia or highly interactive methods are used. However, delivery costs for e-learning (including costs of web servers and technical support) are considerably lower than those for classroom facilities, instructor time, participants’ travel and job time lost to attend classroom sessions.

Moreover, e-learning reaches a wider target audience by engaging learners who have difficulty attending conventional classroom training because they are:

>> geographically dispersed with limited time and/or resources to travel;

>> busy with work or family commitments which do not allow them to attend courses on specific dates with a fixed schedule;

>> located in conflict and post-conflict areas and restricted in their mobility because of security reasons;

>> limited from participating in classroom sessions because of cultural or religious beliefs;

>> facing difficulties with real-time communication (e.g. foreign language learners or very shy learners).

E-learning can offer effective instructional methods, such as practising with associated feedback, combining collaboration activities with self-paced study, personalizing learning paths based on learnersf needs and using simulation and games. Further, all learners receive the same quality of instruction because there is no dependence on a specific instructor. Some questions to ask when choosing among e- learning, face-to-face instruction or other types of informal or on-the-job learning include:

>> What is the relative cost of each type of training?

>> Is learning best delivered in one unit or spread out over time?

>> Does it address a short-term or a long-term learning need?

>> Do participants have access to needed computer and communications equipment?

>> Are participants sufficiently self-motivated for e-learning or self-study modes of learning?

>> Do target participantsf time schedules and geographic locations enable classroom.based learning or other types of synchronous learning?

Can e-learning be used to develop any type of skill?

A training program may aim at developing different types of skills:

>> cognitive skills, which can involve knowledge and comprehension (e.g. understanding scientific concepts ), following instructions (procedural skills), as well as applying methods in new situations to solve problems (thinking or mental skills);

>> interpersonal skills (e.g. skills involved in active listening, presenting, negotiating, etc.); as well as

>> psychomotor skills, involving the acquisition of physical perceptions and movements (e.g. making sports or driving a car).

How can e-learning address these diverse domains?

Most e-learning courses are developed to build cognitive skills; the cognitive domain is the most suitable for e-learning. Within the cognitive domain, thinking skills may require more interactive e-learning activities because those skills are learned better “by doing”. Learning in the interpersonal domain can also be addressed in e-learning by using specific methods. For example, interactive role playing with appropriate feedback can be used to change attitudes and behaviours.

E-learning is a good option when…

>> there is a significant amount of content to be delivered to a large number of learners;

>> learners come from geographically dispersed locations;

>> learners have limited mobility;

>> learners have limited daily time to devote to learning;

>> learners do not have effective listening and reading skills;

>> learners have at least basic computer and Internet skills;

>> learners are required to develop homogeneous background knowledge on the topic;

>> learners are highly motivated to learn and appreciate proceeding at their own pace;

>> content must be reused for different learners’ groups in the future;

>> training aims to build cognitive skills rather than psychomotor skills;

>> the course addresses long-term rather than short-term training needs;

>> there is a need to collect and track data.

Since e-learning is ideal help for all purposes, that it will enhance the facet of classroom training completely in an organization. The most cost-effective application of e-learning may be to complement conventional training in order to reach as many learners as possible.

E-LEARNING : DEFINITION, SCOPE, TRENDS, ATTRIBUTES

E-learning is commonly referred to the intentional use of networked information and communications technology in teaching and learning. A number of other terms are also used to describe this mode of teaching and learning. They include online learning, virtual learning, distributed learning, network and webbased learning. Fundamentally, they all refer to educational processes that utilize information and communications technology to mediate asynchronous as well as synchronous learning and teaching activities. On closer scrutiny, however, it will be clear that these labels refer to slightly different educational processes and as such they cannot be used synonymously with the term e-learning. The term e-learning comprises a lot more than online learning, virtual learning, distributed learning, networked or web-based learning. As the letter “e” in e-learning stands for the word “electronic”, e-learning would incorporate all educational activities that are carried out by individuals or groups working online or offline, and synchronously or asynchronously via networked or standalone computers and other electronic devices.

Individualized self-paced e-learning online refers to situations where an individual learner is accessing learning resources such as a database or course content online via an Intranet or the Internet. A typical example of this is a learner studying alone or conducting some research on the Internet or a local network.

Individualized self-paced e-learning offline refers to situations where an individual learner is using learning resources such as a database or a computer-assisted learning package offline (i.e., while not connected to an Intranet or the Internet). An example of this is a learner working alone off a hard drive, a CD or DVD. 

Group-based e-learning synchronously refers to situations where groups of learners are working together in real time via an Intranet or the Internet. It may include text-based conferencing, and one or two-way audio and videoconferencing. Examples of this include learners engaged in a real-time chat or an audio-videoconference. Group-based e-learning asynchronously refers to situations where groups of learners are working over an Intranet or the Internet where exchanges among participants occur with a time delay (i.e., not in real time). Typical examples of this kind of activity include on-line discussions via electronic mailing lists and text-based conferencing within learning managements systems.

The growing interest in e-learning seems to be coming from several directions. These include organizations that have traditionally offered distance education programs either in a single, dual or mixed mode setting. They see the incorporation of online learning in their repertoire as a logical extension of their distance education activities. The corporate sector, on the other hand, is interested in e-learning as a way of rationalizing the costs of their in-house staff training activities. E-learning is of interest to residential campus-based educational organizations as well.

They see e-learning as a way of improving access to their programs and also as a way of tapping into growing niche markets. The growth of e-learning is directly related to the increasing access to information and communications technology, as well its decreasing cost. The capacity of information and communications

technology to support multimedia resource-based learning and teaching is also relevant to the growing interest in e-learning. Growing numbers of teachers are increasingly using information and communications technology to support their teaching. The contemporary student population (often called the “Net Generation”, or “Millennials”) who have grown up using information and communications technology also expect to see it being used in their educational experiences (Brown, 2000; Oblinger, 2003; Oblinger and Oblinger, 2005). Educational organizations too see advantages in making their programs accessible via a range of distributed locations, including oncampus, home and other community learning or resource centers.

Despite this level of interest in e-learning, it is not without constraints and limitations. The fundamental obstacle to the growth of e-learning is lack of access to the necessary technology infrastructure, for without it there can be no e-learning. Poor or insufficient technology infrastructure is just as bad, as it can lead to unsavory experiences that can cause more damage than good to teachers, students and the learning experience. While the costs of the hardware and software are falling, often there are other costs that have often not been factored into the deployment of e-learning ventures. The most important of these include the costs of infrastructure support and its maintenance, and appropriate training of staff to enable them to make the most of the technology.

A key attribute of information and communications technology is its ability to enable flexible access to information and resources. Flexible access refers to access and use of information and resources at a time, place and pace that is suitable and convenient to individual learners rather than the teacher and/or the educational organization. The concept of distance education was founded on the principles of flexible access (Willems, 2005). It aimed to allow distance learners, who were generally adult learners in full or part-time employment to be able to study at a time, place, and pace that suited their convenience. The goal of distance education was to free these learners from the constraints of conventional residential educational settings. They would not be required to live or attend lectures in locations away from where they may be living and working. The printed distance study materials, which each distance learner received, would carry the core subject matter content they would need including all their learning activities and assessment tasks. Students would be required to complete these tasks, submit their assignments and take their examinations within a set time frame. While these printed study materials allowed distance learners a great deal of freedom from time, place and pace of study, it had its limitations. For one thing, non-printed subject matter content and simulations etc. could not be easily represented in print form. 

Access to information and communications technology changed all that as it offered a range of possibilities for capturing and delivering all types of subject matter content to learners and teachers in distributed educational settings. This meant access to subject matter content and learning resources via networked information and communications technologies across a range of settings such as conventional classrooms, workplaces, homes, and various forms of community centers (Dede, 2000; 1996). Contemporary educational institutions, including conventional distance education providers, often pride themselves in being able to meet the learning needs of their students and staff at a time, place and pace that is most convenient to them. They have been able to do this with the help of information and communications technologies which afford learners access to upto- date information as and when they need them, and also the opportunity to discuss this information with their peers and teachers at their convenience. This is becoming increasingly affordable and palatable with a wide range of software applications and computer conferencing technologies for collaborative inquiry among students and asynchronous discussion (see Edelson, Gordin, & Pea, 1999; Edelson & O'Neill, 1994). These applications enable learners and teachers to engage in synchronous as well as asynchronous interaction across space, time, and pace (Gomez, Gordin & Carlson, 1995; Gordin, Polman & Pea, 1994; Pea, 1994).

Implications for Instructional Design on the Potential of the web and e-Learning

Although the training and development and higher education environments lead K-12 schools in embracing

distance learning technologies there is modest growth in distance education efforts in the K-12 environment,

and the steady rate at which distance learners are enrolling emphasizes the importance of this population (Saba, 2005). In many ways, this uncharted territory offers some of the most exciting challenges to be found in distance education today.

While online learning in K-12 schools is addressing previously unmet needs, it is also making headlines. Policy issues include funding of online learning programs and general resistance to distance learning. Online

learning is often not understood by policymakers resulting in the application of policies developed for physical schools to online programs (Rice, 2006). State governments typically establish virtual K-12 schools directly or provide funding to traditional schools to create online programs. Equivalent funding of online and face-to-face courses implies the instruction delivered is equally effective—an invalid comparison and potentially dangerous assumption as rapid changes in the field of online learning may not result in high quality programs (Conceição & Drummond, 2005). Quality indicators used to measure the success of online programs are similar to those used with traditional K-12 programs including academic performance, retention, academic achievement, and satisfaction (Ronsisvalle & Watkins, 2005). However, Rice (2006) suggested that the effectiveness of distance education has more to do with who is teaching, who is learning, and how that learning is accomplished and less to do with the medium. Distance education in the K-12 arena

is often referred to as “virtual schooling” and learning through virtual schooling is one of the fastest growing areas for K-12 schools (Roblyer, 2006). Virtual schools offer distance education courses in basically two formats: site-based—part of a traditional brick and mortar school—and virtual high school/charter schools—typically non-site based.

Some states, school districts, and local administrators see site-based distance education as a viable option for choice. Mupinga (2005) identified current teacher shortages and overcrowded schools as two motivational factors for the rise in sitebased distance education. Rather than hire new teachers, some rural schools offer online courses, allowing highly qualified teachers to instruct students in locations where teaching shortages exist. With student populations increasing faster than new facilities can be built, distance education classes are one option states are using to serve students without the capital expenses required to build new schools (Ronsisvalle & Watkins, 2005). In addition to teacher shortages, O’Dwyer, Carey, and Kleiman (2007) suggested the need to broaden the variety of courses offered by schools as a reason schools implement online courses. Expanding curricular offerings through online courses may include advanced, remedial, elective, or credit-recovery courses. Ideally, by offering online courses, a small school can provide rich and varied options normally available only at larger schools (Pape, 2005).

There are other benefits to sitebased distance education. Benefits for administrators include the option of ensuring course content is aligned to standards and providing resources to high-risk students. Teachers benefit by having potentially greater contact with students who are not normally communicative in a face-to-face classroom. Benefits for parents include being able to see assignments, resources, and readings available to their child. Learners benefit by having access to all the tools for success available in one setting, being able to review and practice as needed, and going at their own pace (Abram, 2005).  

Most of the emphasis on virtual schooling is at the high school level (Mupinga, 2005). Online high schools are often state-centered initiatives established to expand course offerings and meet the needs of certain student populations. Some online high schools allow students to take courses from home while others require students to take courses in monitored computer labs supervised by teachers or facilitators. A more controversial example of K- 12 online learning is virtual charter schools, which offer distance education to public school students while operating independently of local school districts. Huerta, d’Entremont, and González (2006) identify two forms of virtual charter schools that have developed: home-school and cyber-charter. Home-school charter schools require parents to serve as the primary educator while cyber-charter schools offer computer-based learning either synchronously or asynchronously with teachers filling the role of educational facilitator. In some instances, online programs are now enabling home-schooled students to receive a publicly-funded education in the home environment. Both forms have attracted large numbers of students, impacting the budgets of local districts.

The trends discussed above have at least four potentially profound impacts on the field of ID. These effects concern the student or learner population, research-based approaches, lack of trained professionals, and organizational change. Perhaps the biggest concern is the student. Distance education initiatives may serve the least homogenous group of learners of any other modality or learning environment. We fear that distance education may become little more than a “dumping ground” for credit recovery as well as a repository for those unable or unwilling to function in the more traditional classroom environment (Ronsisvalle & Watkins, 2005). This represents a vast underutilization of an incredibly promising educational medium; it is also the exact opposite population the research says tends to thrive in the distance environment (Kachel, Henry, & Keller, 2005; Sharp & Huett, 2006). K-12 distance education learners include students who have social commitments, are being home-schooled, live in rural areas, are hospitalized, are homebound, who require flexible hours for employment, are incarcerated, who want to enrich their education, are traveling, have difficulty in regular classrooms, or are in need of courses not offered during the regular school day (Mupinga, 2005; Rice, 2006; Ronsisvalle & Watkins, 2005). This brings with it a host of issues that have to be taken into account when considering instructional design parameters for this audience.

Although K-12 students can benefit from the independence offered by virtual schooling, this same independence has the potential for negative impact. While synchronous courses offer real-time interaction with the teacher and, potentially, with peers, a course taught predominantly through asynchronous instruction may offer few opportunities for personal interaction. Like classroom schooling, virtual schooling must address student-related issues including a feeling of isolation and concerns about social development that may exceed classroombased instruction (Cavanaugh, Gillian, Kromrey, Hess, & Blomeyer, 2004). In addition, virtual learning potentially has some specific audience issues. Personal and psychological characteristics of successful online learners include autonomy, metacognition, self-regulatory skills, positive self-efficacy, motivation, and internal locus of control (Cavanaugh et al., 2004; Ronsisvalle & Watkins, 2005). The development of many of these characteristics is age-dependent, raising the possibility that younger students may be less successful online learners. Cavanaugh et al. (2004) stated that younger students require more supervision, simpler instructions, and a more extensive reinforcement system than older students. The question of how effective distance learning can be with younger students has yet to be addressed. The amount of independence given to younger students, the use of synchronous versus asynchronous instruction, the characteristics required of a successful young distance learner, and the technology best used to deliver materials to younger learners are all areas that need further research. Instructional designers bring a much needed and research based perspective on how learners learn to this diverse audience. Ideally, ID professionals would play a key role in researching and designing K-12 distance education environments to carefully accommodate diverse learners with varying degrees of maturity.

We have become a bit cynical in our view that, K-12 educational personnel who always seem to seek out the “magic elixir” that cures all ills, will embrace distance education as the latest in a long line of perfect solutions. ID professionals, perhaps in partnership with academic researchers, can play a key role in making sure that distance education initiatives truly serve the needs of students. Instructional designers must stay on top of the current research and be able to defend decisions regarding who should and should not enroll in the available distance education offerings and promote designs that have the capability to serve the targeted student population. In this way, instructional designers are protecting students by promoting solid distance learning practices based on research and theory. Unfortunately, little research currently exists to inform decisions about online learning in K-12 schools. Instructional designers are uniquely qualified to help fill this research gap. Few high-quality, evidence-based research studies have examined the effectiveness of online learning at the high school level compared to faceto- face instruction, with even fewer studies examining curriculum-specific interventions (Conceição & Drummond, 2005; O’Dwyer et al., 2007).

The majority of research on student success in online courses has been conducted in higher education settings (O’Dwyer et al., 2007; Ronsisvalle & Watkins, 2005). How this research translates to the K-12 setting is unknown. Cavanaugh et al. (2004) caution against applying the findings of higher education research in distance education to the K-12 setting, adding that K-12 distance education is fundamentally unique. ID professionals are needed to direct research concerning which distance education learning models work best with certain groups of students. Finally, the majority of K-12 distance education research has been conducted in grades 6-12. The effectiveness of online learning for all grade levels is, at best, unclear. K-12 instructional designers for distance education need to be aware of the lack of a clear research agenda and the controversies surrounding this new delivery medium. ID professionals have an exciting opportunity to guide the development of K-12 distance education to make sure that the needs of learners are met.

As with research in adult distance education, studies in the K-12 setting focus primarily on comparisons of student achievement in online versus face-to-face courses. The popularity of studies comparing distance courses with face-to-face instruction stems from the longstanding curiosity about the legitimacy of distance education as an alternative to traditional settings (Bernard et al., 2004). Comparison studies in both higher education and K-12 environments appear to show no significant difference based on the delivery medium. Cavanaugh et al. (2004) completed a meta-analysis reviewing web-delivered K-12 distance education programs and found that student achievement was similar between online courses and classroom based courses.

We agree with the suggestion by Bernard et al. (2004) that the need for studies comparing distance education with traditional classroom instruction is nearing its end. ID professionals should begin to direct a research agenda involving comparisons within distance education environments. A review of existing K-12 distance education literature by Rice (2006) supported this assertion, adding that distance education research should move beyond comparative studies to focus on the factors that ensure successful teaching and learning. In general, the requirements of non-traditional settings, like online learning environments, have received only a small amount of research and are not well understood. The systems thinking of an instructional design researcher could be invaluable in the investigation of these models. There are also issues concerning evaluation. Already, it is clear that issues of quality and assessment are as critical in distance education as in traditional forms of education, but nontraditional programs often must prove their worth in ways not expected of mainstream schools. The instructional design perspective can inform evaluation strategies to ensure that naïve questions about technology and online educational delivery are not the primary ones being asked.

What we are witnessing with the current evolution of distance education and the technologies that support it is nothing less than the single most important reorganization of how we will engage learners since we started to gather students together in school buildings. If schools are going to make a commitment to deliver education in this format, it will require a restructuring of how they do business, necessitating the hiring of distance education instructional designers to work with teachers and the local district. ID professionals would bring a much needed awareness of sound distance education design to the process. Since, in the U.S., K-12 schooling is primarily a state and local enterprise, structures needed to achieve a costeffective scale for online learning are only beginning to emerge (most often in the form of regional and statewide consortia, with some private-sector activity). In those few cases where a curriculum has gained national recognition (such as Advanced Placement or International Baccalaureate courses), we are beginning to see national offerings as well. However, it is unclear if the economies of scale promised by e-learning will ever be substantial in the  K- 12 context beyond a variety of niche applications such as those mentioned above. It may be that countries with national curricula will see these benefits long before the other does.

Is e-learning (and the technologies that support it) truly a breakthrough or is it only the latest “miracle” which

promises solutions to all the problems associated with education and training? Clearly, our society loves simple answers to complex problems—especially if those answers require little or no effort. It is impossible to deny the benefits and ubiquity of the Internet. Yet the history of education is a history of so-called advances and new ideas which fail to hold up to scrutiny over time. Rushing to adopt distance education, or any new technology, to avoid being seen as out of touch or outdated certainly is as ephemeral as most fads. We agree with those who argue that education and training are costly endeavors that are not presently serving our schools, our business organizations, or our society well. We need training and educational solutions, and e-learning holds out promise. Unfortunately, much of real promise is buried under the hyperbole of a quick fix, much like a TV commercial that makes exaggerated claims of losing weight while one sleeps. While some may view this as a cynical opinion, our view for the future is actually quite positive: We just need to choose to view e-learning as the question rather than the answer.

In short, the Internet and e-learning make wonderful things possible if we decide, as educators and trainers, to exploit those possibilities intelligently and systematically. The multitude of possibilities outlined in this three part series illustrate that there are opportunities to evolve and to grow the field of instructional design in many directions. At the same time, however, researchers and practitioners are facing such a demand for their talents that getting the support and the time for disciplined research and theory building is often extremely difficult. This makes for tricky but exciting challenges.

For instructional design and technology, this is “stand and deliver” time. Professionals in the field are finally getting their chance to make good on the visions of learning transformed by technology. However, we have neither unlimited time nor unlimited resources to prove our worth to the current leaders aggressively advocating the use of technology in training and education. If the expectations of the public and policy makers are not realized, it will not matter which learning theory, design methodology, academic program, or software company did or did not succeed. The credibility of technology as a transformative force will be damaged. It is incumbent upon all professionals with a commitment to the potential of technology in education and training, no matter what their theoretical or ideological bent, to think outside the box, to collaborate and to advance the common vision. As much as our understanding of technology in education and training has developed over the past 40 years, we still understand only a small fraction of what is required to transform the craft of instructional technology and design into an engineering or science-style discipline. Given the challenges we face, practitioners in the field have little time for ideological bickering about various theoretical positions. No single  line of research can possibly lay a unique claim to ultimate wisdom and understanding. There is much to be accomplished and little time to accomplish it. Let us proceed then, together, with the hard work of building a cumulative and unified base of knowledge for e-learning and the field of instructional design.

ADDIE - The Instructional Design Process

The Five Steps

The ADDIE Instruction Design Process consists of 5 basic steps:

1. Analyze

a. Analyze your learners and gather as much information as you can on them.

b. Analyze your broad goals for the lesson or unit.What is it you’re hoping to achieve?

2. Design

a. Identify learning objectives—what specific skills and knowledge do you wish students to obtain? For example, “Student will be able to describe each step of the ADDIE process.”

b. Identify outcomes—how will you know that the students have achieved your learning objectives? How will you assess learning?

3. Develop

a. Develop your instructional strategies—how will you facilitate students in learning the objectives you identified so that they are able to achieve the outcomes you’ve set for them?

b. Plan the logistics—how will you group students? How will you arrange the classroom? What tools

and materials will students have available to them?

4. Implement—Try out your lesson plan or unit with students.

5. Evaluate—Were you successful? Did students learn? Did they have fun doing it? What should you change for the next time?

Analyze

Developing Your Learning Goals When you design any course, unit or lesson, the first questions you must ask yourself are:

a.What are my goals?

b. What do I hope that students will know at the end of our experience?

c. What do I want students to be able to do?

Obviously your goals will vary, depending on the subject of your course. If you are developing a specific lesson, you will usually only have one or two broad goals. If you are developing a unit or a whole course, you may have several learning goals. Identifying your basic goals allows you to then develop specific learning objectives (Step 2—DESIGN).

Examples:

1. Introduce students to the ADDIE process

2. Provide students with a chance to experience different types of active learning.

3.Allow students to form teams and begin to develop group norms.

Understanding Your Learners

A thorough needs analysis obtains the following information:

1. Your learners' backgrounds (Age, Education, Profession, Position and Organization) and preferred learning styles.

2. Their level of knowledge on the topic*

3.Their expectations from the training*

(*these can be done through quick telephone calls, a brief survey or feedback form)

4. What relevant knowledge and skills do they need to learn? What do they already know?

5.How varied are they in knowledge and learning styles?

6. How well can they learn? What study skills?

7.What motivation and interests, attitudes to teaching/learning methods?

8. What are their obstacles to their learning, such as anxiety, color blindness, lack of concentration, computer access?

Design

Developing Learning Objectives

After identifying your broad learning goals and thinking about your learners and what you know of them, you must then develop specific learning objectives. Although related to your goals, learning objectives are not the

same. Learning objectives are more specific, describing in more explicit detail what you expect that students will know and be able to do.

Rules for Developing Objectives

1. Start your statement with “Student will be able to. . . “

2. Begin each specific objective with an action verb, something that can be measured or observed. For

example: Student will be able to describe the five steps of the ADDIE process. By using specific, measurable words you make it easier to develop your learning assessments. It also communicates more clearly to students what they will be learning in the course.

3.Do NOT begin objectives with words such as “understand” or “know.” We cannot directly observe if someone “understands” material—they must DO something with it for us to be able to determine if they understand.

Designing Outcomes:

Authentic Assessment

If we’ve designed our learning objectives well, then we’ve also created an easy framework for us to begin developing ways to assess learning. There are a variety of ways to evaluate student learning, from tests and papers to projects and presentations. One fact that we do know about how we learn is that we are best able to understand facts and information when we use them “in context”—that is, we interact with and process information in the same ways that we would use that information in the real world. For example, we are better able to learn interviewing skills by actually practicing how to do an interview, rather than writing an essay or completing a test on “interviewing basics.” When we look at evaluating student learning and determining if students have developed the skills and knowledge we defined in our learning objectives, we must focus on creating and using assessment tools that will most effectively allow students to demonstrate their knowledge. This means creating tools that:

1. Provide students with some level of choice. For example, doing a presentation, a skit or a role play. 

2. Are clearly linked to learning objectives. For example, if an objective is “Student will be able to describe the ADDIE process,” then your assessment should provide an opportunity for the student to do that.

3. Allow for concrete skill demonstrations. If the lesson is on how a student would write a business letter, then the student would actually produce a business letter and that letter would be measured against a “sample” letter to determine if it met standards of quality.

Develop

Facilitating Learning

Identifying Instructional Strategies We know that:

1. Students have different learning styles.

2. Learners need to learn skills “in context.”

3. Learning is “social”

3. Students are motivated by activity, appropriate challenge levels and a pace and style that is facilitative, rather than “instructive.” With this in mind, it’s time to develop appropriate instructional strategies.

Guidelines for Selecting Instructional Strategies

1. Begin with a product in mind. When students must “produce” something as part of a lesson, this creates a

goal oriented mindset. Students clearly understand expectations and are automatically more comfortable. ! Reduce the level of threat. Learning is primarily a social activity. We are worried about how we will “look” in

front of teachers and fellow students. We are concerned that we won’t be able to learn the material or that someone will find out we can’t read as well as we’d like. Instructors must develop classroom norms that communicate that it’s safe to learn in their classroom. They should also model their own learning, uncertainty and anxiety when appropriate. If a lesson doesn’t go well, acknowledge that and show students the process

you go through to identify what’s wrong and how to fix it.

2. Establish relevance. We are all motivated by the “WIFFM”—“What’s In It For Me?” Strategies you select should help demonstrate relevance to students so that they see connections and are more motivated to learn. ! Clearly and appropriately link strategies to objectives. If the objective is “The student will be able to cut a board using a circular saw,” clearly any instruction must involve an actual demonstration of how to accomplish this task. Reading about it in a book or listening to a lecture on how to cut a board will not do it.

2. Strategies should match needs and characteristics of learners. Each individual has a “channel” of learning,

ways that allow them to process and use information. Individuals who are more “handson,” do not learn well

through reading a book. Even if you are teaching reading your instruction will be more effective if you include opportunities for movement and touching.

Examples of Active Learning Options

1. Projects and mini projects

2. Case Studies

3. Presentations

4.Think/Pair/Share

5.“One Minute Paper”

6.“The Muddiest Point”

7. Carousel Brainstorm

8. The Fish Bowl

9. Under explain/Learning Pairs

10. Structured Observation

Develop

Classroom Logistics

As important to learning as the specific instructional strategies you use are classroom logistics. Things like class ground rules, the physical layout of the classroom, the use of teams—all of these logistical issues influence learning. 

Some Basic Logistical Principles

1. Rows imply lecture. They make it difficult for students to interact with one another and they put the instructor at the center of the learning experience. Circles, horseshoes and other configurations promote more interaction and a greater sense of community.

2. Have students set ground rules and expectations. Work with students to establish basic expectations—what they can expect from you and what you can expect from them. Use learning contracts, ground rules lists and other tools to include students in the setting and enforcing of individual and group norms.

3. Be consistent. Nothing causes a faster breakdown in norms than inconsistency. Students must understand

expectations and then see that both the instructor and students are held accountable for those expectations.

4. Work in teams but do so strategically. Pay attention to how you form teams. There are times when teams need particular expertise or experience and times when that is not necessary. There are times when it’s appropriate to let students form their own teams and when it’s better for you to make assignments. Your learning objectives and strategies can help you determine the best methods for team formation.

Implement

Putting the Lesson into Practice

This is either the easiest or hardest step in the process. Usually if you’ve planned well, the implementation phase is when you get to see the fruits of your labor. If you haven’t planned, then this is often where you see unmotivated students and ineffective lessons.

When it Works

Probably the best thing about teaching is going through a lesson and seeing students get excited and motivated by the process. Watching them become more skilled or seeing that “light bulb” of understanding go off in their heads is one of the most gratifying experiences there is. Sometimes it seems that we don’t get moments like these often enough, so enjoy them while you can.

When it Doesn’t Work

Sometimes, no matter how well you’ve planned or what you’ve pulled together, the lesson just doesn’t work. Students don’t understand or they seem unmotivated and disengaged. This is often when behavioral issues erupt because students are either challenged too much by the material, or are insufficiently challenged so that they become bored.

When it’s clear that things aren’t going well, you have a few options:

1. Stop the lesson and find out from the students what’s going on. Is it the lesson? Is there something else going on? Sometimes it’s better to stop and deal with whatever open issues may exist than to try to slog your

way through the rest of the plan.

2.Take and break and regroup. Sometimes you need a minute to pull your head together to try something else. Take it if you need it. 

3. Move to another lesson or activity. If it’s REALLY bad, have something else that you can move to easily.

Evaluate

Evaluation—Was it a Success?

There’s no point in conducting lessons that don’t work. But the only way to know if they did, is to evaluate yourself. There are a few factors to consider in this process.

1. Student Reactions

Did students enjoy themselves? Was it interesting and engaging? Were there things that students feel worked

particularly well? That should change? Periodically checking in with students helps build class solidarity and

community and keeps you refreshed with new ideas and possibilities.

2. Student Learning

Of course, the real measure of success is—did the student actually learn the skills? If we go back to step 2

of the ADDIE process where we designed learning objectives and ways to assess student learning, we should be able to tell if students have learned or not by reviewing the results of their assessments. If we’ve paid careful attention to allowing students to demonstrate learning in concrete ways, then we can be relatively

certain that they’ve learned what we wanted them to. If students haven’t learned, then we need to ask ourselves why. What could we do differently the next time? Do we need to address issues of classroom culture? Do we need to try a different strategy? While not every student will be successful, there is always something that we can change in how we teach that can improve learning for more students.

Curriculum and Pedagogy as a Sharing of the Horizons of Understanding

As a teacher, I enter the pedagogical relationship through my own experience, which includes my formative experiences in the world, my training, and my aspirations for both myself and my students. So too does each of my students enter the pedagogical relationship in such a way. Unless there can be a sharing of these stories as a condition of our coming together, there can be no basis for our mutual advancement because it remains perpetually impossible to know who is talking; without such knowledge, what is present to be learned can only remain detached and alienated from those involved.  In the Advanced Curriculum Research course for doctoral students at the University of Alberta, for example, both students and professor participate in the Who Is the One Researching? (WITOR) project. Members work together to clarify the relations between their own biographies and the respective research projects that holds their interest. The effect of such efforts is two fold. On the one hand, actually hearing the stories of others becomes a liminal reminder of the impossibility of corralling all of these stories into one conceptual or interpretive schema, except of course the schema of difference. On the other hand, it is precisely the schema of difference that brings people to an awareness of the need for deep tolerance and acceptance—the qualities without which  there can be no community, no sense of common belonging. Sometimes the conundrum inspired by the irony is the site of provocation—a prelude for hermeneutic breakthrough. This was the case, for example, in another class discussing an article on gay and lesbian experience. Students from China reacted in horror to the possible sociocultural acceptance of gays and lesbians, relating stories from their own cultures of how such people are treated. Facing a lesbian student in the class, someone who had already gained their respect and trust before coming out induced a genuine sense of bewilderment and puzzlement, a new genuine openness to learning, and a reciprocal sharing of assumptions and understandings about sexuality generally.

The sharing of horizons can easily become stuck in a kind of self-aggrandizing narcissism if an effort is not vigilantly made to show how the dynamic at work in the pedagogical situation has reference in the broader world. That is, the sharing of horizons points to the way my horizon is never just my horizon, but one that opens out onto that of another and, as such, is in a condition of perpetual revision toward a more comprehensive understanding and appreciation of the broader world. In this instance is gained the appreciation for how no one story can tell the whole story, and that hermeneutic suspicion is best directed at pretensions to the same—pretensions to a univocal and monological theory of globalization, for example. The economistic determinism at the heart of the neo-liberal agenda of Globalization One must be exposed for the way it limits other ways of human expression and common living (e.g., through aesthetics, spirituality, and altruism). The sharing of horizons within communities of difference helps break down the dichotomy between the private and public spheres, and may serve as a kind of prelude to a theory of justice that honors difference while holding every difference accountable to its influence in the broader public realm. It is one thing to hold private views and to honor the right to privacy for those views. Yet in the age of globalization, where persons and groups now rub shoulders in new and unforeseen ways, the time may soon be near when more open expression of personal convictions is necessitated by the requirement to understand more fully and more publicly the lived-out implications of privately held (including privately held by groups and communities) beliefs. In my graduate seminar on religious and moral education, for example, each person is encouraged to publicly articulate the convictions of their own faith community regarding other faith communities. This becomes a means of facing difference, lifting it out of the realm of abstraction and conceptualization, and embodying it in relations between persons. It is one thing for a Seventh Day Adventist student to state as an abstract principle of theology for his faith community that “the Pope is the Antichrist”; it is quite another to state it while facing directly a Roman Catholic friend and colleague in the class, surrounded

by others now deeply invested in the outcome of such facing. These others are invested partly because the future of the class—its tone, its pedagogical receptiveness, its future possibilities as a place of secure freedom—depends on it. They are also invested because they recognize in such a confrontation an exemplification of their own relations of difference, so that the outcome of this specific case becomes prototypical for the resolution of their own personal challenges.

This kind of outing of difference also assists in helping students better understand the way their assumptions about others are historically constructed; as such, they must be reexamined and re-interrogated for their time boundedness. Of course, historicization as a strategy for opening dialogue contains its own theory of history, and it must be recognized that it does not work well within and among communities where history is taught as a rigid anamnesis—a memorization of how we got to this point as a way of legitimizing why at this point we should never change. Resolving that difficulty must be reserved for another day; here the pedagogical assumption is that history is open or better, that the future is always open, and that an orientation in the present to an open future is an absolutely necessary precondition not only for a world that is more fair and just, but also for one that may be inspired by hope. One of the conditions, then, that the sharing of horizons brings into the classroom can be called the condition of mnemonic reparation, which has special relevance for curriculum in the age of globalization. Nigerian playwright, essayist, novelist, and poet, Wole Soyinka (2000), has called for an international movement to make possible a new kind of reparation in the world for past wrongs, past injustices. This new kind of reparation would not be monetary (“Reparation is not monetary recompense”), but a recovery and making public of the subjugated memories of oppressed peoples. For an example, Soyinka pointed to the UNESCO commitment to the preservation of the slave routes in West Africa, establishing a scientific committee to document, preserve, and open up the landmarks of the slave routes for posterity. In such a way, Africans around the world can better concretize their history to turn it into a living voice within the emerging global community. Also, such mnemonic acts reveal the interdependent nature of every identity.