Team Education 2.0 Week 11 Summary

Case Study:

1. Let’s review the Group Critique I Software again. Your team reviewed the assigned site for the first 3 modules and analyzed the strengths and weaknesses of the web design. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!)

2. Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list?

3. Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

4. How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

We reevaluated the 6^th grade Math Practice part of AdaptedMind website.  We first thought that the site had the ability for students to establish their own learning path.  Also it was discussed that the website measured student’s progress and establishes different levels of learning. 

Through our team discussion, Adelina believes the AdaptedMind website has video tutorials that teach the audience to acquire different skills.  She believes this meets the principles of teaching generic skills and nothing should be added or deleted. 

Katie on the other hand discussed that the learning objectives are not stated clearly and immediate feedback is not always available.  She believes that site is more of a reinforcement website rather than a site for a self-learner.  Katie points out that students must be self-motivated to benefit from this website. So she thinks a live facilitator would help the website.

Nick was in agreement with Katie as far as the learner discovering their own weakness and not a lot of feedback.  He had a great idea about being able to input the answers for each step of the problem, where this could give immediate feedback.

I think this website is great for reinforcement, but I do agree with Ncik that they need to add a place to input the answer for each step and provide feedback.  The learner will better use the site if they know what their weakness is.  Through the research of Beamish (2002), he  asserted that generic skills are relevant to higher education in many ways: they support higher levels of study; they promote independent and effective learners; and they develop resourceful and self-aware students.

Components of Generic Skills

Our team view the components in AdaptedMath as “un-organized laundry list” and “a set of steps”.  It was said that there were overarching categories with series of problems, which there are examples with formula but not necessary explanations for the problem a student maybe having.   Since it does not address specific problems students may have as they do the step by step it is not addresses all issues.  But on the other hand the video tutorial is a set of steps.

According to Chris Lawrence, teaching and learning should be joyous and effective.  It is true that we all learn differently.  How prepared the teacher is for the learning of the students plays an important role in the attitude of the learner.  (Anderson, Blumenfeld, Pintrich, Clark, Marx, & Peterson, 1995). They argued that deeper understanding of the cognitive, motivational, and situated characteristics of learning can help teachers design better instruction.  Motivation is certainly important, as "a student's attitude toward a given course or subject area can be a contributing factor to his achievement in it" (Edwards & Porter, 1970, p. 107).

Simonson and Maushak (2001) have drawn on findings from a number of studies to create a series of six guidelines for effective design of attitude instruction. These are:

·         make the instruction realistic, relevant, and technically stimulating

·         present new information

·         present persuasive messages in a credible manner

·         elicit purposeful emotional involvement

·         involve the learner in planning, production or delivery of the message

·         provide post-instruction discussion or critique opportunities

Question for Team:

How do you address your attitude as a teacher to ensure the learning success of your students?

How do you address the different attitudes of your learners?

 References:

Simonson, M. and Maushak, N. (2001). Instructional technology and attitude change. In D. Jonassen (Ed.), Handbook of research for educational communications and technology (pp. 984-1016). Mahway, NJ: Lawrence Erlbaum Associates.

Edwards, A.L. & Porter, B.C. (1972). Attitude measurement. In The affective domain: A resource book for media specialists (pp. 107-126). Washington, DC: Gryphon House

Beamish, Val. (2002). The impact of skills development (Curriculum 2000) in schools and colleges on higher education. Learning and Skills Development Agency, Skills Development in Higher Education: Forging Links  Conference Report.

Week 11: Kimber Brown Summary and Research

During the critique we studied a website called coolmath.com. During week 11 we were asked to discuss if any items should be added or deleted from the website. We agreed that the elements accomplished the purpose of the website (to help students with algebra.) We all agreed that the website does a great job because it starts at the lowest level of complexity and progresses to a more complex one.


Next we were asked to look at the components of the generic skill for this review and determine how the procedure was presented – a set of steps. We agreed that all the math problems or objectives were presented in a step by step procedure that needed to be followed in order so greater benefit can be obtained.  We agreed that the students need to learn what a factor and a product was first, so they could undo the distributive property.  We agreed that all the math problems presented in this website were presented in a way of a procedure since basic math skills need to be attained before they go into higher level of thinking problems.  Finally we agreed that the basic skills help students acquire generic skills that can be implemented in other subject areas.


For the third question, we after reviewing the coolmath.com website, we agreed that the attitude toward the website remained positive for all of us. Lauren stated, "While it did not change my affective attitude about algebra, in general, in did change my affective attitude or beliefs about working on math via an interactive website." As far as behavioral aspects of attitude, we agreed that the website gives students good habits of algebra and helps them to learn the basics and use them as building blocks for later fundaments of algebra. This definitely gives a positive behavioral attitude on the website since it is accomplishing the purpose of helping students improve in algebra discreetly, without having to get after school tutoring from a teacher.


After the discussion, I decided to research some other math websites to see if the content was valuable enough to share. I found in an article by Linda Lindroth, where she says, "Whether you decide to create a simple search or a robust investigation, your students are almost guaranteed to be excited about a math scavenger hunt." (Lindroth, 2007) That sounded like fun, so I checked it out. In her article she links a scholastic website that I found especially interesting. The link is Math Hunt www.teacher.scholastic.com/mathhunt. I also found that key math topics are integrated into these science and social studies topics. That was very fun and entertaining, even at my age. She also links the reader to another hunt website called Adventures of cyberbee at http://www.cyberbee.com/hunts.html. I found that to be fun and educational too. At www.vickiblackwell.com, I found some more fun hunts, not just math but social studies and science too. This was fun! Finally, with my own prior knowledge I thought of a way to incorporate technology into the classroom with QR codes and the internet. As a teacher, you could find Teachertube videos or websites and link them to the codes. Then you could cut and paste the codes onto the student's homework or quiz reviews. The students could either scan the QR code or enter the shortened url to find the information they need to complete the review or homework. For the students who need more, you could ask them to do the creating for the next chapter or unit. They could find the videos, create the questions, and create the shortened urls and QR codes. That sounds like fun. 


Also if you are thinking that the internet and QR codes are too advanced for earlier elementary grades, think again. Sesame Workshop, the nonprofit organization behind "Sesame Street," last week announced the creation of the Joan Ganz Cooney Center an independent research center that will explore how digital media can help children learn. The center, will focus on the needs of elementary-age children, exploring the role of new platforms such as Web, cellphones, and video games in literacy development in and out of school. (Bradley, 2007)


Do any of you use specific websites to reinforce skills you have taught in your classroom? Do you use QR codes? Would you use QR codes if you knew how? If you wouldn't use them, why not?


Bradley, A. (2007). New Center to Explore Role of Digital Media in Learning. Education Week, 27(15), 5.


Lindroth, L. (2007). How To... Create and Use a Math Scavenger Hunt. Teaching Pre K-8, 37(4), 25.

TechGrads - Week 11 Summary and Research

Module 7 & 8: Generic Skills and Attitudes

1.   Let’s review the Group Critique I Software again. Your team reviewed the assigned site for the first 3 modules and analyzed the strengths and weaknesses of the web design. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!)

2.   Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list?

3.   Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

4.   How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

Team Summary:

1. As a team, we do not think the models are lacking any components of a generic skill, however, the website is lacking instructions on how to use the models presented with students. Procedures are the most prevalent component in learning a generic skill, as stated by Raigeluth (1999). The fact that Naturalmath.com left instructions off of their models is a big problem. We also concluded that some of the models are more appropriate for elementary and others for secondary, but the website itself does not differentiate. 

2. We agreed that the models on Naturalmath.com are of an unorganized laundry list. The models are visuals, but as stated before, there are no steps, directions, or procedures.

3. Since Naturalmath.com consists of mostly visuals with little engagement, the student might seem a little unenthusiastic towards the website. As a team, we believe that the learner must be engaged in the learning process to have a positive attitude about the topic. Games and other interactive content aid in a positive attitude in learning.

4. Due to the fact that Naturalmath.com does not establish a target audience, some students might be turned off the website because of it's elementary appearance. They will turn off motivation to learn before the process can begin. Being motivated to learn is a big factor in having a positive attitude for both the learner and the teacher. The environment and tone of the lesson must reflect a positive, enthusiastic mood in order for both learning and teaching can occur. If the mood conflicts in either the learning or the teaching, there will be a breakdown in the learning process.

Research:  

1. Generic Skills? What are they really? - According to Geoff Petty, generic skills are skills required to be successful on any assessment in any subject. They consist of synthesis, evaluation, analysis, study skills, and social skills. Going back to the Natural Math models, there are no instructions on how to use the models. Therefore, one cannot synthesize, evaluate or analyze the models. 


Petty, G. (2004). Teaching Today. Retrieved April 22, 2012, from http://www.geoffpetty.com/genericskills.html 


2. Learning is a behavior. In order to begin teaching a new behavior, the subject (learner) must have motivation to learn the new behavior. So, this leads us to identify the cognitive and affective aspects of attitude. Charles T. Schmidt, Jr. of The University of Rhode Island sums up the different theories of cognition and behavior. 


Schmidt, C. (2002). Work Motivation Overview. Retrieved April 22, 2012, from http://www.uri.edu/research/lrc/scholl/webnotes/Motivation.htm


3. There are five dimensions of learning according to McRel. Dimension 1 is the idea that attitude and perceptions affect the learning process. "The key element of effective instruction is helping students to establish positive attitudes and perceptions about the classroom and about learning" (McRel 2012).




McRel (2012). Dimensions of Learning. Retrieved April 22, 2012, from http://www.mcrel.org/dimensions/whathow.asp




Discussion:


Review the Dimensions of Learning, especially the 1st dimension. 


We know that the teacher's attitude effects learning. What techniques or strategies can we as instructors do in instruction to help develop a positive attitude of the learner? What can do to eliminate any conflicts or breakdowns in attitudes of both the teacher and learner during the learning process? What is the most critical point that must be executed? 

Team Education 2.0 Week 11 - Nick Goodson

1.   Let’s review the Group Critique I Software again. Your team reviewed the assigned site for the first 3 modules and analyzed the strengths and weaknesses of the web design. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!)

The lessons in AdaptedMind are skill based and mainly leave it to the learner to discover their own weaknesses.  There is no feedback method for evaluating and reporting exactly what the student is doing wrong or what concepts are giving them trouble.  The students or teacher must recognize the weakness  and determine appropriate action which is difficult to do in a website.  A great addition to the site would be the ability to input answers for each step of the problem.  Currently, learners merely input the final answers.  Instead of having a single box, have multiple boxes where learners must type the answers to each step they must complete in order to solve the math problem.  This would add another dimension to the feedback.  Also, if the website could track student progress along multiple skill sets it could build a map of student learning and identify weak areas for the learner to work on. 

2.   Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list?

The procedure for reviewing the method for solving the 6th grade math problems on AdaptedMind was done using video clips.  An instructor explains in the audio track what steps that the  learner should take to solve the problem.  Visual examples are made on screen so that the learner can see how it is done. 

3.   Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

Using AdaptedMinds students use the provided lessons to teach themselves or review mathematical concepts.  "All cognitive strategies share a common goal--to teach students how to interact with the content so that learning becomes more deliberate, self-directed, and self-regulated" (Jitendra, Burgess & Gajria, 2011).  The website is effective on several fronts such as the students ability to work at their own pace, a feedback system, and the ability to have a video explain the steps for the problems.   The purpose is to increase the appropriate behavior attitudes that are required for student success in the school system.  As pointed out in our software critique, the website is very simplistic and the feedback system doesn't offer much in the way of real feedback as far as what the student is doing wrong.  It merely offers words meant to encourage proper behavioral concepts. 

4.   How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

Attitude is extremely important when it comes to conflicts between learning and teaching.  Learners need to have the proper attitude when attempting to learn or nothing will be accomplished.  The same goes for teaching.  The two are not mutually exclusive.  The concepts of teaching and learning must work together to effect change over time and to ensure student learner success. 

Jitendra, A. K., Burgess, C., & Gajria, M. (2011). Cognitive Strategy Instruction for Improving Expository Text Comprehension of Students with Learning Disabilities: The Quality of Evidence. Exceptional Children, 77(2), 135+. Retrieved April 17, 2012, from Questia database: http://www.questia.com/PM.qst?a=o&d=5047178612

Reigeluth, C. (1999). Module 1: Kinds of learning. Retrieved April 16, 2012, from http://www.indiana.edu/~idtheory/methods/m2e.html

Christa Tucker - Tech Grads

1. Problem-Based Learning (PBL) method emphasizes students’ own activity in learning about problems, setting up their own learning goals and actively searching for and analyzing information based on their prior knowledge (Murray-Harvey, 2005).  The models that are present in Naturalmath.com seem to be an effort to introduce generic skills through problem based learning.  However, with only having limited access to the website, it appears that either directions are not clear and/or supplementary material is not available.  
2. The models represented on the Natualmath.com website were an un-organized laundry list.  This is said because there is the scope and sequence or flow of how one model relates to the others.
3. Cognition is a process of thought in which a person first becomes aware of stimuli, evaluates the significance of those stimuli and then considers possible responses (Scherer, 1999).  The Naturalmath.com website does present the information in models in order to trigger the learners thought process.  
4. Reigelth (1999) gives the learner the opportunity to form attitudes about leaning and how instruction is given.  Using this application student’s will be able to determine which methods they feel more comfortable with when estimating, multiplying and problem solving and that there are different approaches to each goal in the application.  The creator of the Natualmath website does encourage the learner to find ways that the models can work for other integers such as negative numbers. 

References

Murray-Harvey, R., Curtis, D. D., & Cattley, G. (2005). Enhancing Teacher Education Students' Generic Skills Through Problem-based Learning. Teaching Education, 16(3), 257-273.

Scherer, K. (1999) Appraisal theory, in: T. Dalgleish and M. Power (Eds) Handbook of Emotion and Cognition,

pp. 637–665 (New York: Wiley).

Team Education 2.0, Week 11

1.   1. Let’s review the Group Critique I Software again. Your team reviewed the assigned site for the first 3 modules and analyzed the strengths and weaknesses of the web design. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!)

Australian National Training Authority (2003), considers generic skills to be very important, because it allows the individual to be flexible, take initiative, and develop the ability to undertake many different tasks. This is because the individual have acquire a set of skills/knowledge which can be used across board. The acquisition of generic skills makes one versatile. Agreeing with Blom and Clayton (2003), “Generic skills are skills that are learned for lifelong learning and living”.

In the same way, the video tutorials on the AdaptedMind website teaches its audience to acquire set of skills from simplicity to complexity. The video tutorials starts from counting numbers to number sense, to addition, to subtraction, to measurements through to higher level of teaching probability and other skills. Students learn the basics of Math, advance and apply them as the concept becomes complex. Considering the above, I think it meets the principles of teaching generic skills and therefore nothing should be deleted or added.

 2. Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list?

The procedure used for presentation was “a set of steps”.

The video tutorials at this site (AdaptedMind), teaches skills by presenting a set of steps that would be used by students to perform a task. Students learn the basics of Math by counting numbers and develop to learn advance level skills by finding the probability of a number.  The procedure involves learning to count, add, subtract, multiply, divide and more. All these skills learnt will help the student perform advance skill in Geometry and Algebra.

3. Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

Munro (2011) describes attitudes as,“how a person perceive things, events  or people”. Attitude can be positive or negative evaluations of objects or thoughts. Attitudes expresses ones disposition towards things. In Rustamov (2011) presentation, he explains the components of attitudes as:

Cognitive; the process by which a skill is acquired (how).

Affective; the reason or purpose for which a skill needs to be learnt (why), dealing with the emotional stimulation.

Behavioral; allowing students to practice or experience the skills learnt and receiving feedback from the teacher.

Relating these to the AdaptedMind site, Cognitive would be the video tutorials offered to help students acquire the skills or knowledge to be able to understand and solve the various Math problems. Affective would be the fun badges earned by students for their accomplishments. These give them a reason to want to implement the skills learnt. Behavioral would be the availability of the practice exercise, where students are able to practice what they have learnt. The site also measures student’s progress on skill they have practice, therefore given them feedback.

4. How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

Learning takes place when there is a behavioral change.

To be able to define the attitude conflicts between the principles of teaching and learning, we need to identify the principles underlying teaching environment to allow learning to take place or a change in behavior. 

A teaching environment that starts at where students are, know where students are going, expect students to get to their goal, support students along the way, use feedback to help students get better, focus on quality not quantity and allow for flexibility. (Partrick, 2010). Students on the other hand may consider these learning principles by Mellon (2007) to close the gap between teaching and learning.

Students may have prior knowledge of a concept, be self motivated, organize their knowledge, direct their goals and target feedback as well monitor those things that have been accomplished.

Therefore a skill have to be taught to allow learning to take place where a change in attitude is visible.

References

Australian National Training Authority. (2003), Defining generic skills NCVER. 

Blom, K. & Clayton, B. (2003), “We Can’t Teach Them That”. Reinstating the place of Generic Skills in VET.

Mellon, C. (2007), Eberly Center for Teaching Excellence.

Munro, J. (2011), Psychology of Exceptional Learning. Learning Attitudes.

Partrick, J. (2010), 7 Principles for Teachers

Rustamov, I. (2011), Attitude Learning EDT 666 Instructional Design 

Team Education 2.0 - Weekly Post by Katie Petty

Week 11 – Module 7 & 8
 
In our Group Critique, we were asked to analyze the 6^th Grade Math portion of the AdaptedMind Website. Our critique rated the website very positively as to the questions asked and the direction of our learning at the time. Now, we that we have an opportunity to evaluate the site with a few more weeks of knowledge under our belt, has given us a great opportunity. As with any creation, things can always be improved, modified, or tried until 100% mastery or perfection occurs.

Addition or Deletion of Components

According to our class reading and overall discussion, dimensions of divergence are all the ways a procedure can vary. In our critique, we stated in the beginning that the AdaptedMind website was procedural in learning by allowing students to take action on a sequence of events. While we found the website had tremendous value in the reinforcement of learning, we did not find that the website was a valuable teaching tool (even though the applied videos could provide this function). The website has a few components that are missing and would need to be added to go beyond simple reinforcement of learning. The two biggest components that stick out in our mind are:

1.    The learning objectives are not stated clearly &

2.    Immediate feedback is not always available.

In our research, we came across Robert Gagne who best describes the reason why the lack of these two components create a dilemma for our website. As he expounds upon the domains of learning, he begins to contract a 10 year old learning math and a 24 year old learning statistics. In both age examples, effective learning is demonstrated but each one has a different path. The 10 year old has a very structured learning process. Everything is laid out for the 10 year with reinforcement rewards built in. As for the 24 year old, Gagne shares, “The difference in the two instances is often summarized by saying that the 24-year-old has become to a large extent a self-learner, whereas the 10-year-old has not yet achieved this state, and has a ways to go before he does” (Gagne, 1972). He explains that the 24 year old has additional knowledge and experience which allows him to be an individual who will seek stimulation and learning for the sake of the experience. This is in contrast to the 10 year old who may not even understand or comprehend the value of what is being taught.

In the AdaptedMind website, example problems are produced and yet very little instruction, if any, is given. When an answer is presented, the student has the option to go do a video lesson, but everything is self-discovery driven. I would propose that it would take a highly motivated 6^th grader, even with the virtual badge reward, a while to go through this website. However, if coupled with a live facilitator and issued as homework, the website takes on a new dimension.

Generic Skill

This is an interesting question and brings to light the major issue our group had with this website. As stated in the question so eloquently, our website presents 6^th grade math concepts and problems in an “un-organized laundry list.” If you go to the AdaptedMind Website to the particular area we are reviewing, you will find overarching categories (such as Geometry, Factoring and Multiples, etc…) followed by a series of problems. As you scroll over the problem hyperlinks, you are given an example with the formula that acts as the solution. If you click on the hyperlink, it takes you to a series of problems that have multiple choice answers. Your progress is measured, video-lessons are offered, and badges are issued for rewards the further you progress. The generic skill in this situation is the ability to follow the procedure once you are on the right path. However, the minimal guidance and the inconsistent method in which feedback is given leads to frustration and thus without anything else the website becomes another deadlink.

References:

Gagne, R. M. (1972). Domains of learning. (Vol. 3, pp. 87-105). Ontario: 

     Kluwer Academic Publishers.

TechGrads- Week 11 Pamela Jefferson

We held a Skype discussion to address the Week 11 questions and came to several of the same conclusions.

1. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!).

Http://www.naturalmath.com/multmodels/3.html has a posted graphic for all of the multiplication models. According to Reigeluth (1999) the most important component of a generic skill is the procedure or set of steps used to perform the skill. The procedure for multiplication is missing from http://www.naturalmath.com/multmodels/3.html. The Multiplication Model section of the site does attempt to address the principle of multiplication by providing a visual aid to help users understand when to apply a particular model. Unfortunately, several of the multiplication models provided are not good representations of the model being addressed. The memorization component is not addressed by http://www.naturalmath.com/multmodels/3.html.

          The sequence of the multiplication models presented on http://www.naturalmath.com/multmodels/3.html does not follow Reigeluth’s recommendation to begin with the easiest cases to account for levels of complexity. Users can of course click on the multiplication models in any order as the website does not function in a linear manner. http://www.naturalmath.com/multmodels/3.html begins with Scale, Stretch followed by Skip Counting, Number Line, Time & Money. If we were to begin with the simplest cases as they are introduced to students in most math curricula we would begin with Skip Counting, followed by Repeated Addition, Sets, and Arrays. Presenting the multiplication models in order of the simplest case would reinforce student’s intuitive models of multiplication as found by Mulligan and Mitchelmore (1997). Mulligan and Mitchelmore (1997) found that second and third grade students used direct counting, repeated addition and multiplicative operation as the intuitive models when solving multiplication word problems.    

Reference

Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children's intuitive models of multiplication and division. Journal for Research In Mathematics Education, 28(3), 309

Reigeluth, C. M. (2012). Module 7: Generic Skills. Retrieved April 15, 2012, Retrieved from http://www.indiana.edu/~idtheory/methods/m7c.html

2. Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list? Multiplication is never presented on Natural Math as a set of steps or list of principles. The multiplication models are just presented as a set of posters that can be used as a visual representation of each model. There are no steps, directions, or procedures.

3. Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

The cognitive, affective and behavioral aspects of attitude make up the three components of engagement. According to Linnenbrink and Pintrich (2003) self-efficacy, a student’s belief that they can do something, results when there is behavioral engagement, cognitive engagement and motivational engagement (affect). It is their belief that self efficacy leads to more engagement which leads to more learning and increased achievement. Because there are no interactive elements on Natural Math I do not think that students would find the site engaging. Research conducted by Yang and Tsai (2010) showed that students that use technology in mathematics learning have more positive attitudes toward mathematics than those that did not. This suggests that the positive attitude students have about using technology can help focus their attention on learning mathematics.

Reference

Yang, D.C., & Tsai, Y.T. (2010). Promoting sixth graders' number sense and learning attitudes via technology-based environment. Journal of Educational Technology & Society, 13(4), 112-125.

Linnenbrink, E. A., & Pintrich, P. R. (2003). The role of self-efficacy beliefs in student engagement and learning in the classroom. Reading & Writing Quarterly, 19(2), 119.

4. How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

Depending on the age of the students there is a potential disconnect between the content on the multiplication models, which may be the reason for a teacher’s desire to use the site, and the students perception of the material. I think that older students would balk at using a site they perceived to be designed for younger students. A negative attitude would already be in place before instruction began. Studies by Pugh and Bergin (2006) suggest that when students have a personal interest in a topic they are more likely to develop “the deep-level, connected knowledge structures needed for transfer” (p. 148). This kind of deep learning, which can be transferred across domains, will not take place if students are unwilling to take part in the experience. A teacher determining the situations and methods for instruction using Reigleuth’s Instructional Design Theory (1999), would probably find a better resource than Natural Math to introduce multiplication models.

Reference

Pugh, K. J., & Bergin, D. A. (2006). Motivational influences on Transfer. Educational Psychologist, 41(3), 147-160. doi:10.1207/s15326985ep4103_2

Reigeluth, C. (1999). Module 1: Kinds of learning. Retrieved April 15, 2012, from http://www.indiana.edu/~idtheory/methods/m2e.html

TechGrads - Rachel Mallory

1. As our team discussed, the multiplication models found on the Natural Math website do not seem to be missing any individual components. What is missing are explicit instructions in how to present or use the models with students. The age of the audience is not clear as some models are appropriate for elementary students and others are more high school level, although the design of the site suggests a younger target audience. There is no sequence of instructions, which is the first issue addressed in principles for teaching a generic skill (Reigeluth, 1999). It would also be better if the multiplication models were arranged in order of the level of complexity. What exists presently on the Natural Math website is an unorganized collection of tactics (Reigeluth, 1999) for teaching multiplication with no authentic sequence or instructions.

2. The closest description of the presentation of this generic skill would be an “unorganized laundry list”. Reigeluth (1999) states the three major components of a generic skill are the procedure, principles, and memorization. The resources available on the Natural Math multiplication models are merely visual aids for teaching a procedure or principle. There is no independent practice for addressing the memorization component.

3. The “About” page on Natural Math cites “the goal of Natural Math is to collect, distribute and create such natural experiences of mathematics” (Droujkova, 2009). Droujkova (2009) defines natural experiences of math as a community of practice, skills essential for life, beauty and fun, learners as creators, and infinite richness and complexity. A study by Deakin University (Bragg, 2007) found that “teachers and curriculum developers should clearly specify learning outcomes related to the games and reinforce their relevance to students.” Students were found to enjoy games that aimed to provide a positive learning experience. Clearly defined learning objectives were suggested to promote a positive attitude towards games as an instructional tool (Bragg, 2007).

4. In general, sites such as Natural Math are more popular than traditional repetitive practice, provided that the site includes activities that are relevant and engaging (Bragg, 2007). McLeod (1992) believes attitudes in education “develop with time and experience and are reasonably stable, so that hardened changes in students’ attitudes may have a long-lasting effect.” Motivation is of particular concern in education today because research links student engagement to student achievement (Bragg, 2007). Achievement itself is no longer enough incentive for students. Since we have been studying various principles of teaching and learning, a common theme emerges. Procedures and principles are the keys to learning (Reigeluth, 1999). A conflict exists when educators fail to teach a procedure or principle that reaches across different content domains. As educational facilitators, I would like to be able to answer questions from teachers about how to make various literacy skills address the components of generic skills found in Module 7 (Reigeluth, 1999).

Bragg, L. (2007). Students’ conflicting attitudes towards games as a vehicle for learning mathematics: a methodological dilemma. Mathematics Education Research Journal, 19(1), 29-44. Retrieved from http://www.merga.net.au/documents/MERJ_19_1_Bragg.pdf&ei=omiLT6-4Ieih2QXj9ZHeCg&usg=AFQjCNHR6sSZ70zrCK3hQBpdCe3tflUZyg

Droujkova, M. (2009). Natural math. Retrieved from http://www.naturalmath.com/site-pages/about-us.html

Reigeluth, C. (1999, March 10). Module 7: Generic skills . Retrieved from http://www.indiana.edu/~idtheory/methods/m7.html