What’s new in Connectivism?

Connectivism is new in that it is:

about the distribution of knowledge in the network and oneself (including our brain – your and my brain), and the solution lies in one’s brain. All problems and solutions are there in the brain – your brain if you want to solve the problem, and my brain if it is my problem and solution.  And what connectivism differs from other learning theories is that we could connect one’s brain to others’ “brains” that will lead to continuously improved and innovative solutions for me and the network in this digital age – networks including yourself with collective wisdom with emergent knowledge.

This relates back to what connectivism is: Knowledge distributed, learning as networked process (i.e. forming connections), principles form base of all design.  And the three levels: Neural, Conceptual and External (people, information sources etc. (Siemens, 2008)

about choices: The focus is on choice of connections and the network process, rather than just the outcome.  A person could choose amongst the connections and networks to suit and improve his or her learning.  See multiple choice in the other post in https://suifaijohnmak.wordpress.com.

about and around the learner: education, learning is now related back to the learner, with teaching and/or facilitating as a support and network, technology as enabler.  You may even claim it as a wholly learner-centred approach to learning. And the best way to learn relates back to the learner – individualised learning based on learning styles, intelligences (the multiple intelligences one has) and connections – network associated with, and his/her choice of support and technology.

Why am I using this static page on Connectivism as my home page?

I noted that the uploading of current posts would take a long time and so I have used this home page for normal uploading of my blog post instead.

You could access my recent posts by clicking the “recent posts” as shown on the side bar.

Thank you for your visit to my blog.

56 thoughts on “What’s new in Connectivism?

  1. Good idea in – what is new in connectivism !.
    Today we have a lot of “wicked problems ” of technology that must be solved. So, I agree that the only way is how to increase the power of my, your other people brains.


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  3. Hi John. You pointed me to this post a few times, I think. I don’t see anything new here, to be honest. Knowledge has always been distributed. Learners have always had choice, and learning has always been learner-centred too. A claim that any pedagogy is wholly learner-centred is extreme, I think. Try to envision a continuum of any of the above three qualities of learning.

    All I see here is a bunch of claims that connectivism is better because it does more of the above than what, previous pedagogies, right? I don’t see anything suggesting connectivism is a learning theory. Connecting people’s ‘brains’ is nothing new, people have shared learning before.

    As far as a ‘wholly learner-centred approach to learning’, I don’t think so. CritLit2010 was a ‘connectivist’ course, and it was more about the sponsors, than the learners. In the end, the sponsors decided that ‘interested learning’ had occurred, based on their observations, prior to any consultation with the learners. And ‘interesting learning’ along with ‘openness’ were the yardsticks to measure the success of that course.

    How is that ‘wholly learner-centred’? On the contrary, I suggest that these connectivist courses are self-serving to the facilitators, served up to ‘prove’ their points.

    Over to you….

  4. Hi Ken,
    That’s fine, especially if you don’t see anything new. What I have mentioned in the ‘what’s new’ summarises what and how we are learning nowadays, compared to the learning that happened in the past decades. What I found was that Connectivism “could” be used to describe and explain those what, how, when, where, who with and why in the learning process.

    Connectivism was proposed by George and further extended by Stephen as a learning theory. Any one could comment and critique on it.

    So, yes, we could use all other learning theories to explain the learning at this digital age, if we like. I would welcome even debates from all theorists and educators.

    As I have explained, any one could propose a theory (whether it was from the previous learning theory) and explain it to us. It’s up to us (or you) to consider it, or to reject it, similar to every learning theories of the past.

    I found it more useful to critique, reflect upon those theories, rather than their mere adoption. When I learnt about the education and learning theories in the past, did we do the same? So, this Connectivism as a learning theory is again a choice for educators and learners to consider.

    If we (or you) like to have a wholly learner-centred course, how about creating it ourselves and see how it works. This is why I have also tried the learner-centred research with Jenny and Roy, where we decided all the learning ourselves.

    Relating to CritLit2010, I am still yet to learn about Stephen and Rita’s views and their measures of success. Everyone is entitled to their views and interpretation of the course, as participants, and that is the exciting part of the learning. I like your sharing with me.

    I have discussed about wholly learner-centred in my other posts on self-directed learning.
    Is self-directed learning welcomed by educators?
    There are many political factors involved in the debate of learner-centred approach in learning and self-directed learning. I could only touch upon it in open discussion. If you like, some private conversation on the subject may be better.

  5. Hi Ken,
    Every learner defines learning differently, and so is my interpretation of Connectivism. Would you agree that Connectivism is a term, or a name that you or me would like to call it, so as to make sense of learning. This is similar to the concept of sensemaking – which is defined as the process of creating situation awareness in situations of uncertainty.

    Here is another important learning that I have which arose out of networked learning or Connectivism. Our prior knowledge was relatively less influential than emotions, beliefs, cognitive factors and mental models – all components of of sensemaking. People (leaders, managers and educators and learners) are more successful in connecting with other people (leaders, managers, colleagues, workmates, educators and learners) if they understand each others’ needs and expectations, and thus be able to form a closer bond both emotionally and cognitively. People who could leverage the affordance due to technology, media and learn effectively through the networks would be at a competitive advantage over those who rely solely on the traditional formal education and learning methodologies. There is no single solution to all learning scenarios, and so every learning must be sensed and acted upon with strategic learning strategies with a contingent and emergent learning approach.
    I still reckon the learner centred approach in education and learning provides the best outcome for the individual in terms of the achievement of personal goals and achievement (ego’s and self actualisation). Education that is building on the individual’s achievement and satisfaction is also the responsibility of institution and society at large. Without satisfied people in institution, how would one expect great performance from people? History tells us the importance of motivation (such as the Maslow Needs Hierarchy) – that people work best when they are motivated intrinsically AND extrinsically, and with the right environment for each of them to excel. Without an adequate culture of nourishment for individuals – with network and technology capacity of action, people would not be able to achieve higher potentials in the networks or COPs. The best way to achieve such nourishment could be through individual leadership empowerment and development.
    So, leadership is no longer a one person leading the way, but a process, a human approach which allows everyone to take up the leadership role, in the networks, to lead and support each other in achieving the individual’s goals. Since each ones goals might be different, such network leadership approach would enhance individual’s understanding and desire of leadership, when they take up leadership position at work, in the community or in government organisation.
    What did you learn from this?

  6. Hi John. I learned that I liked to use avatars as it is a way for me to attempt to look at issues from different perspectives.

    Oh sure, ‘Connectivism’ is a label that George and Stephen have chosen to call thier ideas. Would you agree that they think that this is the definition of learning?

    What is your definition of the ‘learner-centred’ approach? Is this a pedagogical issue?

  7. ‘Connectivism’ is a label that George and Stephen have chosen to call their ideas. Would you agree that they think that this is the definition of learning?”
    Do I agree that they think this is the definition of learning? I think they would be the ones to answer your question, not me.

    My definition of the ‘learner-centred’ approach is: education, learning is now related back to the learner, with teaching and/or facilitating as a support and network, technology as enabler. And the best way to learn relates back to the learner – individualised learning based on learning styles, intelligences (the multiple intelligences one has) and connections – network associated with, and his/her choice of support and technology.

    Is this a pedagogical issue? Why would you think it is a pedagogical “issue”?

    If we are relating Connectivism as a theory of learning, then the focus would be on the learning by the learner. Who would make the decision with regard to learning? Is it the learner or the teacher? Whether he/she would need the support of the teachers, facilitators and technology and network is a decision that the learner needs to make. If the teacher is the one deciding on the learning of the learner in social network or learning networks, then it’s still up to the learner to consider what may be in the best interests for his/her learning – and that’s why it is a learner-centred approach.
    There may also be instances when there aren’t any teachers involved in the learning process, like in a social networked learning, where “we” might be peer learners. What would then be the pedagogical issues then?

    See below explanation about pedagogy from wikipedia.
    Pedagogy is the study of being a teacher. The term generally refers to strategies of instruction, or a style of instruction.

    Pedagogy is also occasionally referred to as the correct use of instructive strategies (see instructional theory). For example, Paulo Freire referred to his method of teaching adult humans as “critical pedagogy”. In correlation with those instructive strategies the instructor’s own philosophical beliefs of instruction are harbored and governed by the pupil’s back-ground knowledge and experience, situation, and environment, as well as learning goals set by the student and teacher.

  8. Hi John thanks. So I think you have answered ‘yes’ to my question about ‘learner-centred’ being a pedagogical issue.

  9. Hi Ken,
    What are the pedagogical issues? Would it depend on the learning scenario? If the learner has no or little experience in learning online or through the virtual or digital networks, then would these learners need more assistance and support from the “teachers” or “peer learners”? Have you considered what the learner needs and expectations are before considering the teaching, instruction or facilitation required? In an online learning environment, a lot of adult educators and learners are learning in a different setting than the “traditional classroom” teaching and learning. There may or may not be any teachers available in the networks. In many cases there are facilitators or instructors (from formal course instructors in HE or institutions, guides (bloggers), helpers (peer learners), networkers or lurkers. So, the approach towards learning in networks could be very different from that in the classroom, and this could be very challenging for both the formal instructors and the learners (in the case of students learning in a formal course). In order to gain a broader and deeper perspective on this (from you and others), would you like to response to this question:
    Why is learner-centred learning a pedagogical issue?

  10. >Why is learner-centred learning a pedagogical issue?

    For starters, because of the issues you raised in your comment preceding this question:

    learner characteristics, support, expectations etc.

  11. Great, Ken.
    I enjoy our sharing. So, there are always various stages in project team working: Forming, Storming, Norming, Performing and Adjourning… and so even in networks. I am not sure which state “we” have past through. What would you suggest?

  12. I don’t know. Who is ‘we’?

    “I” may continue to lead myself to storm the bastille of connectivism but not in true team fashion. Unless followers appear.

    On the other hand, perhaps Sun Tzu’s advice is appropriate:

    Nurture life,
    Occupy high ground
    Your troops will thrive
    Victory will be sure.

  13. So you are looking for victory.
    I could see your huge fork. Ready for the triumph?
    Everyone has followers. Otherwise Twitter and Facebook will be closing down. Have fun and peace.

  14. I will post many more questions on Connectivism if you like.
    What sort of outstanding questions do you have? I know that I don’t know most though.

  15. Let’s see what Sun Tzu says today:

    (The Skilful Warrior)

    He changes his ways
    and alters his plans
    to keep the enemy
    in ignorance.

  16. Hi Ken,
    Does connectivism say anything about it? I was not sure whether it was mentioned or included in the course of Connectivism or form part of the theory. Not? I am also unsure whether the affective domains are addressed in the theory, or included in George proposed principles of Connectivism or Stephen’s proposed properties of networks.
    Reason is important in networks, correct? How about emotions in networks? Is it important?
    I think it might be of interests to the instructors and participants on this emotional intelligence, and that’s why I raised it in my blog posts.
    Do you reckon your big fork is a form of “power”, or you as an “authority figure” with this picture? What sort of emotions do you want to transmit with your posting? Remember the “fight or flight response”? LOL

  17. Hi Ken,
    This sounds philosophical.
    Why would you see enemy? I could only see neighbours, brothers and sisters, under my Catholic “lens”. I also understand that there are lots of spywares, spammers on the web, but I am not referring to these evils.
    Every human is a Creation of my God. How about this? Love your neighbour as thyself and you will have peace and love from God.


  18. >Do you reckon your big fork is a form of “power

    Not at all. When I picked this picture, I tried to find the goofiest-looking devil I could find, to support my ‘devil’s advocate with a twist of humour’ personna. If that picture scares people, that’s great, so funny!

    I wonder if emotions impact on the formation of strong/weak ties? I wonder if emotions are a factor in hub formation? I don’t know enough about network theory to comment further. Is there some language in network theory that sounds ‘affective’? I suppose their must be.

  19. >Why would you see enemy ?

    These are Sun Tzu’s words, not mine. There is no significance in my placing them here: what I have done is place the first words I found at the first page that opened from one of my Art of War translations.

    What I find significant is your interpretation. You have assumed that I am looking for victory over my enemies? How warlike is that?

    I prefer to respect my neighbour. I find that respect conveys a different meaning than love, and I find more utility in it. But I understand how/why Christians use the word love, and the word God, for that matter.

  20. Re Emotional Intelligence.

    Have you read any of Daniel Goleman’s stuff? My personal favourite is his book Primal Leadership.

    A couple of quick notes I made from that book:

    I’ve learned that people will forget what you said, forget what you did, but people will never forget how you made them feel.

    The job of the leader is to make people feel happy.

  21. I have read a few of Daniel’s book, not Primal Leadership.
    Your quote sounds appealing, yes, people will never forget how you made me them feel… good, and better still happy. I appreciate.

    In “The New Leaders” (2002) by Daniel Goleman, he mentioned the self-directed learning is most effective and sustainable when you understand the process of change- and the steps to achieve it – as you go through it. This model of learning was developed by Richard Boyatzis during three decades of work in leadership development… (P138-143). I am not getting any reward or benefits from Daniel in the above quotation, so don’t take this as an advertisement or promotion of his work.
    So self-directed learning has been researched for a long time, and when I read this book many years ago, and reflected on this in 2008 CCK08, I said, wow, it was so powerful. It was any “new” for me though, as I used to learn it like that even when I was in my teens. I reckon many adults would love it once they know and apply such model of learning.
    How does self-directed learning sound to you?

  22. ‘self-directed learning’ sounds to me like some teacher woke up and finally figured out no one was listening to them, and decided that in order to keep people coming/paying the institution for courses, they better try to make it more appealing and create a new buzz-phrase.

    Sorry, I think that ‘self-directed learning, managed for leadership development’ is an oxymoron. Self-directed learning, in the extreme and true sense of it, exists outside of any structure that can be imposed upon it.

  23. May I share my experience? I have been exercising self-directed learning since I was young. Even when I did my undergrad & post-graduate, I found it very fulfilling when I directed my own learning. Is self-directed learning limited to certain types of people with particular learning style, under certain learning context?

    Yes, self -directed learning may not be allowed under certain culture, as conformance to group norms and command-control is the rule to be obeyed by learners.

    Is self-directed learning, managed for leadership development an oxymoron? Would it depend on the “leadership development” that we are referring to? Under a networked learning environment, leadership could be cultivated differently from the traditional “leadership” program, where everyone could lead and excel basing upon their talents and potential. I do agree that “Self-directed learning, in the extreme and true sense of it, exists outside of any structure that can be imposed upon it.” Once upon, I remarked in my blog post that authentic education and great learning starts when you graduate from a formal education program. You could truly lead your way in learning with your passion as your compass. Your companionship and connections would then provide you with the guidance throughout your journey of learning.
    Do you think self-directed learning be “allowed” under a “democratic leadership development”?

  24. >I found it very fulfilling when I directed my own learning.

    It might be good for this discussion if I better knew what you meant by ‘self-directed learning’. Could you elaborate on what you mean by this concept?

  25. Here is a summary: http://en.wikipedia.org/wiki/Self-directed_learning
    My understanding is that if you direct your own learning, based on your passion, interests, talents, and capability, then that is the essence of self-directed learning. Throughout my teaching and learning, both in school and work settings, I realized that many people have the capacity of self-directed learning. Would it be a matter of degree of self-directedness when it comes to learning? Some people feel very comfortable with such self-directed learning, and they could be highly successful in learning. Other people may find it hard, and would prefer to be guided through in their learning journey, especially when they haven’t got full mastery of the skills needed for self-directed learning, or a feeling of incompetence due to the lack of confidence and practice. I think this depends on the learning stage where a person is in, i.e. whether one is in the growth, development, maturity stage of learning development. So, self-directed learning for educators and learners will also depend on the learning ecology – technology/media affordance, and the support from others, and the type of learning and constraints.

    Are you also self-directed in your learning?
    Do you find it easy or hard to achieve?

  26. Hi John. I just read that forum again, thanks. I find it so funny now, what I wrote there under different ‘avatars’. And I find some people so serious, like Roy who had a whole system proposed for separating ideas from the personalities and banning avatars. Must academics be so stuffy all the time? I hope I don’t get that way as I pursue academia further. Does being an academic include taking oneself very seriously? If so, I may be in trouble.

    What manner of mindset would make the comment that ‘avatars’ are tooooo playful (I don’t believe the mindset is endemic to Roy alone, he just evoked it in that forum, I’m not trying to single him out, just make use of his evocation, I like Roy and appreciate his intellect)? No wonder we need ‘self-directed learning’. Directed learning is boring.

    But to answer your question, was I ‘self-directed’ during cck08? Sure, in the sense that I marched to my own drummer and to what I ‘felt’ like learning. And not so sure, in the sense that cck08 did direct one’s learning in specific directions. And when it didn’t, there were group ‘hugs’ and ‘ group thinking’ to pull one back to the herd.

    For me it is always easy to achieve the goals I set for myself, but not always easy to achieve goals that are set for me by someone else. Confidence is important, as you noted.

  27. Hi Ken,
    I love to hear what you shared.
    Relating to the different avatars, since they all represented different perspectives (or sometimes echo chambers), I did find it confusing, and not sure what and how to respond. I love to engage in deeper learning, through sharing in the discourse. How would others view that?
    When sharing in the forum in CCK08, I reckoned many educators took it very seriously, as they were representing themselves as professionals, with a professional tone, based on reasons, and thus might have withheld their emotions of unpleasant feelings (i.e. based on appreciative inquiry). Would this create a sense of discourse and collaboration, so participants (including instructors and others) would find it easier to engage and discuss? Would the introduction of avatars change the atmosphere of discourse? Like to hear more…

    As shared in my past posts, it is easier to “criticise” and comment critically on ideas, not the person, as human are emotional and that could cause uncomfortable feelings. The case Catherine well illustrated the impact of strong emotions in forum discussion. She might have got her points in the debate, however, if she put in other’s position, then she might have realised that it was her views and perspectives only, even if she was right, but not necessarily representative of what others are thinking.
    Another issue relating to strong views (either as a blogger or forum poster) was the pontification (I am right in this view, always type of mindset). Would this leave others with the impression of being stubborn, or narcissistic in personality?

    The research in cck08 did highlight some concerns on such pontification amongst bloggers in particular, and the seemingly narcissistic and the self-promoting attitudes amongst posters.
    Would it be a concern for you (or others) when perceiving other bloggers (or experts)? Would this be another topic of interest?

    So, you have concluded that we needed self-directed learning. Directed learning is boring. I resonate with yours.
    Your observations and reflections on cck08 experience aligned with what we had found in our research, where many respondents did find the “group” learning effect, with some valuing it because of diversity of opinions, whilst others who preferred to learn more independently (and think aloud alone or reflect and challenge oneself) would just lurk or stay away from the debates.
    Yes, it is always easier to achieve the goals you set for yourself. Have you achieved that?
    Every year, I set a few goals myself, with strategies and action plans. But that is like wayfinding and sensemaking preparation only, as serendipity and emergent learning are always giving me new and emergent “lights” in knowledge and learning.
    How would confidence affect our engagement and conversation? Some of the participants of CCK09 & CritLit2010 have already mentioned that they grew in confidence when they had more chances in voicing their opinions, and got feedback and comments from others.

  28. >Would the introduction of avatars change the atmosphere of discourse? Like to hear more…

    >The case Catherine well illustrated the impact of strong emotions in forum discussion.

    I think that deep learning can be a little messy at times, and maybe not appreciated by the faint of heart. Aren’t emotions an important issue in discovery and learning? Aren’t they the beginning, as you yourself have observed and stated elsewhere?

    >Yes, it is always easier to achieve the goals you set for yourself. Have you achieved that?

    It’s more about the journey than the destination. Consider also some terms such as sychronicity, drala and magic.

    >How would confidence affect our engagement and conversation?

    Perhaps there is an inverse relationship between confidence and worrying about how others will perceive you. If one doesn’t worry about the latter, then confidence to express and externalize would increase.

    Using ‘avatars’ is similar to letting others speak for you, thus the worry of how others will perceive you is diminished, and conversation and expression increases. This is my newest theory! hahaha

  29. “Aren’t emotions an important issue in discovery and learning?” Imagine any discovery and learning without emotions, what would it be like for human? What’s the difference of the learning between such human from an artificial intelligent machine that can be switched on and off?

    Why would you worry about how others will perceive you? You have found an avatar speaking for you, as it could diminish the worry of others’ perception. That is interesting.

    I am, however, my own avatar, because I see myself as who I am, as a Catholic and Christian, and a learner in this world of learning. So, to me, learner is more valuable than any professionals on earth, because I think it’s through the humble path of being a learner that one could grow and develop. Growth of human is similar to the growth of faith in religion, it is ongoing, and would enlighten my life.

  30. It is good that you have your religion, John. It provides you with your strength, and you know with certainty who you are.

  31. Thanks for your kind words. As a Catholic, my strength comes from our Saviour Jesus Christ, my Lord, and our God. So, I came from my parents and I will go to the One who created me. There is nothing for me to fear in my life with His help, though I am just a human with all human weaknesses. When I am under anxiety or threat, I could pray to Him, and He would relieve me from such anxiety. When I am suffering from pains, my Lord would carry me through the hard times and strengthen me with His Holy Spirit. That’s my belief and faith.
    I am certain that God creates Human with a purpose – and that is where Salvation through Jesus is revealed to the Mankind.
    Fame and honors are like the clouds, they would come and go, but the Love of God would be like the air in the space, it is here for us to breathe and feel.
    I don’t know if you have a religion. No matter what religion you are in, may God bless you all. He is the divine who loves us all, you and me.

  32. I often admire people such as yourself John who are so sure of their beliefs and able to articulate them at will. I am happy that they are happy. But I shy away from those that are evangelistic. I wonder about cults and group-ish behaviour.

    My religion has no name.

  33. Yes, I saw this when you first posted it on facebook. I wonder how much separation there is between those type of cults and what some call mainstream religions.

  34. I wonder too! Do I know enough about mainstream religions? I can only say I know about Catholicism. Refer to the Holy Bible for acts if we are interested.

  35. Good Ken, I know about Catholicism. You would naturally ask “what do you know?” I am not a theologian. I read part of the Bible, not all of them.
    I didn’t study Nicae Council. I don’t know the answer, may be yes? And you will ask:” What part of the Nicae Council change “what part of Christ’s teachings?” And if I say no, what will you ask? Why? Didn’t it change some of Christ’s teachings?
    You have the response based on the http://en.wikipedia.org/wiki/First_Council_of_Nicaea But it is too difficult to verify yes or no. You can’t check with the deceased. And too many assumptions here. Isn’t it?

    What were the basis of Christ’s teachings? New Testament – the books of the Bible telling of the life and teaching of Christ and his earliest followers.

    What about your response to the question? Like to learn.


  36. But is not Christ’s word a Living Word? If so, then we can check with the deceased, who in this case, still lives….

  37. Yes. How would you like to relate the first question to “If so, then we can check with the deceased, who in this case, still lives….” Do you mean asking someone who is deceased? How? Can we talk to the deceased? May be we could ask, but would we be able to get a response, or check it out? What would you suggest?
    We could ask Christ though, through prayer.


  38. >We could ask Christ though, through prayer.

    I would guess that is your answer to the questions you asked…

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  40. Hi John,

    I have thoroughly enjoyed reading your articles on the development of MOOCs and its success since Siemens and Downes’s “Connectivism and Connective Knowledge” course in 2008, followed by Sebastian Thrun & Peter Norvig’s Artificial Intelligence course which broke the record of online student registrations. I am a currently university student conducting a research analysis on MOOC wanted to privately e-mail you and ask you a few questions regarding MOOCs, but could not find the button to do so (excuse me as I am new to the world of WordPress). Hence I will post them here and if you don’t mind taking some time to give me your feedback, I would really appreciate it.
    You mention that you believe that with the emergence of MOOCs, the “current education model would be “shaken” and further disrupted…” Are you referring to MOOCs constituting a technological discontinuity within the current tertiary education industry? Because I thought that whilst the MOOCs offers a dominant design, it is not a type of discontinuity (As we have already seen this technology in the former development of e-learning and online education, the only difference being that it is now available to a large market, as well as being free).
    You have also made comparisons to traditional forms of learning, and explained how MOOCs can offer the ‘future of education’. I am just not sure whether you mean MOOCs will offer the future of education in regards to ‘online’ teaching & learning, or future of tertiary education overall. Because in my opinion, I would have thought that the tertiary education format of the ‘face-to-face- teaching & learning still stands as the ‘dominant’ design, and due to institutional logics, cannot be easily replaced. Rather, the MOOCs will be a dominant design of the type of ‘e-learning’ and ‘distance education ‘s have seen in history, referring to the likes of University of Phoenix, NYU Online, and Fathom.

    I thank you for taking your time to read this and look forward to your reply.

    Kind Regards,


  41. Connectivism is the basis of how I lead my math instruction in my 7th grade classroom. Students can grasp more difficult concepts when they are given a reason to pay attention. Today, I will be teaching commission rates, but I have incorporated the sale of items that interest my separate classes into the word problems (PSVITA, sports cars, a suite to a Justin Bieber concert, etc.) Thanks for sharing.

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