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The problem solving process begins as soon as the problem solver generates enough information about the problem space to gain an understanding of the problem.

Representation in the problem-solving process refers to how the solver mentally represents the problem. The solver’s representation of the problem is directly related to his or her existing knowledge structure of the content of the problem.

Students have to increase their reflective practice to aid their metacognition and transfer of STEM concepts.

Different individuals have different conceptual knowledge and will make different associations to their knowledge. Exposure to the constraints and affordances of a particular context in which a problem exists will invariably influence the way in which the student represents a problem in a similar context.

Sanders (2009) admitted that it is difficult to prepare a teacher that is competent in all three bodies of knowledge, given the volume of content knowledge necessary to be an effective science, mathematics or technology educator.

This pedagogical approach is not without its challenges, as students may still compartmentalize their knowledge. Also, it is often difficult logistically and in terms of instructional timing for teachers across STEM discipline to collaborate effectively (Crismond, 2011; Kimbell & Stables, 2008).

Good and poor problem solvers differ in their recall of information from previously encountered problems and by extension their ability to transfer concepts to the target problem. This difference exists because poor problem solvers tend to remember surface similarities between problems, while good problem solvers remember underlying conceptual structures that make two problems similar although they have different surface features (Sutton, 2003).

Until student assessment methods are modified to reflect less dependency on standardized tests, engineering and technology educators will garner greater collaboration from math and science teachers when the latter can see that engineering and design-based curriculums does improve students’ ability to solve standardized test problems.

A teacher’s ethical caring means genuine caring, aspiring to understand and make an effort for pupils’ protection, support, and development. Because of this pedagogical caring, the teacher especially pursues pupils’ potential to develop and thus help them to find and use their own strengths.

Pedagogical love has been considered the core factor in the definition of good teacherhood for decades, though the characteristics of a good teacher have always included a variety of features. Features such as the ability to maintain discipline and order, set a demanding goal level, and the mastery of substance have been especially emphasized (e.g., Davis, 1993; Zombylas, 2007; Hansen, 2009)

Love influences the direction of people’s action as well as its intensity. Positive emotions, joy, strength, and the feeling of being capable lead mental energy toward the desired goal (Rantala & Määttä, 2011). Negative emotions, grief, fear, and anger cause entropy, an inner imbalance that burns off energy, brands the target with negative status, and pursues nullifying and undervaluing (e.g., Isen, 2001).

he educator’s task is to provide pupils with such stimuli and environment where students are guided to limit their instincts by controlling enjoyment and vital-based values, in order to be able to achieve higher values and skills (Solasaari, 2003).

Mihaly Csikszentmihalyi (1990, 2000) has launched the concept that refers to an optimal or autotelic experience where people are riveted so comprehensively by a challenging performance that the awareness of time and place blurs. Flow is possible when the challenges in a task are balanced with an actor’s abilities. Flow is an enjoyable state of concentration and task orientation, leading to optimal performance, whether the case is wall creeping, chess playing, dancing, surgery, studying languages, painting, or composing music.

This sets challenges for skill development. If a task is too easy, it will bore. If it is too difficult, it will cause anxiety and fear. The exact experience of flow and the active sense of well-being resulting from the former, encourage people to develop and improve their skills. People are willing to strive for flow whether it was about love for math, art, programming, or orthopedics (Csikszentmihalyi, 1990).

In an interview, Gardner (as cited in Goleman, 1999) said flow is intrinsically rewarding without the hope for reward or threat of punishment. We should use learners’ positive moods (love) and through it get them to learn things about fields they can succeed in. People have to discover what they like, what things and doings they love and do these things. Even a child learns the best when he/she loves what he/she is doing and finds it enjoyable. (p. 126)

Pedagogical love might contribute to pupils’ learning and success by providing them with positive learning experiences, initial excitement, and perceived successes. These are the seeds of expertise as a positive feeling that can be considered the source of human strengths (Isen, 2001).

Pedagogical love springs from an individual learner’s presence persuading it to come forward more and more perfectly and diversely. A skillful educator does not just sit by and watch if a learner makes worthless choices or fails in his or her opportunities to grow and develop.

Haavio emphasized the meaning of pedagogical love in teachers’ work and considered that teachers’ work consists of the following two obligations: attachment to learners and dutiful perseverance of life values.

Pedagogical love speaks to interdependence—the recognition and acceptance that we need others.

Love appears in teaching as guidance toward disciplined work, but also as patience, trust, and forgiveness. The purpose is not to make learning fun, easy, or pleasing but to create a setting for learning where pupils can use and develop their own resources eventually proceeding at the maximum of their own abilities

A loving teacher reveals for a pupil the dimensions of his or her development in a manner of speaking. This is how a pupil’s self-esteem strengthens and he or she can develop toward higher activities from the lowest, pleasure-oriented ones. Achieving high-level skills is rewarding because it brings pleasure, and yet, it often demands—as mentioned previously—self-discipline and rejections

A teacher’s work is interpersonal and relational, with a teacher’s own personality fundamental to building relationships with students. A teacher’s work involves plenty of emotional strain. In addition, a teacher inevitably has to experience frustration in his or her work. There are many situations when a teacher will feel like she or he has failed regardless of the solution he or she creates.

Consequently, teachers are likely to experience guilt because they cannot sufficiently attend to all pupils in an appropriate way that is congruent with the notion of caring.

However, teachers have to realize that their own coping, motivation, and engagement require attention; they are not automatic.

Pedagogical love emerges through teachers’ emotions, learned models, moral attitude, and actions

Good teachers are examples to learners even in the most difficult life situations. Teachers have to believe in their work and endeavour to build a nurturing environment and a more humane world.

To be happy about life, to guide students to see the wonder and joy in the mundane is a teacher’s most important skill. Being able to help students find and negotiate the joy, wonder, happiness, and pain in the everydayness of life is an increasingly important quality in today’s insecurities, with the mounting pressure of increased demands for efficiency

Twitter

~I continue to be astonished every week with how much I am growing and learning in this course.  Not only am I learning how to be an effective online instructor and everything that it entails, but I am also learning a lot about myself.~

I lose track of time and hours have gone by without me even realizing it. 

“What young children perceive that their teachers do plays a more significant role in their socio-emotional outcomes than what teachers report they do” (p. 30).  We have an EVEN bigger impact than we thought!

“Am I providing a bridge for my students from their prior knowledge to where I want them to be and where THEY want to be?” “What am I doing to facilitate their growth not only in building a positive self-image, but also as learners in general?” “Am I REALLY taking into consideration their interests, passions and motivations?” And finally, “What Would Alex Do?”

“I really like how you tell them you are there for them.  A lot of my teachers give us confusing assignments and I never feel like I can ask them questions.” 

When she was done going through everything she said, “Are you actually going to teach this class? Can I take it when you do?” 

  I was spending so much time figuring out the tools that I felt like I wasn’t spending time on content.  I realize now that I needed to spend that time and those tools were part of the content of this course. 

I LOVE learning in general!  I liked learning before…well I never disliked it anyway…well unless it was math…or science…I had no idea what it was like to truly LOVE learning.  Its sad to me that it took me 30 years to experience this.  Did I work A LOT in this course?  Did I give up much of my social life?  Did I stay up too late?  YES, YES and YES.  Was it worth it? Absolutely!  Did I mind? NOT ONE BIT…Reflecting on the fact that I worked so hard and so much on something and not only wasn’t bothered by it, but enjoyed every moment was a HUGE wake up call to me. 

You just have to have passion and a belief in yourself.

This was the only course I have EVER taken in which I will walk away having truly internalized knowledge.  I know that I internalized what I have learned because when I was reviewing my classmate’s courses I didn’t have to refer to a book or a checklist, it was all in my head.  When I look back at my undergrad education, I have always said that I didn’t feel like I actually “learned” anything until I student taught and learned by DOING.  That’s exactly what happened in this course, I learned by doing.  This is only course that has ever provided me with this type of experience and it has shown me what quality education should be, not only online but in a face-to-face situation as well.

We(myself, my classmates AND Alex) worked together in this course to contribute to the construction of our knowledge. 

It wasn’t until this summer when I turned 31 that I finally experienced being a student in a student-centered, constructivist environment that actually got me to THINK.  Not just think, but think critically…It took 31 years for me to experience a true community of learners!  I don’t want other students to have to wait 31 years to experience what its like to REALLY LEARN!

I want to CHANGE someone the way that Alex, ETAP 640 and all of you have CHANGED me.

The ability to solve problems builds on declarative knowledge and procedural knowledge.

eas, such as math versus writing

problem solving involves a sequence of steps, beginning with establishing a representation of the problem, then selecting a strategy that seems appropriate for resolving the problem, followed by evaluating the results of employing that strategy

Declarative knowledge involves information one can state verbally. Therefore, tasks will require students to state, explain, discuss, or declare in some other way what they know

He described declarative knowledge as a network of propositions, whereas procedural knowledge represented productions. While declarative knowledge involves knowing that something is the case, procedural knowledge involves knowing how to do something

To assess problem solving, students are presented a problem to solve or a situation from which they must infer the problem that needs to be solved. Typically, any number of strategies might be used to successfully solve the problem. When scoring student performance where the focus of the assessment is on problem solving, proficiency with particular strategies or other types of procedural (or declarative) knowledge generally is not scored. What is scored are qualities such as the establishment of a clear and appropriate problem representation and sense of goal, the selection of a strategy that is reasonable given the goal to be achieved, and the adequacy with which outcomes from using the selected strategy are evaluated.