I do not think that Sternberg's model can be use to your needs, as described above. You will have to be able to specify WHY children have difficulties in mathematics: Is it because of lack of specific knowledge in the domain, lack of general mental abilities needed, or lack of executive/representational abilities needed. Le tme have your email and I will send material to you directly.

Andreas

Thank you !! I really appreciate all the help.

Can you tell me your email?

A

As a physics professor, I arrogantly think of myself as teaching problem solving. I intend the process that I teach not only models how I solve problems, but I intend it to expose student thinking. 

Let me share some of what I do - mostly adapted from the 3DBeSNUB process taught at BYU-Provo.  Much if it is an attempt to get students to share their thinking, and make it more explicit.

I ask students to represent the problem in multiple ways.   (This is the best vehicle for teaching transfer.)  They include a picture, graph, words, and other appropriate representations like a number line, or a free-body diagram.

I ask them to identify the fundamental principle(s) they expect to use to solve the problem.  (We often express those as equations.)  I ask them how they know to consider those principles and not others.  "How do you know" is probably the most important part of the process in terms of preparing them for the next problem, and is hardest part to mark or grade meaningfully.

I then ask for a symbolic solution.  (This is college level physics.) And then finally a numeric solution with units. 

Finally I ask them to evaluate their answer.  Is it reasonable?  How do you know if it is reasonable?

"How do you know" is the most productive step, when I can get students to buy in.

Having students to trust you with their thinking is a great gift, which you must handle with kid gloves.  You must act in ways which are worthy of that trust, and use their disclosures to help them rather than punish them, or all trust is gone.

My experience with the structure Lillian McDermott calls Checkouts, in the curriculum materials Physics by Inquiry is the best model I have for treating the role of learner with enough dignity to merit this kind of trust.

A checkout is where I interview groups of 2-4 students about their observations and thinking about the activities (experiments and thought experiments).  I am supposed to reflect what they tell me, ask them if that is consistent with what they predicted, and with what they thought before.  That is, I am not supposed to pass judgement about their answers, but encourage them to use high standards when judging their own thinking.  The standard against which they should evaluate an answer is not what the professor thinks, but their own thinking.

Students routinely blind-side me with ways of thinking I had not expected.  I am careful to admit that to students when it happens.   Not knowing something is not a sin.  Avoiding something we don't know, on the other hand, is, and we need to model good behavior.

The pace of covering content by this method is very slow.  But students generally could give their own lecture on the topic after learning it this way, and generally feel capable of doing so.

@Ryan Nelson You describe the best way of teaching. I completely agree with you and one of the reasons that I teach math in 5th grade (although my work as head teacher is heavy) is to apply my knowledge in didactics and pedagogic principles. But I talk about research methods  that mean I have to decide between observation protocols or a model as  Charles, Lester, and O'Daffer proposed. Of course many great mathematicians  and researchers in the field of problem solving,   developed further the model of Polya  (inspired by John Dewey ). «Garofalo and Lester described problem-solving behavior as consisting of four phases of distinctly different metacognitive activities: orientation, organization, execution, and verification. In describing their framework, Garofalo and Lester indicated that shifts from one phase to the next commonly occurred when metacognitive decisions resulted in some form of cognitive action».

Representations in problem solving is a great field that I studied carefully and in my opinion representation Is the key to solution and self regulations is prerequisite 

Hi Zoi - I have done this with students of many ages.  With simplified language, I believe it can be done with younger students - Here is a rubric and a publication that might help.  Best to you! :)

Baron, L. M. (2016). Formative assessment at work in the classroom. Mathematics Teacher, 110(1), 46-52. See http://tinyurl.com/goaoovz

Article Formative assessment at work in the classroom: Assessment to...

Thank you  @Loraine Baron. Very helpful publication