In research knowledge construction, as far as I can manage to understand your question, might mean the methods and procedures through which knowledge is formulated. Various ways exist to constitute and communicate knowledge and, fundamentally speaking, constructing knowledge pertains to the activity that language has, its role for instance, in formulating and analysing the object of science (whatever that might be). Imagine it as having various building blocks (let's say language, ideas, objects, methodology) out of which you build an edifice which, as it accumulates in time, becomes what we generally term knowledge - what people speak about, know, and what students are taught in various disciplines in school and university.

Reconstructing knowledge, in this very same context that I am pursuing, means to take these building blocks - which act as the fundamentals of science, technology, religion, history - as we have inherited them either culturally (in a non-controlled context) or through academia (in a controlled context), and rearranging them in a different manner (it might also mean uncovering "lost" knowledge, for instance, the method of Foucault's discourse analysis, what he termed "archaeology of knowledge"). Let us say that the first reading of a text stimulates the construction of knowledge (through discussing what the text, generally speaking, is about) while subsequent rereadings (multiple, as might happen in a classroom for instance) partake in the process of re-constructing this knowledge. For example, with the help of the teacher or lecturer, aspects of the work in question might change their meaning so as to fit into the larger body of knowledge to which this work alludes. In this way, both parties - students and teachers - participate in the construction and reconstruction of knowledge, enlarging our perception of the ideational world we have inherited and us, as people.

Deconstruction, on the other hand, is a concrete term in the humanities that relates, very roughly summarising, to Jacques Derrida's theory of the illusory nature of a central and stable signified (see Ferdinand de Saussure's linguistic theory of the sign) which he names "the transcendental signified" and the ensuing "play" of signifiers which is endless. For example, if you check a word in a dictionary it uses other words to explain the target word in question, but you might look up all the words in the explanation which would relate and refer to other words and so on ad infinitum. De-constructing knowledge in educational research context might mean to elaborate the ways in which language is translucent, i.e. semi-transparent, like a glass which changes the object that we see and think of, through refraction - all this meaning that language cannot be and is not neutral, but always betrays an ideological, cultural, social, or otherwise aesthetic position (Roland Barthes has written a lot on this topic). In these lines of thought, to deconstruct a text means to show/communicate to the students the ideological background from which it has taken its meaning and sense; the ideas which it conveys in a denotative sense; the author behind the text with his/her agenda, feelings, desires, fears; the history which gave rise to its style and thought framework.

Constructing, reconstructing, and deconstructing texts and knowledge(s) is one of the most interesting and illuminating things to do in a classroom and outside it!

Hope this helps!

Thank you