Designing for mathematical abstraction

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as designing for abstraction. In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing for abstraction. Through the case study, we elaborate a number of design heuristics that we claim are also identifiable in the broader literature on designing for mathematical abstraction. Our previous work on the micro-evolution of mathematical knowledge indicated that new mathematical abstractions are routinely forged in activity with available tools and representations, coordinated with relatively naïve unstructured knowledge. In this paper, we identify the role of design in steering the micro-evolution of knowledge towards the focus of the designer's aspirations. A significant finding from the current analysis is the identification of a heuristic in designing for abstraction that requires the intentional blurring of the key mathematical concepts with the tools whose use might foster the construction of that abstraction. It is commonly recognized that meaningful design constructs emerge from careful analysis of children's activity in relation to the designer's own framework for mathematical abstraction. The case study in this paper emphasizes the insufficiency of such a model for the relationship between epistemology and design. In fact, the case study characterises the dialectic relationship between epistemological analysis and design, in which the theoretical foundations of designing for abstraction and for the micro-evolution of mathematical knowledge can co-emerge. © 2010 Springer Science+Business Media B.V

Novel polyimide compositions based on 4,4': Isophthaloyldiphthalic anaydride (IDPA)

A series of twelve high temperature, high performance polyimide compositions based on 4,4'-isophthaloyl diphthalic anhydride (IDPA) was prepared and characterized. Tough, film-forming, organic solvent-insoluble polyimides were obtained. Three materials were semicrystalline. Several gave excellent long-term thermooxidative stability by isothermal thermogravimetric analysis (ITGA) at 300 C and 350 C in air when compared to Kapton H film (duPont). One extensively studied material displayed different levels of semicrystallinity over a wide range of final cure time/temperatures. The polyimide from IDPA and 1,3-bis (4-aminophenoxy 4'-benzoyl) benzene exhibited multiple crystallization and melting behavior, implying the existence of two kinetic and two thermodynamic crystallization and melting transitions by differential scanning calorimetry (DSC)

Far O\u27er The Deep Blue Sea

[Verse 1]The moon is beaming brightly love, Upon the deep blue seaA trusty crew is waiting near,For thee, dear girl, for thee!Then leave thy downy couch, my love, And with thy sailor flee;His gallant bark shall bear thee safe,Far o\u27er the deep blue sea,Far o\u27er the deep, the deep blue sea. [Verse 2]The storm-bird sleeps upon the rockNo angry surges roarNo sound disturbs the slumb\u27ring deepNot e\u27en the dipping oar:No watchful eye is on thee now,Then,dearest, hie with me,And share a daring sailor\u27s love,Far o\u27er the deep blue sea. [Verse 3]She comes! she comes! with trembling stepOh! happy shall we beWhen safely moor\u27d, on other shores,From ev\u27ry danger free!Now, speed thee on my trusty bark,Our hopes are all on theeBear, bear, us to our peaceful homeFar o\u27er the deep blue sea

Processable polyimide adhesive and matrix composite resin

A high temperature polyimide composition prepared by reacting 4,4'-isophthaloyldiphthalic anhydride with metaphenylenediamine is employed to prepare matrix resins, adhesives, films, coatings, moldings, and laminates, especially those showing enhanced flow with retention of mechanical and adhesive properties. It can be used in the aerospace industry, for example, in joining metals to metals or metals to composite structures. One area of application is in the manufacture of lighter and stronger aircraft and spacecraft structures

Why Most of Our Indians are Dependent and Non-Citizen

Address delivered by Brigadier General R.H. Pratt. Date and location of address are not known. Date is presumed to be between 1904 and 1915.https://digicom.bpl.lib.me.us/books_pubs/1085/thumbnail.jp

Indian Schools: An Exposure

Opening lines: I am asked to talk to you for thirty minutes about Indian Schools. I speak from wide, long, and varied experience with the Indians. R.H. Pratt, Brigadier General, U.S.A.https://digicom.bpl.lib.me.us/books_pubs/1090/thumbnail.jp

Handbook of science activities and materials to be used in preparing children in Newton for school camping

Thesis (Ed.M.)--Boston Universit