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What is the best didactic and number sense-promoting method for reading decimal numbers?

For instance, is it best to teach students to read the number 3.14 as 'three and fourteen hundredths' instead of 'three, point, one, four'? I am looking for studies and references about this matter

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    $\begingroup$ Young students need to learn the meaning. For high school and college students I would read this as 'three point one four'. There is a 3rd way: 'three and 1 tenth and 4 hundredths'. (I know of no studies.) $\endgroup$
    – Sue VanHattum
    Apr 11, 2023 at 23:54
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    $\begingroup$ Be very careful: if you teach them to read $3.14$ as three comma fourteen and $3.2$ as three comma two, they might start to think that $3.14>3.2$ because fourteen is larger than 2. $\endgroup$
    – Dominique
    Apr 12, 2023 at 7:39
  • $\begingroup$ @Dominique, YES, THIS A SIDEEFFECT OF THIS WAY OF READINT IT IN YHIS WAY. $\endgroup$ Apr 12, 2023 at 15:37

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One reference is James Hiebert's chapter on "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" in the book Analysis of Arithmetic for Mathematics Teaching. He doesn't ever address the digit by digit reading of decimals ("three point one four"), but he does say that

Perhaps the most important conclusion that can be derived from reviewing previous research and ana­lyzing current textbooks is that instruction must spend more time and attention helping students establish rich meanings for decimal symbols.

A first useful activity, in third or fourth grade, involves base-10 blocks where the large block is assigned the unit. The class then can discuss what a tenth would look like, with the flat becoming a tenth. (If base-10 blocks are not available, a square cardboard piece can be the unit with strips representing tenths.) A day of activities would include building concrete representations of spoken decimals (e.g., “two and seven tenths”) and verbalizing the number represented with concrete materials (e.g., 1 large block and 3 flats)....

After numerous oral activities, the written notation can be introduced. Activities then can include building concrete representations for numerals and writing numerals for concrete representations. It is only at this point that the textbook activities will have some meaning for the students....

After several days with tenths, and before beginning addition or subtrac­tion, hundredths can be introduced with the concrete materials as both tenths of tenths and hundredths of the unit. The same sequence of ac­tivities can be followed as with tenths: (a) using verbalizations and con­crete representations only, (b) changing the unit block, and (c) eventually introducing the written symbol and showing connections between con­crete and written representations.

This supports introducing decimals through verbal representations like "three and fourteen hundredths." However, as Sue already pointed out,

[A] contrast in whole number and decimal language arises from the fact that there are a variety of acceptable ways of saying decimal numbers. For example, there are two common ways of saying 2.38, “two and thirty-eight hundredths” and “two and three tenths, eight hundredths.” Note that the first form implies two counting units (ones and hundredths) and the second form implies three counting units (ones, tenths, and hundredths). Whole numbers, on the other hand, are usually said in only one way. The number 47 could be said “four tens, seven ones” but it is almost always said “forty seven.”

Hiebert suggests that having students grapple with these different readings will support their understanding of the properties of decimal notation. In his analysis of two textbook series, he says

There is no explicit attention given in either series (Grades 3-6) to the remaining two properties: The value of a digit is its face value times its place value and the value of the numeral is the sum of the value of the digits. Of course, the authors may assume that such properties will gener­alize automatically from whole number notation, but no help is given stu­dents in recognizing the similarities between whole number and decimal notation. An even more serious deficiency is that students’ attention is never drawn to the power provided by these properties. The quantity represented by 2.16 can be described in many ways—two hundred sixteen hundredths, or twenty-one tenths six hundredths, or one and eleven tenths six hundredths, and so on. None of these noncanonical forms are explored; only the canonical form, two and sixteen hundredths, is presented.

So I think it's didactically beneficial to teach students how to read decimals flexibly and to be able to make intentional choices. The reading "three point one four" can be used when we need to refer to the numeral 3.14, e.g. "three point one four can be read multiple ways." And as Sue also already pointed out, "three point one four" may be preferable when working with older students. They often deal with continuous quantities, and "three point one four" supports the interpretation of 3.14 as one number among the continuum of the real numbers, or as a measurement of a continuous quantity to a certain precision.

A natural follow-up question is "When is the best time to introduce the reading 'three point one four' to students?" I don't have an answer to this, but perhaps others can chime in. Regardless, I think this advice from Hiebert applies, wherever students are in their understanding of decimals:

The evidence on students’ failure to connect symbols with referents suggests that instruction will succeed in helping students build appropri­ate connections only if it is intentionally designed to do so. Although the exact nature of the “best” instruction is not yet clear, several features that are sure to be included in effective instruction are (a) explicit attention to connections between meaningful, familiar referents and symbols that re­present them, (b) reflection on the semantic characteristics of written symbols, and (c) the development of a rich language that can be used to talk about the symbols.

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