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Drawings of plant structures from Marcelli Malpighii ... Anatome plantarum.
Page 151 from Marcelli Malpighii ... Anatome plantarum

Concepts across the Sciences: Scale, Proportion, and Quantity

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This post is by Jacqueline Katz, the 2022-2023 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

Scale, proportion, and quantity are three concepts that appear across all scientific disciplines. A quantity is an amount or number; scale is the size of an image or model in relation to the actual object; proportion is one quantity compared to another. Of these three concepts, scale can be the most challenging, especially for objects as large as planets and as small as molecules. Recent and historical scientific images provide a focal point to explore scale.

Using a microscope, Marcello Malpighi created hundreds of images of animal and plant tissues. Malpighi published many of his plant illustrations in “Anatome plantarum” between 1675 and 1679. Distribute this page at the start of a unit on plants, photosynthesis, or microscopy, and allow time for students to make and record initial observations and reflections on the Primary Source Analysis Tool. Once students have made individual observations, provide time for them to discuss in small groups or as a class.

Next, ask students to cut out each of the six figures and to determine which figures are “zoomed in” portions of other figures. Provide groups of students with whiteboards, so they can draw arrows between the various figures to represent these connections. As students are working with the figures, remind them to record additional questions that come up in their groups.

After students develop a working diagram, ask them to justify their choices using evidence they have observed. For example, one student group may claim that Figure 105 is a zoomed-in portion of Figure 103 due to the similarity in pattern, as well as the presence of thin veins connected to thicker veins. Invite student groups to share their thoughts, noting that multiple hypotheses can be generated to explain a single observation.

Ask students to rate the confidence they have in their diagram and to revisit their questions. It is likely that students will bring up the ideas of scale and proportion in their questions. For example, students may ask if the image labeled E is actually the same size as the structure labeled D in Figure 105. Ask students what Malpighi could have included to increase their confidence. Students likely will bring up the ideas of scale and proportion; they may explain that it would be useful if Figure 105 was significantly smaller than Figure 104 or if measurements were provided. Ask students to add scale bars to Malpighi’s illustrations; what unit of measurement would they associate with these structures? Centimeters? Nanometers?

To start a unit on plants or photosynthesis, focus on Figure 106. Ask students to make predictions about the function of the structures they see and then revisit their Primary Source Analysis Tool.l. Throughout the unit, revisit their initial predictions; like Malpighi, the students will likely not know the function of the stomata that are pictured.

This primary source helps students see the importance of scale and proportion in the study of biology, as well as construct knowledge about important biological concepts. Similar objectives can be met by using other illustrations from Malipghi’s book or by searching through other “scientific illustrations” at the Library of Congress.

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  1. El Lenguaje matemático, es esencial en los planes de educacion(fines y retos de la pedagogía y didáctica en su expresión curricular) para el desarrollo humano y social. Los órdenes de magnitud y cantidad, son fundamentales, como base en los procesos de avistamiento, comprensión y construcción de mundos, expresados como “juicios de valor”, en el proceso enseñanza-aprendizaje, para posibilitar los ajustes de observacion (observador) mediante la percepción de la “realidad” y la búsqueda o delimitacion del “concepto de verdad”.

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