Embryology

Many school textbooks claim that similarities between embryos of different organisms provide evidence for evolution. This was suggested by Charles Darwin in The Origin of Species and championed by Ernst Haeckel, a German biologist and philosopher. 
Haeckel proposed that animals undergo a re-run of their ancestor’s evolution as they develop in the womb. His theory is summed up in the phrase, "ontogeny recapitulates phylogeny". Haeckel published pictures showing remarkable similarity in the anatomy of embryos of different animals, claiming that this supported his theory. Unfortunately for the long-term credibility of his theory, his drawings were fraudulent. 

Figure 1. Haeckel's drawings of vertebrate embryos, 1874

Haeckel's drawings greatly exaggerate the similarities between the embryos of different vertebrates. This has been known for almost a century.  Historian Jane Oppenheimer has written that Haeckel's "hand as an artist altered what he saw with what should have been the eye of a more accurate beholder. He was more than once, often justifiably, accused of scientific falsification." 

In 1997 a British embryologist named Michael Richardson and his colleagues published photographs comparing actual embryos with Haeckel's drawings in the journal Anatomy and Embryology. This was reported in the prestigious journal Science in 1997, under the headline: "Haeckel's Embryos: Fraud rediscovered". Figure 2 shows diagrams based on Richardson's photographs (central box) compared to Haeckel's diagrams. The similarities seen by Haeckel are almost entirely fictional.

Figure 2. Haeckel's drawings compared with actual embryos (from Wells, 2000)

Surprisingly, many school textbooks still refer to Haeckel’s work, and some even reproduce diagrams based on those drawn by Haeckel. For example, Advanced Biology by Michael Kent (Oxford University Press, 2000) states:Observations have shown that species that are known to be closely related show a similar embryonic development. Therefore, species that show a similar embryonic development are assumed to be closely related, even if the adult stages are very different. For example, echinoderms (the phylum containing starfish and sea urchins) are believed to be related to chordates (the phylum including vertebrates) because of similarities in their early embryonic development. (page 439)It then has a figure which is seen to be based, with slight simplifications, on Haeckel’s drawings. 

Figure 3. From Advanced Biology by Michael Kent (OUP, 2000)

Similarly, Advanced Biology by  Roberts, Reiss and Monger (Nelson, 2000) has a short section on Embryology which claims that: 
the presence of branchial grooves (relics of gill slits) and segmental muscle blocks in the human embryo...are suggestive of a fish ancestry. (p.730)This section does acknowledge flaws in Haeckel's drawings of insect larvae: 
...there may have been some wishful thinking on Haeckel's part!But it does not mention Haeckel's fraudulent diagrams of animal embryos.

Longman GCSE Biology by Bradfield and Potter (2002) also uses evidence from comparative embryology, with a diagram given showing ‘gill pouches’ in bird, reptile, human and pig embryos. 

Figure 4. From Longman GCSE Biology (2002)

Comparing the ways in which the embryos of different animals develop can give clues about how closely related they are. It also reveals remarkable common features. Human embryos have structures resembling gills for a brief period in their development.In fact embryos never have gills, and calling features of human embryos 'gill slits' is merely to read Darwinian theory into the evidence.

Biological Science 1 and 2, edited by Soper (Cambridge University Press, 1997) also use evidence from comparative embryology, and discuss Haeckel's idea that 'ontogeny recapitulates phylogeny.'
Whilst this principle over-generalises the situation, it is attractive and there is some evidence to support it. (p. 899)The book then presents diagrams of tortoise, rabbit and chick embryos, which appear to be based on some of Haeckel's fraudulent drawings.

Figure 5. From Soper (Ed.) (Cambridge University Press, 1997)

Parents, teachers and pupils should be aware that one of the key evidences for evolution used by these textbooks is flawed. 

References

J. W. Oppenheimer 'Haeckel's variations on Darwin', pp. 123-135 in Heonigswald and Wiener (Eds) 'Biological Metaphor and Cladistic Classification' (University of Philadelphia Press, 1987)
E. Pennisi, 'Haeckel's embryos: fraud rediscovered', Science 277: 1435 (1997)
M.K. Richardson et al., ‘There is no highly conserved embryonic stage in the vertebrates: implications for current theories of evolution and development’, Anatomy and Embryology, 196(2):91–106, 1997
J. Wells,  'Icons of Evolution: Science or myth?' Regnery Publishing, Washington DC, 2000