''A Mathematician's Lament'', often referred to informally as Lockhart's Lament, is a short book on

mathematics education In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical know ...

by Paul Lockhart, originally a research mathematician at

Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...

and U.C. Santa Cruz, and subsequently a math teacher at Saint Ann's School in

Brooklyn Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

for many years. This strongly worded

opinion piece An opinion piece is an article, usually published in a newspaper or magazine, that mainly reflects the author's opinion about a subject. Opinion pieces are featured in many periodicals. Editorials Opinion pieces may take the form of an editorial, ...

is organized into two parts. The first part, "Lamentation", criticizes the way mathematics is typically taught in American schools and argues for an aesthetic,

intuitive Intuition is the ability to acquire knowledge without recourse to conscious reasoning or needing an explanation. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledg ...

, and problem-oriented approach to teaching. The second part, "Exultation", gives specific examples of how to teach mathematics as an art. The author of this book, as well as of the books titled ''Measurement'' (2012) and ''Arithmetic'' (2017), is not to be confused with either

the historian ''The Historian'' is the 2005 debut novel of American author Elizabeth Kostova. The plot blends the history and folklore of Vlad Țepeș and his fictional equivalent Count Dracula. Kostova's father told her stories about Dracula when she was ...

or the astronaut who are also named Paul Lockhart.

Background

This book was developed from a 25-page essay that was written in 2002, originally circulated in typewritten manuscript copies, and subsequently published by

Keith Devlin Keith James Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

on his online column for the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

webzine An online magazine is a magazine published on the Internet, through bulletin board systems and other forms of public computer networks. One of the first magazines to convert from a print magazine format to an online only magazine was the computer ...

''MAA Online''. Lockhart has since written ''Measurement'' (2012) and ''Arithmetic'' (2017).

Summary

In the first part, “Lamentation”, Lockhart emphasizes mathematics as an art. He criticizes

for prioritizing rote memorization and notation, which he argues is of little interest to the average student. Lockhart pushes instead for a focus on

mathematical proofs A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof c ...

and showcasing the beauty in mathematics, absent of any application. He also criticizes the use of two-column proofs in the teaching of geometry for obscuring this beauty and misrepresenting how mathematicians create proofs. In the second part, “Exultation”, Lockhart gives specific examples from

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

to argue that math primarily arises from

play Play most commonly refers to: * Play (activity), an activity done for enjoyment * Play (theatre), a work of drama Play may refer also to: Computers and technology * Google Play, a digital content service * Play Framework, a Java framework * P ...

. He argues that this play should be the primary focus of mathematics education.

Reception

Daniel Farlow and William Schmidt, writing in ''

Math Horizons ''Math Horizons'' is a magazine aimed at undergraduates interested in mathematics, published by the Mathematical Association of America. It publishes expository articles about "beautiful mathematics" as well as articles about the culture of mathem ...

'' and ''

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...

'', respectively, praised Lockhart's criticisms of mathematics education. Schmidt, however, also criticized Lockhart's proposed approach to math education for exacerbating preexisting inequalities within the education system. Timo Tossavainen, writing in ''

The Mathematical Intelligencer ''The Mathematical Intelligencer'' is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes ...

'', criticized Lockhart for "overlook ngwhat is realistically possible in mathematics teachers’ education", but he ultimately praised the book as a "necessary reminder of how all is lost if the joy of doing mathematics and the students’ right to experience it are not at the heart of mathematics education."

References

External links

Lockhart's Lament
the essay which prefigured ''A Mathematician's Lament'', by Paul Lockhart
Lockhart's Lament
about the earlier essay, by