This paper concerns mathematics education in Sweden in relation to Ludwig Wittgenstein and John Dewey . Both Wittgenstein and Dewey were critical of an essentialistic, or dualistic, view of knowledge as a distinct (mental) phenomenon distinguishable from the (physical) result. This kind of view is commonly expressed in the research on mathematics education , where mathematical understanding is seen to take place in the mind or the brain, and the calculation that takes place on paper is a more or less contingent result of the mental process. I will exemplify how this view has influenced the classroom practice in Sweden and will argue that as well as being philosophically problematic in the framework of Wittgenstein and Dewey, it is counterproductive as regards the aims of mathematics education .