How large are double markups?

How Large Are Teacher Effects?

It is widelv accepted that teachers differ in their effectiveness, yet the empirical evidence regarding teacher effectiveness is weak. The existing evidence is mainly drawn from econometric studies that use covariates to attempt to controlfbr selec tion effects that might bias results. We use data from a four-year experiment in which teachers and students were randomly assigned to classes to es...

Running Head: How Large Denominators Are Leading to Large Errors 1 How Large Denominators Are Leading to Large Errors

When it comes to fractions and working with them, they can be difficult to understand. Through our research, we attempted to bring a greater understanding to how we as individuals learn fractions. With this, we can move forward to teach fractions in a way that lets us have a better understanding of fraction magnitudes and how to work with them. For our study, we tested three hypotheses. First, ...

Food Taxes: How Likely Are Likely Effects?

How Large Are Left Exact Functors?

For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving) functor from K to Set is small, that is, a small colimit of representables. In contrast, for the (presheaf) category K = Alg(1, 1) of unary algebras we construct a functor from Alg(1, 1) to Set which preserves finite prod...

How Large Are the Spectral Gaps?

Let D be a bounded domain in R whose boundary has a Minkowski dimension α < n. Suppose that EΛ = {e } λ∈Λ , Λ an infinite discrete subset of R, is a frame of exponentials for L(D), with frame constants A,B, A ≤ B. Then if R ≥ C ( B|∂D| α A|D| ) 1 n−α , where C depends only on the ambient dimension n and |∂D| α denotes the Minkowski content, then every cube of sidelength R contains at least one ...