![]() Beckmann provides are suggestions ("good to use") but the real test is whether they are useful to the thinker in the midst of their mathematical reasoning.īeckmann, S. In summary, I don't think there is support for a definitive list of benchmarks. ![]() ![]() Numbers can be replaced by nearby benchmarks that make for quicker calculation, if the aim is to just ballpark an answer (an often quite useful strategy for many real world applications). In that case, $2000$ is useful.Īnother type of mathematical reasoning that might benefit from a benchmark is estimation. For example, in my response to another question (seen here), I wrote about student reasoning that transforms a subtrahend into the number $2000$. I should think any useful number used in reasoning could be called a benchmark. But reasoning allows them to practice conjecture, work through coming up with a justification for their answer, and eventually have a way to defend their answer other than "this is what the procedure produced." There are algorithms some students are taught to use for fraction comparison, which allow them to replace mathematical reasoning with a couple of memorized steps and some arithmetic. The intent is to encourage reasoning rather than procedure. In this case, the benchmark is used as a reference point for comparison of fractions. However, the use here is clear: a benchmark number is a number useful in reasoning about a problem. I can't say whether others use benchmarks the same way (a quick look at some other books I have within arms reach doesn't show up the term). Students would choose a fraction benchmark that helps them compare. It's clear from this text that the numbers are somewhat arbitrary there's not meant to be a definitive list of benchmark numbers. When students are trying to determine which fraction is larger, $\frac$, and $1$ are good to use as benchmarks. As such, it's often a good place to check for things like this.īenchmarks (also called "landmarks") are introduced in the context of comparing fractions. The book is intended to help strengthen teachers knowledge of the mathematics behind the ideas in elementary curricula (especially reform curricula, I think). If the Mentor fails to complete the required renewal process, all rights of the Mentor in the Mentors’ Network and to the Training Materials will terminate.A decent volume on elementary mathematics is Mathematics for elementary teachers (Beckmann, 2010). Mentor may use the Training Materials pursuant to the Use Agreement so long as the Mentor completes the Annual Mentor Renewal process including the completion of the required Mentor Renewal Workshop and associated survey.if the Mentor becomes aware that the Training Materials have been sold or commercially distributed or otherwise used in a manner that is not authorized by this Use Agreement. Mentor will take all necessary and appropriate action to safeguard the Training Materials from any use that is not permitted by this Use Agreement (including but not limited to the sale and/or commercial distribution) and will immediately notify Acadience Learning Inc.display the PowerPoint slides contained within the Training Materials in the course of training within the scope of use authorized above in Section 1.download the Training Materials onto the computer that Mentor uses to conduct training within the scope of use authorized above in Section 1, and.The scope of use authorized above in Section 1 print a paper copy of the Training Materials for Mentor’s own use in preparing for and providing training within.The provisions of the preceding paragraph to the contrary notwithstanding, Mentor may:.The Training Materials may not be copied, distributed, displayed, or reproduced in any format or media (e.g., print, DVD, web pages, learning management platforms) without the prior written permission of Acadience Learning Inc.Alteration includes, but is not limited to, changes to font, sequence, content, or the removal of the words “Acadience” or “Acadience Learning Inc.” No part of the Training Materials may be used to make other works based, in whole or in part, on the Training Materials. The Training Materials may not be altered or incorporated into or compiled with other materials, either in whole or in part, by any means, electronic, print, or otherwise, without the prior written permission of Acadience Learning Inc.
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