Open-middle Questions
https://www.openmiddle.com/whats_open_middle/
This concept of open-middle is actually promoted by the above website.
https://www.teachersfirst.com/single.cfm?id=18498
The above is a review of the book on this open-middle.
tag(s): logic (232), problem solving (281), statistics (129)
In the Classroom
Bookmark this site to find math problems correlating to your teaching standards or content. This site is perfect for finding materials to differentiate instruction with different student ability levels. Have students share their results and discuss their problem-solving process on your interactive whiteboard. Take screenshots of the different solutions and include on your class website. Another option is to take a picture of student's written solutions, then use ThingLink, reviewed here, to extend student learning by having them add an audio recording describing their mathematical thinking. Share their ThingLink images on your website, or add to your student's digital portfolio on Seesaw, reviewed here, or another portfolio creation site. As students become more proficient in sharing their mathematical thinking and problem-solving activities, consider using their math talks as part of an ongoing podcast using Buzzsprout, reviewed here, as a way to extend student learning and promote math conversations and help students understand that there may be many different ways to arrive at the right answer to a problem. Buzzsprout features free and easy to use tools including the ability to create and schedule podcasts to be released on any date and time you desire.
The above review is more like an advertisement of the methodology.
A more useful review is from a journal.
Relation of Scores on the Open Middle Test to Self-Control and Academic Achievement of Inner-City Fourth-Grade Children
Abstract
The construct validity of the Open Middle Test, a measure of children's social problem-solving ability, was investigated by assessing its relationship to self-control (Self-control Rating Scale) and academic achievement (Wide-Range Achievement Test). Subjects were 113 minority fourth graders from two urban parochial schools. A significant correlation was obtained between Open Middle Test effectiveness scores of first responses and WRAT Reading scores. No other correlations were significant. However, mean differences were significant for Open Middle Test effectiveness ratings of first responses and chosen responses, suggesting possible deficits in the evaluation of self-generated problem solutions. Implications of the results for training programs and for the use of the Open Middle Test as an outcome measure are discussed.
suggesting possible deficits in the evaluation of self-generated problem solutions
This is to be expected because students cannot be expected to create their own questions.
https://www.openmiddle.com/subtracting-mixed-numbers/
Just called middle open. The end is also open.
https://www.openmiddle.com/which-circle-is-bigger-middle-school/
How do we mark this? Looking at the answer, so complicated. I would just try both methods. The answer is different.
The problems are, these questions are good for argumentative discussions with lots of ambiguity. For science and engineering, choices are limited. We must obey laws.
My student ask me if middle questions need not be answered. No. You must ask yourself these questions. All require explanations, answers are not sufficient.
The assumpition here is that problems are solved through innovative thinking that involves bizarre and unexpected options.
Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.
However, this depth of knowledge is irrelevant when designing things. Engineers spend most of their time designing new things that work. They cannot afford the luxury to do the ultimate trial and error. So most innovations in engineering come through following laws and established procedures.
By following these procedure, the solutions just appear magically. There is no need to use higher depth of knowledge because this knowledge is gained through experimentations. Just do them first. Then we work out how to solve them later.
This kind of thinking is important for engineers when they are given problems to solve. They are not expected to come up with solutions that break all the rules and standard procedures that are known to be working.
Most engineering problems are caused by engineers who do not bother to obey the laws of nature such as the conservation of mass. Relying more on their gut feelings than obeying rules of nature and mathematics. This method of solving problem should be disallowed. They must follow all the rules of nature and sound engineering first, before they are allowed the freedom to break them with justifications and experimentations.
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