Can Guided Notes Support Students’ Note-taking in Mathematics Lectures?

In traditional mathematics lectures the instructor normally writes the definitions, theorems, and proofs covered on the board, and gives informal oral explanations that help to make sense of them. The students have to take notes. However, there are serious problems concerning students’ note-taking in traditional mathematics lectures. Students often cannot think about the information presented during the lecture as they are busy writing. Making sense of the content later is also difficult because many students do not include the lecturer’s oral explanations in their notes. One approach to addressing these problems can be the use of guided notes: a modified version of the instructor’s notes with certain blanks the students have to fill in during the lecture. We investigated to what extent guided notes can support students in their note-taking in mathematics lectures in a study using a mixed-method design. This study provides on the one hand quantitative data suggesting that guided notes are perceived as beneficial by many students for several aspects of their note-taking. On the other hand, it offers qualitative data illustrating how the use of guided notes can influence these aspects. The results indicate in particular that the use of guided notes can address some of the problems concerning students’ note-taking in traditional mathematics lectures, while it can also lead to new problems that one needs to be aware of.

Sense Logic

Traditional mathematical logic is "what follows from what".Sense logic - "what belongs to what".Traditional mathematical logic is "a collection of abstract objects not related to the outside world."Sense logic is "a set of objects and events that describe the state of the real world."Below, we present a new paradigm of logic based on semantic connections between the considered objects of any nature. The Sense Logic is not a part of traditional mathematics. Its main task is to describe the phenomena of the real world from the standpoint of their semantic coherence.

SOFT MEASUREMENTS IN THE MACROECONOMIC EVENTS RECONSTRUCTION

In the context of the limitations of traditional mathematical methods in the study of nonstationary economic objects, which in their dynamics constantly experience external disturbing influences, it becomes very important to search for methods that can compensate for this lack of traditional mathematics. In this regard, the potential of soft mathematical measurements that can take into account both quantitative and qualitative information about the object during the study is of particular importance. The description of the results of economic and mathematical verification of the hypothesis of the existence of complex and nonstandard economic phenomena in the historical process – systemic economic crises – is a clear illustration of the effectiveness of the new economic and mathematical method.

Sense Theory. Sense Function

The Sense Theory is not a part of traditional mathematics. It is a new paradigm of how we can formalize complex cognitive processes of the human brain. The basis of the theory is a sense function which determines sense conformity between a set of objects or/and events and a single subject (described object/event). The sense function has a series of unique properties that can help find associative connections between trillions different-type objects/events.By the function, we can investigate a whole process of forming a single sense of big data set of different business or scientific events.

Corequisite Mathematics Remediation: Results Over Time and in Different Contexts

Traditional mathematics remediation is based on the theory that traditional mathematics remedial courses increase students’ subsequent academic performance. However, most students assigned to these courses do not pass them and thus cannot graduate. An alternative approach, corequisite remediation, assigns students instead to college-level quantitative courses with additional academic support, often aligned to a student’s major. Here, we report the longer-term results of a randomized controlled trial comparing corequisite remediation (with statistics) and traditional algebra remediation (297 students per group). The corequisite group not only demonstrated significantly higher quantitative course pass rates but also success in many other disciplines, as well as significantly higher graduation rates. We also report the results of two quasi-experimental analyses (propensity score matching) demonstrating higher pass rates for corequisite mathematics remediation with 347 additional students in different settings. Policies requiring corequisite mathematics remediation can result in greater student success than is obtained with traditional remediation.

The Effect of Constructivist Mathematics on Achievement in Rural Schools

International assessment data indicate American students are not competing with their counterparts in other countries. The mathematics curriculum and pedagogy are not preparing students to compete in a global economy. This study compared student achievement using sixth grade mathematics results from the Illinois Standards Achievement Test. Specifically, the study compared the results of students in three different rural school districts, all of whom were receiving instruction in three different mathematics curricula. In one district, students received seven years of the K-6 Everyday Mathematics curriculum which was compared with students who received seven years of instruction using a traditional mathematics curriculum in the second district and in the third district scores were compared with students who were taught using a traditional mathematics curriculum supplemented with Mountain Math. The results of this study indicate the constructivist K-6 elementary mathematics curriculum did not lead to higher levels in math achievement when compared with the traditional methods of instruction.

Ciência, misticismo e educação: uma análise russelliana da pretensa neutralidade da matemática frente à religião

ResumoO propósito deste artigo consiste na elucidação dos elementos da obra de Bertrand Russell (1872-1970), eminente matemático e filósofo, que tornem possíveis os debates acerca da pretensa neutralidade da matemática diante dos misticismos que sempre estiveram presentes na história da humanidade, mas que, devido aos equívocos que impregnaram sua perspectiva, consideramos, muitas vezes, genericamente obscurantistas e perniciosos. Para isto, tornou-se necessário evidenciar as abordagens à ciência, aos misticismos e à educação na obra russelliana. Pretende-se, portanto, destacando a possibilidade de compreender a matemática como credo, demonstrar que posturas decorrem da tradicional educação matemática que podem favorecer posturas de intolerância religiosa e sugerir, também com Russell, a introdução de uma postura de enfrentamento.Palavras-chave: Matemática; Bertrand Russell; Misticismo; FilosofiaScience, mysticism and education: a russellian analysis of the supposed neutrality of mathematics towards religionAbstractThe purpose of this article is to elucidate the elements of the work of Bertrand Russell (1872-1970), eminent mathematician and philosopher, which make possible the debates about the alleged neutrality of mathematics towards the mysticism that has always been present in human history, but due to misconceptions that pervade their perspective, we consider often generically obscurantist and pernicious. For this, it was necessary to highlight the approaches to science to mysticism and education in Russell's work. It is intended, therefore, highlighting the possibility of understanding mathematics as creed, show that attitudes stem from traditional mathematics education that can foster religious intolerance poses and suggest, also with Russell, the introduction of a confronting posture.Keywords: Mathematics; Bertrand Russell; Mysticism; Philosophy