Why Elementary Algebra Can, Should, and Must Be an Eighth-Grade Course for Average Students

1987 ◽  
Vol 80 (6) ◽  
pp. 428-438 ◽  
Author(s):  
Zalman Usiskin
Keyword(s):  
Mathematics Education ◽  
Secondary Mathematics ◽  
Ninth Grade ◽  
Eighth Grade ◽  
First Year ◽  
National Council ◽  
Seventh Grade ◽  
Elementary Algebra ◽  
Grade Levels ◽  
One Year

Elementary or first-year algebra is the keystone subject in all of secondary mathematics. It is formally studied by students from grade levels as early as seventh grade and as late as college, but begun and completed more often in ninth grade than at any other time. The main purpose of this article is to question that timing. The conclusion to be argued here is that most students should begin the study of algebra one year earlier than they now do. This conclusion is contrary to a recommendation currently subscribed to by the National Council of Teachers of Mathematics and to the views of a number of leaders in mathematics education. I attempt to show here that these leaders have been misguided.

Academically Talented Students' Achievement in a Flexibly Paced Mathematics Program

1994 ◽  
Vol 25 (5) ◽  
pp. 495-511
Author(s):  
Carol J. Mills ◽  
Karen E. Ablard ◽  
William C. Gustin
Keyword(s):  
Sixth Grade ◽  
First Year ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Wide Range ◽  
Mathematics Knowledge ◽  
Mathematics Program ◽  
One Year ◽  
Talented Students ◽  
Academically Talented Students

Third- through sixth-grade mathematically talented students (n = 306) enrolled in a flexibly paced mathematics course made achievement gains far beyond the normative gains expected over a one-year period. When compared to students several grade levels higher, these highly able students gained as much as 46 percentile points from pre- to posttesting. Above-grade-level testing revealed that the students possessed a wide range of mathematics knowledge prior to entering the course with some students scoring at exceptionally high levels. With an individualized learning pace, some students as young as fourth grade completed the arithmetic/prealgebra sequence in their first year and returned the second year to successfully complete the beginning algebra sequence. Restricting such students to a rigid instructional pace and a “grade-appropriate” curriculum may place them at risk for declines in motivation and achievement.

scholarly journals Analysis of content and pedagogical content knowledge in secondary mathematics teachers' preparation programs : perceptions of novice teachers, cooperating teachers, and university professors

2018 ◽  
Author(s):  
◽  
Angela Dorsey
Keyword(s):  
Teacher Preparation ◽  
Mathematics Education ◽  
Novice Teachers ◽  
Content Knowledge ◽  
Cooperating Teachers ◽  
Secondary Mathematics ◽  
Pedagogical Knowledge ◽  
National Council ◽  
University Professors ◽  
Math Teachers

Previous research focused on characteristics of effective teachers, teacher recruitment or new pathways to teaching (Ball and Forzani, 2009; Ronfeldt et. al., 2014). However, there is a gap in the research regarding the best path to prepare secondary math teachers. Universities create a customized path of preparation based on their beliefs within the scope of a set of standards given by organizations such as the National Council for Teachers of Mathematics or National Council for Accreditation of Teacher Education. Further research supports the necessity for both content and pedagogical knowledge (Ball, 2000; Graham and Fennell, 2001; NCATE, 2010; Thames and Ball, 2010). Therefore, the purpose of this qualitative case study pursues to increase the research by uncovering perceptions of secondary math teacher preparation with the standards, content knowledge, and content pedagogical knowledge. The study included two universities? programs to gain awareness as to the interpretations of novice teachers, cooperating teachers, and University professors of the pre-service training program used to prepare future secondary mathematics educators. The findings suggest: while only the Mathematics Education Professor at both Universities were the only study participants to have a vast knowledge of the standards it did not seem to impede on the overall preparation of the novice teacher. Novice and Cooperating teachers lacked the vision for the purpose and value of upper level math classes required for the degree. Both Novice and Cooperating Teachers wanted an increase in opportunities for real-world content pedagogical situations along with differentiation, co-teaching, and Special Education. Novice teachers acknowledged the need for relationships with University professors and peers in their path toward preparation. Lastly, Mathematics Education Professors stated value in making connections between courses and research to high school math. Furthermore, the finding suggest for teacher preparation program: to prepare secondary math teachers for the current culture of mathematics education, content and pedagogical courses should not be separated and a push to increase program enrollment should be a priority.

Mathematics in Our Schools and Its Contribution to War

1943 ◽  
Vol 36 (7) ◽  
pp. 310-311
Author(s):  
Sophia H. Levy
Keyword(s):  
High School ◽  
Secondary Schools ◽  
High School Graduates ◽  
Secondary Mathematics ◽  
Large Drop ◽  
Elementary Algebra ◽  
Intermediate Algebra ◽  
University Enrollment ◽  
One Year ◽  
The University

Until a year ago, statements that our high school graduates could not do arithmetic were dismissed as of no consequence, in fact, were almost not believed. But Admiral Nimitz's letter concerning the failures in arithmetic tests given recruits entering the Navy, coming as it did at the very beginning of the War, got people more “arithmetic minded” in a few weeks than had all the efforts of teachers of mathematics in our secondary schools and colleges in nearly twenty years. Suddenly arithmetic has been revived. Suddenly there has been a large increase in the number taking courses in mathematics in the secondary schools. Suddenly there has been a large increase in the number taking courses in secondary mathematics at the University. During the semester now closing we have had 3600 students in our department as against 3000 one year ago. This is an increase of 20%, though our University enrollment dropped from 15,000 to 11,000, and enrollment in advanced courses in mathematics suffered a large drop during the same interval. We have had 1100 people taking courses in secondary mathematics. We have had 500 taking intermediate algebra with background of but one year of elementary algebra.

Experimental Programs: Predicting students’ success in first-year algebra

1962 ◽  
Vol 55 (8) ◽  
pp. 651-654
Author(s):  
Ward Ewing Barnes ◽  
John William Asher
Keyword(s):  
Middle Class ◽  
Ninth Grade ◽  
The Other ◽  
Eighth Grade ◽  
First Year ◽  
Mathematics Courses ◽  
Suburban Community ◽  
Students Success ◽  
Guidance Department ◽  
Selection Of

Selection of students for ninth-grade algebra or general mathematics courses is common. The problem presented generally is who shall be advised to take algebra and who shall not. This study was conducted in a typical, large, middle-class, suburban community where, near the end of eighth grade, the guidance department recommends that about half the students take algebra and the other half take general mathematics during ninth grade. How do the guidance people arrive at their decision? Might they be better off using a different method than they are now using?

scholarly journals Methods of Pedagogical Control of Motor Abilities Development in Seventh-Ninth Grade Boys

2015 ◽  
pp. 3 ◽  
Author(s):  
О. В. Іващенко ◽  
С. С. Єрмаков ◽  
Т. В. Карпунець ◽  
Ю. В. Крінін ◽  
С. В. Назаренко
Keyword(s):  
Physical Education ◽  
Factor Structure ◽  
Discriminant Function ◽  
Reference Point ◽  
Ninth Grade ◽  
Mathematical Statistics ◽  
Eighth Grade ◽  
Seventh Grade ◽  
Motor Abilities ◽  
Methodological Approaches

The research objective is to define methodological approaches to pedagogical control of the level of motor abilities development in middle schoolers.Materials and methods. To achieve the objectives set, the research relied on following methods used: analysis of scientific and methodological literature, pedagogical testing and methods of mathematical statistics. The participants in the study were 24 seventh grade boys, 17 eighth grade boys, and 17 ninth grade boys.Research results. The discriminant function can serve as a classifier for the age peculiarities of motor and functional readiness in seventh-ninth grade boys. The discriminant function equations allow to correctly classify 95.8% of the grouped data.The priority in the factor structure of readiness of the seventh grade boys belongs to the functional, coordination and strength readiness. For the eighth grade boys, it is functional, coordination and strength readiness, and for the ninth grade boys — strength, functional and coordination readiness.Conclusions. The final pedagogical control of motor and functional readiness of the seventh grade boys can use the first discriminant function with emphasis on the most informative variables. Such physical education can be considered effective if the results shown by the seventh grade boys  are classified as results similar to those displayed by the eighth grade boys.In the final pedagogical control of motor and functional readiness in eighth grade boys, the reference point is the results of the ninth grade boys with emphasis on the most informative indicators of the discriminant function.

scholarly journals DIFFERENTIAL CALCULUS: THE USE OF NEWTON’S METHODUS FLUXIONUM ET SERIERUM INFINITARUM IN AN EDUCATION CONTEXT

2015 ◽  
Vol 65 (1) ◽  
pp. 39-65
Author(s):  
Paolo Bussotti
Keyword(s):  
Mathematics Education ◽  
General Theory ◽  
Differential Calculus ◽  
History Of Mathematics ◽  
First Year ◽  
Education History ◽  
Mathematical Concepts ◽  
History Of ◽  
One Year ◽  
The University

What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton’s Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise. Key words: mathematics education, history of mathematics, Newton, fluxions, tangents, maxima and minima, problem solving approach to mathematics education.

scholarly journals Cardiovascular risk factors associated with acute myocardial infarction and stroke in the MADIABETES cohort

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. A. Salinero-Fort ◽  
F. J. San Andrés-Rebollo ◽  
J. Cárdenas-Valladolid ◽  
M. Méndez-Bailón ◽  
R. M. Chico-Moraleja ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Blood Pressure ◽  
Antihypertensive Drugs ◽  
Hdl Cholesterol ◽  
First Year ◽  
Backward Elimination ◽  
One Year ◽  
Time Varying Covariates

AbstractWe aimed to develop two models to estimate first AMI and stroke/TIA, respectively, in type 2 diabetes mellitus patients, by applying backward elimination to the following variables: age, sex, duration of diabetes, smoking, BMI, and use of antihyperglycemic drugs, statins, and aspirin. As time-varying covariates, we analyzed blood pressure, albuminuria, lipid profile, HbA1c, retinopathy, neuropathy, and atrial fibrillation (only in stroke/TIA model). Both models were stratified by antihypertensive drugs. We evaluated 2980 patients (52.8% women; 67.3 ± 11.2 years) with 24,159 person-years of follow-up. We recorded 114 cases of AMI and 185 cases of stroke/TIA. The factors that were independently associated with first AMI were age (≥ 75 years vs. < 75 years) (p = 0.019), higher HbA1c (> 64 mmol/mol vs. < 53 mmol/mol) (p = 0.003), HDL-cholesterol (0.90–1.81 mmol/L vs. < 0.90 mmol/L) (p = 0.002), and diastolic blood pressure (65–85 mmHg vs. < 65 mmHg) (p < 0.001). The factors that were independently associated with first stroke/TIA were age (≥ 75 years vs. < 60 years) (p < 0.001), atrial fibrillation (first year after the diagnosis vs. more than one year) (p = 0.001), glomerular filtration rate (per each 15 mL/min/1.73 m2 decrease) (p < 0.001), total cholesterol (3.88–6.46 mmol/L vs. < 3.88 mmol/L) (p < 0.001), triglycerides (per each increment of 1.13 mmol/L) (p = 0.031), albuminuria (p < 0.001), neuropathy (p = 0.01), and retinopathy (p = 0.023).

scholarly journals Mortality in older adults following a fragility fracture: real-world retrospective matched-cohort study in Ontario

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Jacques P. Brown ◽  
Jonathan D. Adachi ◽  
Emil Schemitsch ◽  
Jean-Eric Tarride ◽  
Vivien Brown ◽  
...  
Keyword(s):  
Cohort Study ◽  
Hip Fracture ◽  
Fragility Fracture ◽  
Mortality Risk ◽  
Real World ◽  
First Year ◽  
Matched Cohort ◽  
Matched Cohort Study ◽  
Fracture Cohort ◽  
One Year

Abstract Background Recent studies are lacking reports on mortality after non-hip fractures in adults aged > 65. Methods This retrospective, matched-cohort study used de-identified health services data from the publicly funded healthcare system in Ontario, Canada, contained in the ICES Data Repository. Patients aged 66 years and older with an index fragility fracture occurring at any osteoporotic site between 2011 and 2015 were identified from acute hospital admissions, emergency and ambulatory care using International Classification of Diseases (ICD)-10 codes and data were analyzed until 2017. Thus, follow-up ranged from 2 years to 6 years. Patients were excluded if they presented with an index fracture occurring at a non-osteoporotic fracture site, their index fracture was associated with a trauma code, or they experienced a previous fracture within 5 years prior to their index fracture. This fracture cohort was matched 1:1 to controls within a non-fracture cohort by date, sex, age, geography and comorbidities. All-cause mortality risk was assessed. Results The survival probability for up to 6 years post-fracture was significantly reduced for the fracture cohort vs matched non-fracture controls (p < 0.0001; n = 101,773 per cohort), with the sharpest decline occurring within the first-year post-fracture. Crude relative risk of mortality (95% confidence interval) within 1-year post-fracture was 2.47 (2.38–2.56) in women and 3.22 (3.06–3.40) in men. In the fracture vs non-fracture cohort, the absolute mortality risk within one year after a fragility fracture occurring at any site was 12.5% vs 5.1% in women and 19.5% vs 6.0% in men. The absolute mortality risk within one year after a fragility fracture occurring at a non-hip vs hip site was 9.4% vs 21.5% in women and 14.4% vs 32.3% in men. Conclusions In this real-world cohort aged > 65 years, a fragility fracture occurring at any site was associated with reduced survival for up to 6 years post-fracture. The greatest reduction in survival occurred within the first-year post-fracture, where mortality risk more than doubled and deaths were observed in 1 in 11 women and 1 in 7 men following a non-hip fracture and in 1 in 5 women and 1 in 3 men following a hip fracture.

scholarly journals Across the COVID-19 Waves; Assessing Temporal Fluctuations in Perceived Stress, Post-Traumatic Symptoms, Worry, Anxiety and Civic Moral Disengagement over One Year of Pandemic

2021 ◽  
Vol 18 (11) ◽  
pp. 5651
Author(s):  
Alessio Gori ◽  
Eleonora Topino
Keyword(s):  
Perceived Stress ◽  
State Anxiety ◽  
Moral Disengagement ◽  
Online Survey ◽  
Well Being ◽  
First Year ◽  
Effective Interventions ◽  
Post Traumatic ◽  
One Year ◽  
Traumatic Symptoms

This study aimed at investigating the psychological effect of the COVID-19 pandemic in Italy by analysing the trends of perceived stress, post-traumatic symptoms, state anxiety, worry, and civic moral disengagement in four different moments from March 2020 to March 2021. The study involved a total of 1827 Italian participants (30% men and 70% women; Mage = 34.72; SD = 12.40) divided into four groups to which an online survey was administered. The first group completed the survey in March 2020, the second one in August 2020, the third one in November 2020, and the fourth one in March 2021. Results highlighted significant decreases in post-traumatic symptoms and a significant increase in civic moral disengagement over the first year of the COVID-19 pandemic. The levels of perceived stress, worry, and state anxiety remained constant. The correlations between the variables at different times were also explored, as well as gender differences over the year. The COVID-19 emergency has had significant effects on the mental state of the population, with important repercussions for individual and collective well-being during but probably also after the pandemic. This study offers a clear snapshot of the psychological outcomes over one COVID-19 pandemic year, providing important information that may contribute to tailor more effective interventions for mental health.

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