Mathematics

ABSTRACT While the Common Core State Standards (CCSS) and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence (NGA & CCSSO, 2010), several student-related and teacher-related factors may hinder student access to the general education curriculum for secondary students with emotional and behavioral disorders (EBD). Consequently, secondary students with EBD often fail to receive equitable, high quality mathematics instruction that is age-appropriate. The authors identified the challenges associated with teaching mathematics to secondary students with EBD and provided practical suggestions based on the limited existing research base to help special educators understand how to teach mathematics to secondary students with EBD.

While the Common Core State Standards (CCSS) and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence (NGA & CCSSO, 2010), several student-related and teacher-related factors may hinder student access to the general education curriculum for secondary students with emotional and behavioral disorders (EBD). Consequently, secondary students with EBD often fail to receive equitable, high quality mathematics instruction that is age-appropriate. The authors identified the challenges associated with teaching mathematics to secondary students with EBD and provided practical suggestions based on the limited existing research base to help special educators understand how to teach mathematics to secondary students with EBD.

1. Solve for x in the following simultaneous equation x y x z = 100, 000 x y / x z = 10 (x y) z = 1, 000, 000 a. 10 c. 3 b. 2 d. 100 Solution: 1. 100, 000 x 10 = 1, 000, 000 (x y x z) (x y /x z) = (x y) z x 2y =x yz 2y=yz z=2 2. 10 6 = 1, 000, 0000 (x y /x z) 6 = 1, 000, 000 (x y /x z) 6 = x yz x 6y /x 6z = x yz x 6y /x 12 = x 2y x 6y – 12 = x 2y 6y – 12 = 2y 4y = 12 y = 3 x y x z = 100, 000 x 3. x 2 = 10 5 x 5 = 10 5 x = 10 2. Solve for x and y in the following. 27 x = 9 y (81) y (3-x) = 243 a. (1,3) c. (1,3/2) b. (3,1) d. (3/2,1) Solution: (3 3) x = (3 2) y = 3 5 3 3x = 3 2y ; 3x = 2y 3 4y. 3-x = 3 5 ; 3 4y+(-x) = 3 5 ; 4y – x = 5

Publication Date : July 11 , 2017          Number of Pages: 31
In this paper we study and solve a mathematical olympiad problem that
was featured in the sixteenth Korean  Mathematical Olympiad in 2003.
This problem is published in the February 2006 issue of the journal
Crux Mathematicorum; issue No2 , Volume32 , page86.
We state the Problem.
Problem1:  16th Korean Mathematical Olympiad      April 12-13 ,
                      Time: 9 hours
  Show that there exist no integers x , y , z  with x non-zero ,  satisfying
                              2 x^4 + 2(x^2)(y^2) + y^4 = z^2 .
    Here is  how this paper is organized:
1) Introduction : Pages 1-9 .  Results1 , 2 , 3 , and 4  , are all stated in the
introduction ; on pages4-6. Result1 is well known in elementary number
theory , and it is stated without proof. It is used to prove Results2 and 3.
Result4 , is  also stated without proof; it gives the well known 3-parameter formulas , that describe the entire family of Pythagorean
Triples.  Propositions1 and 2 are also stated in the introduction , on
page7.
2)Fermat's Principle(or Method) of Infinite Descent: Pages9-15.
3)Proof  of Result2: On page 16.
4) Proof of Result3: Pages 17 and 18.
5) Proof of Proposition1: Pages19-21.
6) Proof of Proposition2: Pages 22-29; in this proof Results 2 , 3 , and 4
    are all used; together with Lemma1( stated on page22 and proved on
      pages22 and 23).
7) Solution to Problem1 : Pages 30 and 31. The solution makes use of
  Fermat's Principle of Infinite Descent , as well as Propositions 1 and2.

There are very few papers in forensic literature in which scapular dimensions have been used for estimation of living stature. Allowing the forensic duty to estimate the living stature of skeletal remains, using intact or fragmented scapulae, the Authors have performed multiple regression analysis between the measurements taken from 80 scapula (40 male and 40 female) belonging to a skeletal collection with anthropometric known data. Seven parameters (max length, max breadth, max acrocoracoid distance, length of acromion, max length of coracoid, length of glenoid cavity, width of glenoid cavity) have been recorded. By statistical analysis multiple and linear regressions have been obtained. The results show that living stature may be determined by using regression formulae of single or associated parameters taken from whole or fragmented scapulae. In absence of intact or fragmented long limb bones, scapula sample can be reliably employed for the estimation of stature in forensic pract...

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and

Evaluation of the severity of valvular mitral stenosis and measurements of the effective rheumatic mitral valve area by noninvasive echocardiography has been well accepted. The area is measured by the two-dimensional planimetry (PLM) method and the Doppler pressure half-time (PHT) method. Recently, the proximal isovelocity surface area (PISA) by color Doppler technique has been used as a quantitative measurement for valvular heart disease. However, this method needs more validation. The aim of this study was therefore to investigate the clinical applicability of the PISA method in the measurements of effective mitral valve area in patients with rheumatic valvular heart disease. Forty-seven patients aged from 23 to 71 years, with a mean age of 53 +/- 13 (25 male and 22 female, 15 with sinus rhythm, mean heart rate of 83 +/- 14 beats per minute, with rheumatic valvular mitral stenosis without hemodynamically significant mitral regurgitation) were included in the study. Effective mitral valve area (MVA) derived by the PISA method was calculated as follows: 2 x Pi x (proximal aliasing color zone radius)2x aliasing velocity/peak velocity across mitral orifice. Effective mitral valve areas measured by three different methods (PLM, PHT, and PISA) were compared and correlated with those calculated by the "gold standard" invasive Gorlin's formula. The MVA derived from PHT, PLM, PISA and Gorlin's formula were 1.00 +/- 0.31cm2, 0.99 +/- 0.30 cm2, 0.95 +/- 0.30 cm2 and 0.91 +/- 0.29 cm2, respectively. The correlation coefficients (r value) between PHT, PLM, PISA, and Gorlin's formula, respectively, were 0.66 (P = 0.032, SEE = 0.64), 0.67 (P = 0.25, SEE = 0.72) and 0.80 (P = 0.002, SEE = 0.53). In conclusion, the PISA method is useful clinically in the measurement of effective mitral valve area in patients with rheumatic mitral valve stenosis. The technique is relatively simple, highly feasible and accurate when compared with the PHT, PLM, and Gorlin's formula. Therefore, this method could be a promising supplement to methods already in use.

The present study investigated whether changes in response bias (log b) affect discriminability (log d) in a delayed conditional discrimination (DCD) task. Eight rats were trained on an DCD task and response bias was manipulated by changing the reinforcement ratio (RR) for correct responding on the two response alternatives. Three findings emerged. First, changes in RR produced changes in log b and the magnitude of these changes was related to the value of the RR. Second, log d was affected by changing RRs. Third, the effect of changes in RR on log b was larger after longer delays. These results suggest that log d and log b are not independent and it is concluded that changes in response bias (log b) may affect the discriminability measure log d. This implies that changes in log d may be mediated by changes in response bias and it is therefore recommended that log d and log b values are both reported when investigating effects of, for example, pharmacological manipulations on DCD performance.

ABSTRACT This study investigated the role of strategy instruction and cognitive abilities on word problem solving accuracy in children with math difficulties (MD). Elementary school children (N = 120) with and without MD were randomly assigned to 1 of 4 conditions: general-heuristic (e.g., underline question sentence), visual-schematic presentation (diagrams), general-heuristic + visual-schematic, and an untreated control. When compared to the control condition that included children with MD, an advantage at posttest was found for children with MD for the visual-schematic-alone condition on measures of problem solving and calculation accuracy, whereas all strategy conditions facilitated posttest performance in correctly identifying problem solving components. The results also suggested that strategy conditions drew upon different cognitive resources. The General-heuristic condition drew primarily upon the executive component of working memory (WM), Visual-schematic condition drew upon the visual component of WM and the combined strategies condition drew upon number processing skills.

English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic Math (DSM) on word problem solving for Latino ELLs. The strategy provides performance-contingent feedback based on the student’s reading and language comprehension level. A multiple baseline design was used to assess 6 second-grade Latino ELLs at risk for math failure/math disability. As compared with the baseline phase, DSM increased word problem solving for all the participants. All students’ level of performance was maintained during follow-up sessions. The results suggest the intervention facilitated math problem–solving performance.

The study proposes a recommendation that links knowledge management and performance improvement. The company that is under study allows this recommendation to take place at its Foundry Group (FG). The recommendation is designed to help the FG overcome the ...

Experiments were performed to test specific predictions of an integrated red cell model developed by Lew and Bookchin [Lew, V.L., Bookchin, R.M. J. Membrane Biol. 92:57-74 (1986)], that K-permeabilized human red cells suspended in low-K media would dehydrate and lose an alkaline, hypertonic fluid with excess K over accompanying anions, and that cell dehydration would precede medium alkalinization. Red cells were suspended at about 30% hematocrit in an initially K-free Na-saline and permeabilized to K by the addition of valinomycin. The results showed that by the time a quasi-steady state had been reached the cells had lost the equivalent of a hypertonic fluid containing about 180 mM KCl (SCN) and 10 mM KOH, and that cell dehydration did precede alkalinization of the medium, in good agreement with the theoretical predictions. Since these experiments critically test the interaction between transport, pH and volume regulatory functions in the human red cell, the observed agreement validates the basic assumptions and structure of the integrated model. The functional implications of these results are discussed.

Can we afford to wait any longer? Pre-school children are ready to learn mathematics Abstract South African students' poor mathematics performance on national and international tests can be attributed to the gap the children begin schooling with from different socio economics homes. Wright et al assert that this gap continues to grow the longer students are in school. Early childhood research highlights the significant educational gains of exposing young children to quality, structured mathematical play or activity that goes beyond what is learned within the family and community. South Africa has high levels of poverty and inequality and also has tremendous difficulties in overcoming these inequalities. Most provision of quality pre-school education is private, self-funded and not targeted to poor children resulting to different levels of mathematics readiness prior entry to primary school. This paper argues for quality mathematics interventions, longitudinal studies on impact o...