The Development of a Quadratic Functions Learning Progression and Associated Task Shells

Graf, Edith Aurora; Fife, James; Howell, Heather; Marquez, Elizabeth

doi:10.1002/ets2.12234

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…Students' difficulty in transforming 𝑎𝑎𝑎𝑎𝑥𝑥𝑥𝑥 2 + 𝑏𝑏𝑏𝑏𝑥𝑥𝑥𝑥 + 𝑐𝑐𝑐𝑐 = 0 into 𝑓𝑓𝑓𝑓(𝑥𝑥𝑥𝑥) = 𝑎𝑎𝑎𝑎(𝑥𝑥𝑥𝑥 − ℎ) 2 + 𝑘𝑘𝑘𝑘 coincides with the findings of Parent (2015), who asserted that students prefer the standard form of the quadratic equation more than the standard form the vertex form because the learners generally are not used to dealing with graphs and tables. Results also support the evidence that students may have learned the procedural rules in association with transforming the standard form of QE into vertex form or vice versa; however, they may not understand the implications or the mathematical meanings, causing them to have difficulty in distinguishing the different forms (Graf et al, 2018).…”

Section: Learning Difficulties In Algebra During the New Normalsupporting

confidence: 67%

Academic Achievement in Algebra of the Public High School Students in the New Normal

Rodrigo

Alave

2021

PSSJ

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This study describes the academic achievement level in Algebra of the public secondary school students in the new normal as a whole and when grouped according to sex and parent's highest educational attainment. Utilizing descriptive-comparative and correlational designs, the academic achievement level, significant differences and relationships among the variables, and the perceived learning difficulties in Quadratic Functions were determined using mean, Mann-Whitney, Kruskal Wallis, Chi-square test of association, Spearman rank correlation, and frequency and percentage distribution. Results showed that the academic achievement level was low; no significant difference and relationship between sex and academic achievement level; there was a significant difference and relationship between parent's highest educational attainment and achievement level, and students' top difficulty is transforming quadratic functions into the form f(x)=[a(x-h)^2]+k. Therefore, Algebra teachers, school heads, and parents should take necessary interventions to address the problem.

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Section: Learning Difficulties In Algebra During the New Normalsupporting

confidence: 67%

Academic Achievement in Algebra of the Public High School Students in the New Normal

Rodrigo

Alave

2021

PSSJ

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“…The 3 rd order regression (y = ax 3 + bx 2 + cx + d) also has a turning point which causes the modeling to be biased to achieve its maximum point. Therefore, the multiplication of leaf length and width data in the 2 nd and 3 rd order regression modeling must be limited so that the correlation has no bias and is always positive [15,16,17]. Generally, the higher the order of the regression model, the better the model in data forecasting, as presented in previous research [18].…”

Section: Mathematical Model Designmentioning

confidence: 94%

Plant Growth Prediction Model of Red Chili (Capsicum annuum L.) by Different Manipulation Environment

Putra¹,

Sutiarso²,

Nugroho³

et al. 2022

Advances in Biological Sciences Research

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Several factors influence plant growth, including sun intensity, nutrient content, soil moisture, temperature, genes, and hormones. Many studies have been carried out in constructing plant growth models to simulate plant growth in different treatments. This study aims to develop a mathematical model with a linear regression approach and an artificial neural network. This research method used an experimental design using three treatments consisting of control (T1), 50% shade (T2), and 80% shade (T3). Each treatment had five replications of the chili plant. The tools and materials used were red chili (Capsicum annuum L.) seeds of 30 DAP, a greenhouse of 3 x 3 meters, a drip irrigation control system, 25 x 30 cm polybags, and fertile soil media. The results showed that linear regression models of the 1 st and 2 nd order could be used to predict plant growth with an average RMSE value of 1.53. In contrast, the use of artificial neural networks showed a smaller RMSE value of 0.12 which means that the artificial neural network method was better at predicting plant growth.

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“…Since O(n) is more efficient than O(n 2 ), we can see that MSD-Splitting improves the efficiency of the C4.5 algorithm. The improvement in efficiency will be greater for larger data sets due to the quadratic time complexity of the standard C4.5 algorithm's method of finding the ideal split point, which grows at a faster rate as the number of values and possible split points increases [30].…”

Section: Effect On Efficiencymentioning

confidence: 99%

“…Since the Census Income data set is significantly larger than the Heart Disease data set, the difference between the execution time of our initial model and our optimized model is significantly greater for the Census Income data set than for the Heart Disease data set. This is due to the behavior of the previously mentioned quadratic time complexity of our initial model [30]. In order to account for the different sizes of the data sets, we must compare the efficiency of our two models separately for each data set.…”

Section: B Efficiencymentioning

confidence: 99%

Optimizing the C4.5 Decision Tree Algorithm using MSD-Splitting

Rim¹,

Liu²

2020

IJACSA

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We propose an optimization of Dr. Ross Quinlan's C4.5 decision tree algorithm, used for data mining and classification. We will show that by discretizing and binning a data set's continuous attributes into four groups using our novel technique called MSD-Splitting, we can significantly improve both the algorithm's accuracy and efficiency, especially when applied to large data sets. We applied both the standard C4.5 algorithm and our optimized C4.5 algorithm to two data sets obtained from UC Irvine's Machine Learning Repository: Census Income and Heart Disease. In our initial model, we discretized continuous attributes by splitting them into two groups at the point with the minimum expected information requirement, in accordance with the standard C4.5 algorithm. Using five-fold cross-validation, we calculated the average accuracy of our initial model for each data set. Our initial model yielded a 75.72% average accuracy across both data sets. The average execution time of our initial model was 1,541.57 s for the Census Income data set and 50.54 s for the Heart Disease data set. We then optimized our model by applying MSD-Splitting, which discretizes continuous attributes by splitting them into four groups using the mean and the two values one standard deviation away from the mean as split points. The accuracy of our model improved by an average of 5.11% across both data sets, while the average execution time reduced by an average of 96.72% for the larger Census Income data set and 46.38% for the Heart Disease data set.

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The Development of a Quadratic Functions Learning Progression and Associated Task Shells

Cited by 5 publications

References 22 publications

Academic Achievement in Algebra of the Public High School Students in the New Normal

Academic Achievement in Algebra of the Public High School Students in the New Normal

Plant Growth Prediction Model of Red Chili (Capsicum annuum L.) by Different Manipulation Environment

Optimizing the C4.5 Decision Tree Algorithm using MSD-Splitting

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