### 数学代写|数学建模代写math modelling代考|PROGRAM COMPONENTS

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|数学建模代写math modelling代考|The Scope and Sequence of the Program

This program addresses elementary word problem solving including four basic operations. It may serve as a supplemental program with an aim to help students with LDM learn big ideas in elementary math problem solving that involve four basic operations: addition, subtraction, multiplication and division. This program will cover additive problem solving (e.g., part-part-whole and additive compare problems), and multiplicative problem solving (e.g., equal groups and multiplicative compare problems). The tasks involved in this book are those typically found in elementary math textbooks, which roughly represent about $67 \%$ of the elementary math content.

The COMPS program involves three parts: (1) five units on additive word problem solving that involves addition and subtraction; $(2)$ five units on multiplicative word problem solving that involves multiplication and division; and, (3) two units on solving complex word problems such as those involving pictographs, irrelevant information, and mixed additive and multiplicative multi-steps.

In both Part I and Part II, the first Unit (i.e., Unit 1 or Unit 5 ) engages students in learning mathematical models through representing the problem in the model equation (see Figure Cl-2 in page 5 for an example: unit rate $\times$ # of units = product). During the model equation representation stage, word problem stories with no unknowns will be used. The purpose of presenting story situations with no unknowns is to provide students with a complete representation of the problem structure so that mathematical relations in the problem are clear to the students. In addition, self-regulation questions pertinent to Word Problem Story Grammar (Xin, Wiles, \& Lin, 2008) (see Figure Cl-2, lower panel) will be used as a heuristic to help students analyze various situated word problems/stories and represent the information from the problem in either the Part-Part-Whole (PPW) model equation or the Equal Groups (EG) model equation.

The second Unit in Parts 1 and 2 (i.e., Unit 2 and Unit 7 ) engage students in solving either PPW problems (Part 1) or EG problems (Part 2) with an unknown, after they learn the problem structure representation in Unit 1. The third and fourth Units in Parts 1 and 2 (i.e., Unit $3 \& 4$; and Unit $8 \& 9$ ) introduces a variation of either the PPW or the EG problem structure. In particular, students will learn to represent (Unit 3) and solve (Unit 4) additive compare problems using a variation of the PPW model equation, or represent (Unit 8) and solve (Unit 9 ) multiplicative compare problems using a variation of the EG model equation. The fifth unit in Parts 1 and 2 (i.e., Unit 5 and Unit 10 ) will engage students in solving mixed additive (Unit 5 ) or mixed multiplicative problems (Unit 10 ).

## 数学代写|数学建模代写math modelling代考|Target Audience and Users of the Program

Addition and subtraction problem solving covered in Part 1 are consistent with the math content typically presented in second or third grade math curricula. Therefore, it can be used for third or fourth grade students with LDM (or even older students with LDM) who have not mastered additive problem solving. Multiplication and

division in Part 2 are consistent with the math content typically presented in third and fourth grade math curricula and can be used by 4 th or 5 th grade student with LD (or even older students with LDM) who have not mastered multiplicative problem solving. This program can serve as a supplement to regular school math instruction. As this program teaches big ideas in additive and multiplicative problem solving, students will be equipped with a tool to learn math problem solving systematically and hopefully catch up with their normal-achieving peers within a short period of time as supported by previous research (Xin \& Zhang, 2009; Xin et al., 2011).

The COMPS program can be used as Tier II or Tier III intervention models within the context of Response to Intervention (RtI) model. It can be easily integrated into regular inclusion classrooms as part of Tier I instruction. The COMPS program can be used by regular classroom math teachers (special education or regular education teachers), Instructional Supporting Team interventionists, school psychologist, tutors who work with students with LDM in after-school programs, and anyone who works with students with LD in math problem solving.

The COMPS program is also useful for professional development and for the preservice training of prospective elementary teachers, special education in particular, to enhance their content knowledge in elementary mathematics problem solving.

## 数学代写|数学建模代写math modelling代考|INTRODUCTION

Before introducing the sample teaching scriptas a guide to facilitate the implementation of the COMPS program, I would like to introduce few salient components in the COMPS program, which include: (1) Singapore bar models (Singapore Ministry of Education, 1981) to facilitate the transition from the semi-concrete model to the abstract mathematical model; (2) word problem [WP] story grammar (Xin et al., 2008) self-prompting questions to facilitate problem representation using COMPS model diagrams; and (3) a cognitive heuristic DOTS checklist (Xin et al., 2008) to facilitate the entire problem solving process. Then, I will present a general description of the instructional phases when implementing COMPS, followed by a summary of various additive and multiplicative word problem situations.

Singapore Bar Models (SBM) to Facilitate the Transition to Mathematical Models
SBM refers to a visual representation of relations among quantities (including known and unknown quantities) in the problem using a rectangular bar. In particular, each quantity in the problem will be represented by a segment of bar, the size of which corresponds to the numerical value of that quantity in comparison to the other quantity involved. Students will then solve the problem through directly analyzing the relations depicted by the bar models. Similar line models, rather than bar models, appear in the Chinese math textbooks (Shanghai Elementary and Secondary School Curriculum Reform Committee, 1995) in teaching word problem solving.

Regardless of whether bar models or line models are used, they are good tools for representing the concept of composite units, or units made of ones. The bar model can be used as a tool for nurturing and reinforcing the concept of composite unit and to facilitate students’ transition from counting by ones to operating by composite units. The bar model also bridges the conceptual gap between concrete modeling (operating on the ones) and abstract representation of mathematical models as presented in the COMPS diagram equations. As such, I will use the SBM in the beginning stage of the modeling and practice sessions to help students understand the relations among the quantities, and then map the information from the problem to the COMPS diagram expressed in an algebraic equation. In summary, the SBM makes the connection and transition between the concrete model (operating at the unit of Ones; see Slide 1-1-2 in Unit 1 Lesson 1) and the symbolic equation model (see Slide 1-1-3 in Unit 1 Lesson 1).

## 数学代写|数学建模代写math modelling代考|The Scope and Sequence of the Program

COMPS 课程包括三个部分： (1) 涉及加法和减法的加法单词问题解决的五个单元；(2)涉及乘法和除法的乘法应用题的五个单元；(3) 两个单元解决复杂的单词问题，例如涉及象形文字、无关信息和混合加法和乘法多步骤的问题。

## 数学代写|数学建模代写math modelling代考|Target Audience and Users of the Program

COMPS 计划可在干预响应 (RtI) 模型的背景下用作二级或三级干预模型。作为一级教学的一部分，它可以很容易地集成到常规的包容性课堂中。COMPS 计划可供普通课堂数学教师（特殊教育或普通教育教师）、教学支持团队干预者、学校心理学家、在课后项目中与 LDM 学生一起工作的导师以及与 LD 学生一起工作的任何人使用。数学问题解决。

COMPS 计划还有助于专业发展和未来小学教师的职前培训，特别是特殊教育，以提高他们在解决小学数学问题方面的内容知识。

## 数学代写|数学建模代写math modelling代考|INTRODUCTION

SBM 是指使用矩形条直观表示问题中数量（包括已知和未知数量）之间的关系。特别是，问题中的每个数量将由一段条形表示，其大小对应于该数量与所涉及的其他数量相比的数值。然后学生将通过直接分析条形模型所描绘的关系来解决问题。类似的线模型，而不是条模型，出现在中国数学教科书（上海市中小学课程改革委员会，1995）中，用于教授应用题解题。

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。