A Comprehensive Collection of Elementary School Mathematics Teaching Paper Samples (Elementary School Mathematics Teaching Papers)

Since the implementation of the new curriculum, various versions of elementary school mathematics experimental textbooks that have been reviewed and approved by the National Textbook Review Committee have all made reasonable selections and careful designs regarding the content of “exploring patterns.”

Examining the Educational Value of “Exploring Patterns”

The process of exploring patterns in mathematics is actually a comprehensive application of both plausible reasoning and deductive reasoning. In the past, we emphasized deductive reasoning more while weakening plausible reasoning, which affected the development of students’ creativity.

Plausible reasoning is diverse, with inductive reasoning and analogical reasoning being the two most widely used forms. As Poincaré once said, “Logic is used for demonstration, intuition for invention.”

Therefore, in the thinking activities of exploring mathematical patterns, both plausible reasoning to discover mathematical patterns and deductive reasoning to verify them are essential to ensure the correctness of conclusions.

Allowing students to discover and explore hidden patterns or trends in given situations, emphasizing the process of exploring patterns, experiencing methods of exploration and discovery, and cultivating students’ observational, analytical, comprehensive, inductive, and reasoning abilities, enhances their exploratory awareness and interest in learning mathematics.

Analysis of the Design Characteristics of Current Textbooks

Since the implementation of the new curriculum, various versions of elementary school mathematics experimental textbooks that have been reviewed and approved by the National Textbook Review Committee have all made reasonable selections and careful designs regarding the content of “exploring patterns.”

However, the content selections of different textbook versions vary significantly, and their编排 approaches also differ.

In both the Su Jiao Ban and Ren Jiao Ban textbooks, the content related to “exploring patterns” is independently designed as thematic units across two academic stages, using the teaching of exploring patterns as an important载体 for cultivating plausible reasoning abilities such as induction and analogy.

A further review of each volume reveals that, in other learning areas, exploratory content related to mathematical patterns is also穿插 arranged in a dispersed and渗透 manner, emphasizing让学生经历知识的探索过程 and integrating the discovery and exploration of patterns throughout the entire teaching process. However, there are noticeable differences in the content selections among different textbooks.

The design of thematic units in the Su Jiao Ban textbook primarily involves students exploring patterns in real-life contexts, such as interval排列, simple combinations, and simple periodic phenomena.

Additionally, through平移 methods, students explore and discover patterns in simple graphic coverage phenomena. This process involves autonomous exploration and collaborative exchange, employing basic problem-solving strategies such as listing, drawing, calculating, and orderly thinking.

It aims to develop students’ ability to discover and summarize patterns, initially foster an awareness of reviewing and reflecting on the exploration process, and enhance their ability to solve corresponding simple practical problems.

In contrast, the Ren Jiao Ban textbook features relatively more independently designed units on “exploring patterns,” distributed across various grades.

The selected content mainly includes patterns in graphical changes, numerical sequence changes, and operational activity changes.

The design of the content is highly active and exploratory, with some content directly incorporated into mathematical practical activities.

Rational Construction of Content and Form

The “Standard” places “exploring patterns” in a prominent position.

On one hand, in the teaching of规律性知识 such as formulas, rules, and algorithms, it emphasizes allowing students to experience the process of discovery and exploration;

On the other hand, it treats “exploring patterns” as independent content within the Number and Algebra section to strengthen the teaching of this knowledge.

Therefore, the content of “exploring patterns” in elementary school mathematics primarily involves exploring patterns in numbers, expressions, and shapes, and should be designed using a combination of集中 and分散 approaches.

This means setting up independent units at different stages with appropriate themes for learning “exploring patterns,” while also using the learning of related content as a载体.

Through a dispersed and渗透 approach, guide students to experience the process of knowledge exploration, discover hidden patterns and trends in given situations, and cultivate their plausible reasoning abilities, such as induction and analogy.

The design of “exploring patterns” content should reflect characteristics such as the lifelikeness of material selection, the趣味化 of情境设置, and the多样化 of presentation methods.

In other words, it should start from examples in children’s daily lives, designing realistic and meaningful content to make mathematics learning more lifelike, socialized, and趣味化;

It should begin with creating problem situations, posing open and challenging questions to promote students’ active engagement in observation, experimentation, conjecture, verification, reasoning, and communication. At the same time, the content should be presented in丰富多彩 forms, such as graphics, comics, tables, and text.

When students explore patterns, they need to extract information from the题干, tables, and dialogues between characters. Sometimes there is多余 information, requiring students to select, and sometimes there is不足 information, requiring students to find indirect ways to obtain it. This allows students to experience the exploration process of “real-world topics—posing mathematical problems—establishing mathematical models—researching or applying mathematical methods to solve problems.”

Appropriately Balancing the Hierarchical and Exploratory Nature of Content Design

The thinking of lower-grade students is primarily concrete, so the learning content at this stage should更多地反映简单图形的变化规律.

At the same time, combine number recognition and calculation with thinking training on the arrangement patterns of numbers and expressions to develop students’ number sense and symbol sense.

In middle and upper grades,更多地运用数学思想方法和已经掌握的数学工具 should be used to explore problems and solve them.

The learning of “exploring patterns” should start from first grade and run through the entire elementary school stage. Meanwhile, based on the age characteristics of students and the logical sequence of mathematical knowledge development, it should be arranged in a manner that is由浅入深、循序渐进.

In current textbooks, the answers to “exploring patterns” problems are often unique, with few divergent questions, which limits students’ thinking.

Therefore, textbooks could provide some open-ended training questions, fostering students’ divergent thinking abilities through the selection of presented information and the diversity of problem-solving strategies.

Hence, the process of exploring patterns must involve a certain quality of thinking, embodying the exploratory nature of problem-solving.