本文選題：合情推理能力 + 小學(xué)數(shù)學(xué)��； 參考：《華中師范大學(xué)》2017年碩士論文

【摘要】：合情推理是最具數(shù)學(xué)學(xué)科特征的內(nèi)容之一,在小學(xué)數(shù)學(xué)教學(xué)中不可或缺。學(xué)生的數(shù)學(xué)合情推理能力是衡量其數(shù)學(xué)素養(yǎng)的重要指標(biāo),它不僅有利于培養(yǎng)創(chuàng)新意識和發(fā)散性思維,還能夠提高解決問題的能力。然而,由于我國數(shù)學(xué)教育對合情推理的研究時間不長,當(dāng)前教學(xué)中學(xué)生合情推理能力的培養(yǎng)有些迷茫。本文試圖從理論上對小學(xué)生數(shù)學(xué)合情推理能力作一些探討,在實(shí)踐中探尋小學(xué)生數(shù)學(xué)合情推理能力培養(yǎng)中的問題及改進(jìn)策略。本文除緒論外,總共包括四個部分。第一部分旨在闡明小學(xué)生數(shù)學(xué)合情推理能力的含義、組成因素及其表現(xiàn)。小學(xué)生數(shù)學(xué)合情推理能力是指小學(xué)生在具體的數(shù)學(xué)問題情境中,根據(jù)已有的基礎(chǔ)知識和經(jīng)驗(yàn)(即原有的認(rèn)知結(jié)構(gòu)),通過觀察、歸納、類比、猜想等思維過程,運(yùn)用估算、畫圖、列表等數(shù)學(xué)方法對所學(xué)知識推斷出某些合乎情理的結(jié)果時所表現(xiàn)出來的一種個性心理特征。它由數(shù)學(xué)觀察能力、數(shù)學(xué)歸納和類比推理的能力、數(shù)學(xué)猜想能力、清晰表達(dá)數(shù)學(xué)思維的能力、合情推理元認(rèn)知能力組成。第二部分梳理了小學(xué)數(shù)學(xué)合情推理的課程安排,并結(jié)合典型課時內(nèi)容進(jìn)行分析。以人教版小學(xué)數(shù)學(xué)教科書為例,從不同學(xué)段、不同課程版塊兩個維度對教科書中適合滲透合情推理教學(xué)的課程內(nèi)容進(jìn)行梳理,并挑選五個課時分別突出合情推理能力各組成因素的培養(yǎng)特點(diǎn)。第三部分主要分析了小學(xué)生數(shù)學(xué)合情推理能力培養(yǎng)中的問題及其原因。由于數(shù)學(xué)課標(biāo)對“合情推理能力”的表述籠統(tǒng),當(dāng)前的評價(jià)目標(biāo)導(dǎo)向不明確,加之教師的數(shù)學(xué)素養(yǎng)水平有限,導(dǎo)致教師對合情推理能力的認(rèn)知不夠深入,對其培養(yǎng)重視不足,合情推理能力的培養(yǎng)過程缺乏嚴(yán)謹(jǐn)性,培養(yǎng)方法單一。第四部分針對小學(xué)生數(shù)學(xué)合情推理能力培養(yǎng)中的問題,提出了三個方面的改進(jìn)策略。首先,教師要準(zhǔn)確理解合情推理能力。不僅要研讀課標(biāo)和教材,把握合情推理的本質(zhì);還要更新教學(xué)理念,注重合情推理能力的培養(yǎng)。其次,教師要合理把握不同學(xué)段學(xué)生合情推理能力的培養(yǎng)特點(diǎn)。第一學(xué)段重在培養(yǎng)學(xué)生的數(shù)學(xué)觀察、猜想能力,第二學(xué)段重在培養(yǎng)學(xué)生的數(shù)學(xué)歸納、類比推理能力。最后,教師要多渠道拓寬合情推理能力的培養(yǎng)方法。通過創(chuàng)設(shè)數(shù)學(xué)問題情境、鼓勵大膽猜想、出聲思維訓(xùn)練來引發(fā)、形成和深化合情推理。
[Abstract]:Reasonable reasoning is one of the most characteristic contents of mathematics, which is indispensable in mathematics teaching in primary school. Students' mathematical reasoning ability is an important index to measure their mathematical literacy. It is not only conducive to the cultivation of innovative awareness and divergent thinking, but also to improve the ability to solve problems. However, due to the short time of research on reasonable reasoning in mathematics education in our country, the cultivation of reasonable reasoning ability of middle school students in current teaching is somewhat confused. This paper attempts to make some theoretical discussion on the mathematical reasoning ability of primary school students, and to explore the problems and improvement strategies in the cultivation of pupils' mathematical reasonable reasoning ability in practice. In addition to the introduction, this paper consists of four parts. The first part is to clarify the meaning, composition and expression of pupils'mathematical reasoning ability. Elementary school students' mathematical reasoning ability refers to the basic knowledge and experience (i.e. the original cognitive structure) of elementary school students in the specific mathematical problem situation, through observation, induction, analogy, conjecture and other thinking processes, the use of estimation, drawing, and so on. A psychological characteristic of personality when mathematical methods such as lists infer reasonable results from what they have learned. It consists of the ability of mathematical observation, mathematical induction and analogy reasoning, mathematical conjecture, the ability to express mathematical thinking clearly, and the metacognitive ability of reasonable reasoning. The second part combs the elementary school mathematics reasonable reasoning curriculum arrangement, and unifies the typical class time content carries on the analysis. Taking the primary school mathematics textbook as an example, this paper combs the curriculum content suitable for permeating the reasonable reasoning teaching from two dimensions of different learning stages and different curriculum sections. Five classes were selected to highlight the characteristics of each component of reasonable reasoning ability. The third part mainly analyzes the problems and causes in the cultivation of mathematical reasoning ability of primary school students. Due to the general description of "reasonable reasoning ability" in mathematics class standard, the unclear orientation of evaluation goal and the limited level of teachers' mathematical literacy, the teachers' cognition of reasonable reasoning ability is not deep enough, and the training of reasonable reasoning ability is not paid enough attention to. The training process of reasonable reasoning ability is lack of rigor, and the training method is single. In the fourth part, aiming at the problems in the cultivation of pupils' mathematical reasoning ability, three improvement strategies are put forward. First of all, teachers should accurately understand the ability of reasonable reasoning. We should not only study the curriculum standard and teaching material, grasp the essence of reasonable reasoning, but also renew the teaching concept and pay attention to the cultivation of reasonable reasoning ability. Secondly, teachers should grasp the characteristics of reasonable reasoning ability of students from different learning stages. The first stage focuses on cultivating students' ability of mathematical observation and guess, and the second paragraph focuses on cultivating students' ability of mathematical induction and analogical reasoning. Finally, teachers should broaden the cultivation method of reasonable reasoning ability through multiple channels. By creating mathematical problem situations, encouraging bold conjecture and sound thinking training, the rational reasoning is formed and deepened.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G623.5

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