The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

This article draws on the simple context of a two animal farm to create an engaging and mathematically meaningful problem solving task for students. It aims to encourage students to think systematically and to present their findings methodically. The task is structured sequentially, making it suitable for primary school students from Year 1 to…

The purpose of this article is to introduce a lesson fondly referred to as the 'Lego Shop' lesson. It stands out as not only the most engaging lesson we've conducted but is also highly adaptable to accommodate a diverse range of learners. Successfully implemented across all year levels, from Foundation to Year 6, this lesson has proven to be…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. "Figuring Out Fluency in Mathematics Teaching and Learning" offers educators the inspiration to develop a deeper understanding of procedural fluency, along with…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

In this article, the authors share the potential for two types of atypical arrays (composite and partially hidden) to stimulate initial multiplicative ideas and strategies from students in a second-grade classroom. Composite arrays are defined here as nonarrays that are composed of multiple smaller complete arrays. The atypical arrays were…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

In this article, the author describes how to help develop students' conceptual understanding of fractions through the tactical card-based game Nearest to One. Nearest to One promotes number-sense based strategies for comparing fractions, such as benchmarking (e.g., Is the fraction greater or less than one-half?) and building to the next whole,…