04/04/2024 / Education

Two years ago, here at MiddleWeb, I wrote the article How We Pumped Up Our Math Vocabulary Study, in which I shared my action research on the language of math. I discovered that as the math curriculum became more complex, so did the terminology that the students were expected to know.

Thanks to my research, I was able to develop many math vocabulary strategies and experienced great success with my fifth graders.

My latest research led me to the work of Jo Boaler, Stanford University Professor of Mathematics Education, co-founder of youcubed, and author. Years ago, educators used â€śMad Minutesâ€ť to time students to determine how fluent they were with a particular multiple or operation. I learned from Boalerâ€™s paper *Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts* that:

A discussion in the Cambridge Mathematics Express (Issue 4, February 2017) states that â€śNumber sense is not a term that all researchers define in exactly the same way, but includes counting and comparing skills and the flexible ability to compute and represent numbers. It can be improved through teaching.â€ť

The first thing I tell my students is that there is always more than one way to solve a math problem. It is important that students understand the many ways numbers can be logically manipulated in different ways yet result in the same correct answer.

Solving is less about using a certain procedure and more about the skill in thinking about numbers, along with the learning of operations and concepts that must occur in order to help develop mathematical reasoning strategies. If a student does not *understand* the concept or procedure, the probability of error is high and their confidence level generally plummets.

The National Council of Teachers of Mathematics *Procedural Fluency: Reasoning and Decision Making, Not Rote Application of Procedures Position (January, 2023) *offers declarations that â€śdescribe necessary actions to ensure that every student has access to and develops procedural fluency.â€ť These declarations are:

The difference is immense between rote memorization and the use of teaching strategies that allow students to work flexibly and thoughtfully with numbers. When students learn number sense and can use multiple strategies, they have choice in how they can logically solve a problem.

They work with numbers in word problems, scenarios, games, math tricks, etc. that allow them to manipulate numbers and their relationships with their mind. This leads to knowledge that can be built upon with more complex concepts. In other words, it builds a strong foundation from which students can grow in mathematics.

I believe that teaching number sense and allowing students to work with numbers in multiple ways will also lead to less anxiety with this subject area. Timed tests have been shown to cause stress as the tests feel competitive and leave a student feeling defeated, rather than eager to learn.

Throughout my research, Iâ€™ve come across many scholars who are against national/state curriculum or standards that direct students should memorize math facts including the multiplication table up to 12 by the age of 9!

There are several ways to incorporate number sense into the math classroom. Jo Boaler offers several at youcubed.org to get you started. Number Talks are also a wonderful way to get students to think about, visualize, and discuss different ways to solve math problems. This video by Jo Boaler, What is Number Sense? is very helpful in showing teachers how to share different methods of solving a few problems.

Number flexibility is an important part of number sense. My class has enjoyed the following games/projects from youcubed.org:

There are many more tasks and activities on youcubed.org that can be used to stimulate number sense. In addition, as Iâ€™ve written about in a previous article, The Magic of Math: Have Fun with Final Activities, using the work of Dr. Raj Shah. I found great engagement in using his math â€śtricks.â€ť The â€śHandshake Scenarioâ€ť and â€śSix Digits Become Threeâ€ť are engaging number sense activities that truly make students of all math abilities manipulate numbers and talk strategies.

As a lifelong learner, Kathie is an avid reader and researcher of educational practices and techniques. Collaborating with colleagues and globally on X-Twitter and expanding on her education adventures at www.kathleenpalmieri.com are ongoing practices.

Kathleen Palmieri

Kathleen Palmieri is a National Board Certified Teacher, a National Board for Professional Teaching Standards Learning Facilitator, and a fifth grade educator in upstate New York. She reviews professional texts and is an educator researcher and writer. As a writer with a passion for pedagogy, Kathleen's focus is on education practices, and strategies, as well as her own experiences as an educator. Educator well being is a priority, thus the name "Mindful Teaching Moments". Mindfulness along with knowledge is important. She has presented at math conferences, writing workshops, actively collaborates in literacy projects, and networks globally.Â