Recently, I turned 60 years old (also expressed as 720 months, or 21,915 days, or 525,960 hours, or 31,557,600 minutes), and over that time I’ve seen many great debates in the education policy arena. Often those debates reach equilibrium with a realization of what Jim Collins (author of *Built to Last* and *Good to Great*) calls “the genius of the AND.” Collins points out that successful businesses realize that there is validity in each of diametrically different points of view, and the most successful companies respect and leverage both—especially when there is no clear right or wrong. The idea of the genius of the AND has found a home in the work of improving literacy outcomes (successfully, in my opinion), and I believe the same can happen with improving math achievement in the United States.

At the National Association of State Boards of Education, of which I am the President & CEO, we recognize the importance that state boards of education and state policymakers can have in prioritizing areas for action and improvement. A recent issue of our journal, *The State Education Standard,* is devoted to Advancing Math & Science Instruction. In it, various authors address different aspects of the current state of math and science education. One of the key takeaways for me is that there is a great deal of agreement on various aspects of how to improve math achievement, and there are also some areas where honest disagreement exists. When I see the disagreement, I challenge myself to examine how both sides might be respected to further the best interest of students.

I loved reading the different points of view expressed in the recent *Education Next* forum on “Rethinking Math Education.” The two sets of authors nicely lay out their points of view. In each article I found ideas I agreed with and ones to which I objected. Reading between the lines, and leveraging some of my other knowledge about education reform and mathematics, I began to see the areas of agreement, and also opportunities for embracing the AND.

Here are the concepts about mathematics achievement on which I think we can all agree:

**All students are mathematically capable.** Let’s face it, the biggest obstacle to more students being successful in mathematics is the pernicious myth, all too pervasive in our society, that “some people just aren’t good at math.” In too many cases, rather than continuing to work with students until the students reach confidence and comfort with mathematics, adults (especially parents and teachers) will convey (explicitly and implicitly) that they are simply not equipped to do mathematics. Once the student accepts that fiction as reality, the battle is lost.

The research is clear that the premise is patently false. Everyone can be competent and confident with math—we all need to believe this and act accordingly. We should all make a shared and tireless commitment to put a stake in the heart of this crushing lie. It should be as unacceptable to say “Johnny just can’t do math” as it would be to say “Johnny just can’t read.”

**More students can be successful mastering high level mathematics.** The status quo is unacceptable—both in absolute terms and in terms of equity. We know doing better is within our reach. There are plenty of case studies and proof points. One of my favorites is illustrated in the movie *“*Stand and Deliver*”* about the great Jaime Escalante and the success of students (mostly low-income and ethnic minority students) at James A. Garfield High School in Los Angeles in passing the Advanced Placement Calculus exam. I have seen other schools and classrooms experience similar successes.

**There is good understanding about what different and better math instruction looks like.** As with many content areas, there is no one-size-fits-all for what can work to help more students succeed in math. The National Council of Teachers of Mathematics published *Principles to Actions: Ensuring Mathematics Success for All* (2014), and the *Catalyzing Change* series of curriculum guides. The Southern Regional Education Board has their *Powerful Mathematics Instructional Practices**. *Other quality curriculum models are also available. High quality instructional materials matter a lot, too. The Zearn math learning platform has shown tremendous success. EdReports.org has rated a number of math instructional products.

**Deliberately focus on parents as partners.** Any effort to improve instruction requires attention to the needs of parents and caregivers. Parent support can make a big difference in the implementation of new approaches, especially if parents see how they can help their child. I sympathize with the frustrations that many parents feel when they cannot help their children with math homework because it is different than how they were taught. Just because a student is approaching a mathematical concept in a different way than how the parent or caregiver learned it should not prevent them from supporting numeracy development. We can help parents better understand and play their important role in supporting learning.

**Teachers need to be better equipped and supported to teach math. **This is true for every subject area for which we know we can do better. The recent burst of activity around the science of reading and the ensuing signs of improvement in reading proficiency are results of the significant effort being made to help and coach more teachers in understanding what great literacy instruction is all about. It is all about teacher content knowledge, aligned curriculum, quality pedagogy and disposition. Coaching also has great power to improve teacher practice. Authors Barak and Mims and Levitt and Severts would certainly agree on the importance of well-equipped and supported teachers.

**Focus is needed on elementary and middle school math.** Given that the two articles address high school math, one might think that the focus should be there. But the sad reality is that a student’s ability to be successful in *any* high school math class, calculus or otherwise, is determined in elementary and middle school. Far too many students have given up on math by then. No matter where one stands on what math is taught in high school, we can agree that more students should emerge from middle school confident and capable in mathematics.

**More math teaching should be done in the context of practical application. **Nothing brings math alive, and makes retention more likely, than when it is learned in the context of real world problems and experiences. I always found students who were enrolled in construction trades and other career focused programs at career-technical education centers to have a very robust understanding of the applicable mathematics, as well as comfort in understanding math as a tool to solve problems.

In the spirit of the “genius of the AND,” here are my ideas for charting a course forward.

**More students need to master algebra II and calculus, but if that can’t happen in the near term, let’s accept accomplishment in other rigorous math that keeps the doors to future success open for more students.** This is a lesson that we can learn from higher education and the strategies being used to recast developmental mathematics. When many institutions of higher education figured out that they were losing a great number of students in what noted mathematician Uri Treisman called “the burial ground for aspirations” — developmental mathematics — they began to design different and better math knowledge development strategies. High school is to higher education what middle school is to high school. When high school students come to the door of higher education unprepared or underprepared, the traditional solution has been to remediate them in separate, isolated, and lengthy sequences of math courses (a strategy that historically failed). Efforts to find a better way, a way that allowed more students to be successful, led many higher education institutions to embrace approaches, like co-requisite classes, to equip students with the math they need to succeed in their chosen field of study. (I tip my hat to Complete College America and the Dana Center at the University of Texas-Austin for having led the charge in this work nationally.)

This approach has helped more students reach higher levels of math competency, and, more importantly, degree completion and gaining access to meaningful high-paying jobs. No one criticized this approach for failing to insist that students learn to the highest levels of math, because it made a huge difference for many lives by equipping them with the math needed to complete their degree programs and launch careers. If it is unlikely that a middle school student entering high school will complete the *ideal* path of math achievement, however we might define it, wouldn’t it make sense to identify a rigorous alternative math pathway that could align to a meaningful career pathway for which the student might achieve success?

**Create mechanisms to ensure rigor.** There is a fear that any alternative to the algebra/calculus route will not be rigorous. This fear can be easily addressed by enabling mechanisms that ensure rigor. After all, if a student gets a 4 on the AP Statistics exam, isn’t that a sign of a mathematical disposition that would both have value as is, as well as signal a student’s capability to master other types of math?

**Set targets for more students to become proficient in algebra/calculus and also for more students to be proficient in other rigorous math. Create mechanisms that gauge progress toward equity. **There is so much room for improvement to achieve measurable and significant increases in all areas of math achievement. That means all perspectives can come out ahead. The greater the improvement, the better the system becomes at helping more students reach higher and higher levels of math. In the long term, more will achieve at the highest levels. If the fear is that change will widen the equity gap, let’s establish the mechanisms to make sure that doesn’t happen.

**Share the responsibility to ensure all students are confident and comfortable with mathematics.** One of the key strategies in improving literacy has been to ensure that all teachers play a role in it. This includes social studies teachers, science teachers, math teachers, art teachers. The same is needed for math. Every discipline has quantitative aspects that can be explored using math.

It’s always interesting to read differing views on a particular topic in education. As a perennially hopeful person, I try to look beyond the areas of disagreement to find the common ground — and there is a lot in the mathematics space. The National Association of State Boards of Education is launching a State Mathematics Improvement Study Group for state board of education members and support staff to increase awareness and understanding of the issues. I hope that, with good information and technical assistance, state policymakers can catalyze state-designed initiatives to improve math outcomes. History has shown that when such initiatives are designed by multiple partners and when the diverse points of view are understood and respected, transformative change is possible. Now is the time to make this happen in math education.

*Paolo DeMaria is president and CEO of the National Association of State Boards of Education.*

Last updated August 11, 2022

## FAQs

### What is the main focus of mathematics education? ›

Mathematics provides an effective way of **building mental discipline and encourages logical reasoning and mental rigor**. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.

**What are the current issues in mathematics education? ›**

These issues are related to classroom management, ethnicity, lack of trained teachers, inequity, lack of teaching aids and materials, lack of textbooks, lack of time for students, lack of clear objectives, gender issues, and issues of mathematical contents and pedagogy.

**Why is mathematics important give 5 reasons? ›**

Someone who understands math is able to understand basic life skills such as managing a budget, building furniture, forecasting, and telling time. **Math helps you understand costs, balance a bank account, and subtract balances which are essential skills as adults.** **Math makes you a better cook.**

**What contribution can the learning of mathematics make towards the individual and national development? ›**

Such modeling is basic to all engineering, plays a vital role in all physical sciences and **contributes significantly to the biological sciences, medicine, psychology, economics and commerce**. Mathematics has been successfully used in the development of science and technology in 20th –21st century.

**What are the two main goals of mathematics education? ›**

CONCEPTUAL FRAMEWORK The twin goals of Mathematics in the basic education levels, K to 10 are **Critical Thinking and Problem Solving**.

**Why is mathematics important in our life give atleast 10 reasons and explain? ›**

Math **helps us have better problem-solving skills**.

Analytical thinking refers to the ability to think critically about the world around us. Reasoning is our ability to think logically about a situation. Analytical and reasoning skills are important because they help us solve problems and look for solutions.

**What is the biggest problem in learning mathematics for students? ›**

**Inconsistent results in addition, subtraction, multiplication, and division**. Inability to visualize; appearing absentminded or lost in thought. Difficulty remembering math facts, concepts, rules, formulas, sequences, and procedures. Inconsistent mastery of math facts.

**What are the difficulties and challenges of mathematics teaching? ›**

Math teachers face three major challenges: **Their beliefs about teaching and learning, their content and pedagogy knowledge, and time for reflection**.

**What are the factors affecting teaching and learning of mathematics? ›**

**Gender, socio-economic status, and parents' educational level are factors that have been analyzed in this study as predictors of math achievement.**

- Gender. ...
- Socio-Economic Status. ...
- Parents' Educational Level. ...
- Instructional Strategies and Methods. ...
- Teacher Competency in Math Education. ...
- Motivation or Concentration. ...
- Instrument.

**What is the importance of learning mathematics in the modern world in your daily lives? ›**

Mathematics has a number of very useful benefits to our mind if we go into its study. It **develops our reasoning, helps us to have analytical thinking, quickens our mind, generates practicality and also its use can be applied in the day to day**.

### What is the role of mathematics How has it contributed to our world today? ›

The body of knowledge and practice known as mathematics is derived from the contributions of thinkers throughout the ages and across the globe. **It gives us a way to understand patterns, to quantify relationships, and to predict the future**.

**What is the importance of mathematics in helping us to solve our societal problems? ›**

Mathematics **makes our life orderly and prevents chaos**. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.

**What are the benefits of learning mathematics? ›**

By studying math you **develop analytical skills and an analytical attitude**. You learn to pay attention to all the assumptions involved in a given problem or situation, and you learn to break down a complicated problem into a series of tractable steps.

**What is the most useful about mathematics? ›**

Mathematics **makes our life orderly and prevents chaos**. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.

**How will math help us in the future? ›**

Math has many benefits that many people don't even realize. It can **help develop specific areas of the brain and improve analytical and reasoning skills**. It can help students become more practical and be beneficial in everyday situations.

**What are the aims and objectives of teaching mathematics in primary? ›**

The goals of the primary mathematics curriculum are: **Stimulate interest in the learning of mathematics**. Help students understand and acquire basic mathematical concepts and computational skills. Help students develop creativity and the ability to think, communicate, and solve problems.

**What is the importance of mathematics in primary education? ›**

The teaching of mathematics should **enhance children's ability to think and reason, to visualize and handle abstractions, to formulate and solve problems**. The problem-solving method of teaching is good in teaching mathematics at the primary level.

**What are the five goals of mathematics? ›**

The content of the mathematics standards is intended to support the following five goals for students: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations.

**What is mathematics in your own words? ›**

Mathematics is **the science and study of quality, structure, space, and change**. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

**What is the most important contribution of mathematics in humankind essay? ›**

**Math helps us have better problem-solving skills**

With math, we can think analytically and have better reasoning abilities. Analytical thinking means the ability to think critically. Reasoning is the ability to think logically. Analytical and reasoning skills are essential as they help us solve problems.

### What is the most important contribution of mathematics in humankind Brainly? ›

One of the most important contributions of math is that **we humans can easily calculate** and this has made our lives so much easier.

**What are barriers to the teaching and learning of mathematics? ›**

It was found that the problems are multifaceted and accordingly the solutions require overall effort from all concerned stakeholders. The problems range from **pedagogical, social, economical, administrative and policy aspects to attitude of students and teachers, competence of teachers, methodology of teaching** etc.

**Why teach mathematics to all challenges explain? ›**

Aspects of our lives can be described in mathematical concepts and **it helps develop mental skills including solving problems and making decisions**. The reason mathematics helps develop and improve such skills is that many areas of the brain are active when students think with numbers and about formulas.

**Why do students lack interest in mathematics? ›**

One of the main reasons for student's reluctancy toward mathematics is their **lack of understanding and self-perception of low content knowledge**, which let them to have a negative perception. Students stated that their negative perception was not new, but instead something they knew since elementary.

**What are the factors affecting mathematics performance? ›**

**The students' attitude, teachers' attitude, teaching methods, classroom environment**, were noted as key factors in almost all articles reviewed [12, 13, 14]. There seemed to be consistency too that parents can exert a positive influence on their children's mathematical performance [1, 4, 7, 14, 15].

**How do you overcome math difficulties? ›**

**Ten Ways to Reduce Math Anxiety**

- Confidence + Preparation = Success (Math Anxiety Formula).
- You Are Not Alone! ...
- Ask Questions. ...
- There is More than One Way to Solve a Problem. ...
- Overcome Negative Self Talk. ...
- Read Your Math Text. ...
- Consider Math as a Foreign Language. ...
- Develop Responsibilities for Your Success.

**How can we improve poor performance in mathematics? ›**

**How to improve math skills**

- Wrap your head around the concepts. ...
- Try game-based learning. ...
- Bring math into daily life. ...
- Implement daily practice. ...
- Sketch word problems. ...
- Set realistic goals. ...
- Engage with a math tutor. ...
- Focus on one concept at a time.

**What factors affect children's learning of mathematical concepts? ›**

**Environmental Factors that Influence Early Math**

- Number Competence. Your child will develop basic numerical abilities if you introduce them to numbers through formal or informal contact. ...
- Early Literacy. ...
- Family Influence on Child Education. ...
- Socio-economic status. ...
- Gender. ...
- Parental Influence.

**What are important factors influencing the choice of particular method and approach in mathematics classroom? ›**

Choosing an instructional method then requires the instructor to consider at least three main aspects: 1) **the learning objectives, to make sure the method is appropriate, 2) the nature of the materials and 3) how we want students to interact with this information**.

**What are the factors that affect effective teaching and learning? ›**

**Many Factors Determine Good and Effective Teaching**

- · An engaging personality.
- · A passion for the subject matter.
- · Demonstrated command of the subject matter.
- · Willingness to acknowledge your missteps.
- · Receptive to other's opinions.
- · Being fair and transparent.

### What are the values of teaching mathematics? ›

**3 important values of teaching Mathematics**

- Practical Value.
- Cultural Value. ADVERTISEMENTS:
- Disciplinary Value.

**How do you appreciate mathematics in your life? ›**

**Appreciate Math Everyday!**

- Appreciate the math that goes into your technology. Almost all of the entertainment we enjoy wouldn't be possible without math. ...
- Consider the math that makes travel possible. ...
- Don't take your education for granted. ...
- Give thanks for math at mealtimes. ...
- Be grateful for good health.

**What is the importance of mathematics essay? ›**

**Mathematics makes our life orderly and prevents chaos**. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.

**How do you use math in your daily life essay? ›**

Real Examples of Maths in Daily Life

**When we have to call someone on our phone we use numbers**. To make the payments, be it to a vegetable vendor, milkman, for electricity bill or phone bill, the knowledge of numbers is very important and the knowledge of numbers is an integral part of Maths.

**Do you agree that mathematics is useful in understanding the world we live in? ›**

**Mathematics is very useful and important in understanding the world we live in**. Mathematics is the foundation of the various structures we find in the world. The application of mathematical theories and branches like trigonometry helps us with construction purposes. For example, the construction of buildings.

**Why should problem-solving be a focus of the mathematics curriculum? ›**

The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization. Problem-solving **allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures**.

**Why is mathematics important give 5 reasons? ›**

Someone who understands math is able to understand basic life skills such as managing a budget, building furniture, forecasting, and telling time. **Math helps you understand costs, balance a bank account, and subtract balances which are essential skills as adults.** **Math makes you a better cook.**

**What is the importance of teaching mathematics in the primary grades? ›**

**Help students understand and acquire basic mathematical concepts and computational skills**. Help students develop creativity and the ability to think, communicate, and solve problems. Help students develop number and spatial sense and the ability to appreciate patterns and structures of number and shapes.

**Why is it important to develop mathematics in teaching? ›**

It helps children make sense of the numbers, patterns and shapes they see in the world around them, offers ways of handling data in an increasingly digital world and makes a crucial contribution to their development as successful learners.

**What is difference between mathematics and mathematics education? ›**

In any program of college study, you will take a group of core courses in your major and related fields as well as classes in other disciplines. However, one crucial difference between mathematics and math education degrees is **the focus of the degree program**. A math major has just one main subject area to study.

### What are the importance of learning theories in mathematics education? ›

Learning theories are critical because they “**help us to understand both how knowledge is created and how people learn**” Harasim (2017).

**What is the best method of teaching mathematics in primary grades? ›**

**10 Strategies for effectively teaching math to elementary schoolers**

- Use hands-on learning methods. ...
- Incorporate visuals. ...
- Integrate math games into math lessons. ...
- Connect math concepts to everyday life. ...
- Allow students to explain their reasoning. ...
- Give frequent feedback and direction. ...
- Reward progress. ...
- Personalize lessons.

**What is the best way to teach mathematics in primary grades? ›**

**7 Effective Strategies for Teaching Elementary Math**

- Make it hands-on. ...
- Use visuals and images. ...
- Find opportunities to differentiate learning. ...
- Ask students to explain their ideas. ...
- Incorporate storytelling to make connections to real-world scenarios. ...
- Show and tell new concepts. ...
- Let your students regularly know how they're doing.

**What factors affect children's learning of mathematical concepts? ›**

**Environmental Factors that Influence Early Math**

- Number Competence. Your child will develop basic numerical abilities if you introduce them to numbers through formal or informal contact. ...
- Early Literacy. ...
- Family Influence on Child Education. ...
- Socio-economic status. ...
- Gender. ...
- Parental Influence.

**How important is mathematics today in our generation? ›**

**It develops our reasoning, helps us to have analytical thinking, quickens our mind, generates practicality and also its use can be applied in the day to day**. The mathematics is present in our daily lives.

**What is the importance of mathematics in the modern world? ›**

**It gives us a way to understand patterns, to quantify relationships, and to predict the future**. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

**What do we value in mathematics and its teaching and learning? ›**

CONCLUSION There are mainly ten values in learning mathematics. They are practical value, intellectual value, social value, moral values, disciplinary values, cultural values, international values, aesthetic values, vocational values and psychological values.

**What is the nature of mathematics education? ›**

Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.

**Why is mathematics a core subject in school education? ›**

Mathematics is included in the core curriculum of primary and secondary programmes because **it is recognized that students develop the kinds of skills that they need to function effectively in their personal and working lives by doing and learning mathematics**.

**What is mathematics teaching and learning? ›**

Mathematics Teaching and Learning is an international book series that aims to provide an important outlet for sharing the research, policy, and practice of mathematics education to promote the teaching and learning of mathematics at all school levels as well as teacher education around the world.

### What other learning theories can we implement in teaching mathematics effectively? ›

Therefore, teaching methods must be re-examined, taking into account the three major learning theories: **behaviorism, cognitivism, and constructivism**. Behaviorism is a teacher-centered instruction, while cognitivism states learning is based upon how people mentally process stimuli encountered.

**What are the theories of mathematics education? ›**

Four philosophies of learning are contrasted, namely **'simple' constructivism, radical constructivism, enactivism and social constructivism**. Their underlying explanatory metaphors and some of their strengths and weaknesses are contrasted, as well as their implications for teaching and research.

**What are the benefits of applying learning theories when developing educational strategies? ›**

The theories provide information about the relationships among strategies, context, and learner characteristics for better integration, and, most importantly, learning theories **allow for reliable prediction of the effectiveness of the selected instructional strategies**.