Changing New Mexico’s mathematics story

"Our family doesn't do math."

Jeffrey Houdek has heard versions of that sentence from parents throughout his years as a mathematics educator.

It is an ordinary enough comment, sometimes offered with a laugh or a shrug. A parent struggled with mathematics in school, perhaps their parents did, too. Math was hard. Math was intimidating. Math was something other people were good at.

And somewhere along the way, a child may begin to understand something much larger than the arithmetic in front of them: people like us aren't math people.

Houdek, a lecturer in K-12 mathematics education in the University of New Mexico's Department of Teacher Education, Educational Leadership and Policy, finds the social acceptance of that idea striking.

Families who would never casually announce that reading simply is not something they do can speak openly about an inability to do mathematics. Being bad at math, he said, has become socially acceptable and can even be socially reinforced.

But Houdek challenges the premise underneath the statement and says everyone can learn it.

For educators preparing New Mexico's future teachers, that deceptively simple exchange points toward something much larger. Children do not arrive at mathematics as blank slates. They bring previous successes and failures, confidence and anxiety, language and culture, family experiences and ideas about who is supposed to be good at math. Their teachers bring histories of their own.

Changing New Mexico's mathematics story, then, cannot begin and end with what happens when a child opens a textbook. It also happens in the preparation of the teacher standing beside them.

At The University of New Mexico College of Education & Human Sciences (COEHS), faculty approaching mathematics education from different disciplines are examining what future teachers need to help more children develop mathematical understanding and a belief in their own capacity to learn.

Their work crosses mathematics methods, special education, multilingual education and teacher preparation. Each brings a different perspective to a common question: what does a teacher need to know, understand, and be able to do to help a learner become confident in mathematics?

For COEHS Dean Kristopher M. Goodrich, the question reaches beyond teacher preparation. It is part of a larger challenge facing New Mexico: connecting policy, standards, preparation and classroom practice so that each informs and strengthens the others.

"New Mexico already has innovative people, programs and practices throughout the state. Our opportunity is to connect that work more intentionally. Policy should inform preparation. Practice should inform policy. Standards should be accompanied by the preparation, professional learning and resources educators need to implement them well. Sustainable change happens when those pieces function as parts of the same system."

One place to begin is with the people preparing to become teachers.

"New Mexico already has innovative people, programs and practices throughout the state. Our opportunity is to connect that work more intentionally. Policy should inform preparation. Practice should inform policy. Standards should be accompanied by the preparation, professional learning and resources educators need to implement them well. Sustainable change happens when those pieces function as parts of the same system."

- Kristopher Goodrich, dean, College of Education and Human Sciences

The Teacher as Learner

Houdek came to mathematics education by an unconventional route. He began college studying aerospace engineering before realizing near the end of the program that he did not want a career in the field. Mathematics did resonate. He changed direction, earned a mathematics degree and entered corporate work.

Then life changed direction again.

After the death of his younger brother prompted him to reconsider what he wanted from his life, Houdek left the corporate world and moved with his family to his grandparents' cattle ranch outside Las Vegas, New Mexico. He became involved in the community and began coaching young people.

Something clicked.

"I was coaching and coaching and I loved it so much where I thought, you know, my backgrounds in math and I love coaching, I should be coaching math," Houdek recalled.

He became a middle and high school mathematics teacher, later earned a master's degree in mathematics education and eventually arrived at UNM, where his role shifted again: from teaching mathematics to preparing others to teach it.

That experience has taught him that preparing a mathematics teacher begins with understanding that teacher as a learner.

When Houdek first began teaching elementary mathematics methods at UNM, he assumed future elementary teachers would arrive with the foundational mathematics knowledge necessary for the course.

Then his class worked with fractions, and many students struggled. His response was not simply to identify what they did not know. It was to change what happened in his own classroom.

Houdek began incorporating additional mathematics content into the methods course. Future teachers work through mathematics themselves, examining not simply how to arrive at an answer but why a process works, how a problem can be represented in different ways and how mathematical reasoning can be explained to someone else.

Over the course of a semester, he saw something change. Competency begins to produce confidence.

That relationship matters because teachers' own experiences with mathematics eventually enter the classrooms they lead.

Teaching is filled with competing demands: schedules change, assemblies happen, fire drills interrupt lessons. When a teacher is uncomfortable with a certain subject or content area, it can become the default to postpone when something has to give.

"I think it's incumbent upon us to help our future teachers be both more confident and more competent in math," Houdek said.

But knowing mathematics is only one part of becoming a mathematics teacher.

Knowing Mathematics and Knowing Learners

Allison Nannemann, Ph.D., associate professor of special education, approaches mathematics from the perspective of learners who struggle.

Students with disabilities can face particularly significant challenges in mathematics, but Nannemann argues that knowledge developed within special education has applications well beyond students with identified disabilities. Many learners need additional time, different representations, explicit instruction or another pathway into a mathematical concept.

The point is not to prescribe one method for every learner, it is to become better at seeing the learner in front of you. Students bring different needs, but they also bring different strengths.

As Nannemann puts it, students "don't only come with needs, they come with needs and strengths. And when we put them together, it creates a really powerful force."

Preparing teachers to recognize both requires something different from mathematics competency alone.

"To be a really effective teacher of a subject, you need to know how to teach that subject," Nannemann said.

Houdek arrives at much the same intersection from another direction.

"We need our mathematicians to be better teachers. We need our teachers to be better mathematicians."

Without that combination, he sees risks from both directions.

Teachers uncertain about mathematics may become uncomfortable watching a student wrestle with a problem and rush to provide the next step. Those with deep content expertise but less understanding of pedagogy may struggle to understand why something obvious to them is not obvious to a learner.

Either way, something important can disappear.

"We're stealing their struggle," Houdek said.

Productive struggle asks something different of the teacher: enough mathematical confidence to remain present when an answer does not come quickly and enough pedagogical knowledge to know when to intervene, when to offer another pathway and when to let the learner keep working.

The space between "I don't know" and "I understand" becomes part of the lesson.

And what happens in that space can shape more than mathematical knowledge, it can shape identity.

Becoming a Knower and Doer of Mathematics

Amy Brass, Ph.D., brings that question directly into mathematics methods work with future elementary teachers.

Her work asks future educators to examine not only how they will teach mathematics, but also their own relationships with the subject. Mathematics becomes more than a sequence of procedures and correct answers. Reasoning, discussion, multiple representations and real-world application become part of learning to think mathematically.

Nannemann sees their work as complementary.

While Nannemann often concentrates on helping learners who are struggling gain access to mathematics, she describes Brass's work as helping learners build from established foundations toward increasingly sophisticated mathematical understanding.

"She's working from the middle up," Nannemann said. "I'm working from the bottom to the middle."

Somewhere between those directions is the learner.

"We are knowers and doers of mathematics," Nannemann said. "We all have potential to be knowers and doers of mathematics."

But even that understanding becomes more complicated when another boundary begins to soften: the one between mathematics, language and culture.

Listening for the Mathematics

For Carlos LópezLeiva, Ph.D., professor in the Department of Language, Literacy, and Sociocultural Studies (LLSS), mathematics does not exist separately from the language and culture through which people understand and express it.

"Mathematics is cultural; how we understand numbers is cultural," LópezLeiva said. "Mathematics is a cultural activity."

That matters particularly in New Mexico, where future teachers may work with children who reason and communicate across English, Spanish, Indigenous languages and other languages spoken in their homes and communities.

Translation alone is not always enough.

A student may understand a mathematical relationship while expressing that understanding differently from the way a teacher expects. A concept may move between languages or be represented through experiences and cultural traditions that do not precisely mirror those of the teacher.

The educator has to learn to listen for the mathematics underneath the expression.

LópezLeiva has brought that perspective into mathematics methods and into the LLSS course Language, Culture and Mathematics, exploring intersections that traditional methods coursework may not always foreground.

It widens the question again.

Knowing the content matters.

Knowing how to teach it matters.

Knowing the learner matters.

Knowing how to recognize the learner's thinking matters.

And none of that knowledge resides entirely within a single discipline.

Nannemann has watched faculty expertise around mathematics education emerge across COEHS from different academic traditions. For her, an important part of the work is creating the space for those perspectives to encounter one another.

"We may all have a similar goal of supporting mathematics education, but we're coming at it differently," she said. "Different doesn't have to be a problem when it's built on a foundation of respect."

The goal is not uniformity.

It is coherence.

The Spaces Between

The same challenge exists beyond the college. Teacher preparation contributes knowledge about how educators learn to teach. special education contributes expertise about individual learner needs and instructional supports. Mathematics education contributes disciplinary knowledge and pedagogy. Multilingual and sociocultural scholarship contributes understanding of how language, culture and community shape learning.

Practicing educators bring the realities of classrooms. Families bring knowledge of their children and communities. Policymakers establish standards, resources and structures. None operates in isolation.

And some of the most consequential work may happen not within any one of them, but in the spaces between them.

Between what research reveals and what policy requires.

Between what standards expect and what implementation demands.

Between what universities teach and what educators encounter when they enter classrooms.

Between what a teacher intends and what a learner experiences.

Those spaces are where information can either stop or continue moving.

For Goodrich, strengthening those connections is essential to creating sustainable educational change.

"We have to resist the temptation to treat educational challenges as a sequence of isolated problems. A standard without preparation and support for implementation is incomplete. Teacher preparation disconnected from the realities of classrooms is incomplete. Policy developed without the knowledge of educators, communities and researchers is incomplete. The work is in building the connections among them."

That does not require everyone in the system to approach mathematics in the same way.

It requires the different parts of the system to learn from one another.

Nannemann sees signs of that possibility as New Mexico gives increasing attention to mathematics and as different areas of expertise begin intersecting within teacher preparation.

The opportunity is not simply to generate another intervention.

It is to allow knowledge to travel.

From classroom to university.

From university to classroom.

From research to policy.

From policy into implementation.

And from implementation back into the questions researchers, educators and policymakers ask next.

The continuum resides in those exchanges.

And the people moving through it carry knowledge, too.

Returning to New Mexico's classrooms

Many of the future teachers entering preparation programs today were educated in the same New Mexico schools they are preparing to serve.

They bring those experiences with them.

For some, that includes gaps in their own mathematics preparation. But framing future educators only by what they may not yet know misses something equally important.

They know New Mexico. They have sat in its classrooms. They understand its communities. They have experienced its educational system from the learner's side.

Houdek sees that lived experience as an asset.

"They're from New Mexico, they understand New Mexico, they grew up in New Mexico," he said.

He has seen the power of that connection outside education, too. Houdek recalls a physician from a small community near Las Vegas who returned home to practice medicine. Beyond the quality of care he provided, Houdek remembers what the physician represented simply by being there.

"He's one of us, and look what he did," Houdek said.

Teachers who return to their communities can carry that same possibility.

They return, but they do not return unchanged.

And neither does the system.

Changing Our Story

A child hears, "Our family doesn't do math."

Perhaps that child believes it.

Perhaps mathematics becomes something to endure rather than explore. Perhaps the child carries that belief through elementary school, middle school and high school.

Years later, that learner may walk through the doors of a teacher preparation program.

There, someone asks the learner to look at mathematics again. Not simply to memorize another procedure, but to understand why it works, to explain it another way.

To struggle with a problem without interpreting struggle as proof of inability. To recognize mathematics in language, culture, work, family and community. To discover strengths alongside needs.

Competency grows. Confidence follows.

Then that future teacher walks into a New Mexico classroom and stands beside another child. This time, when the child struggles, the teacher does not rush to take the struggle away.

When the child approaches a problem differently, the teacher knows to look for the thinking underneath it.

When the child needs more time, another representation or another pathway, the teacher has more tools available.

And when that child begins to wonder whether mathematics belongs to other kinds of people, the teacher is prepared to offer a different story.

The cycle has returned to a familiar place.

But it has moved forward.

Houdek learned to think about progress that way during his years in the classroom: not simply where a learner stood at a particular moment, but whether that learner was growing.

Get a little better every day. Get a little stronger every day.

At the scale of an educational system, growth is more complicated, but the movement can be similar. A learner becomes a teacher. Practice generates knowledge. Knowledge shapes preparation. Preparation changes practice. Experience reveals something new. And the next time the system comes around, it carries that knowledge with it.

"The goal is not a single initiative or a moment when we declare the work finished. It is a system capable of learning from itself and improving over time," said Houdek. "Policy informs preparation. Preparation changes practice. Practice gives us new knowledge. That knowledge comes back into the system and helps us make the next decision better. Each time we complete that cycle, we should be further forward than where we began."

And perhaps, somewhere in that next turn, a child goes home from school with a mathematics problem. Maybe someone sits down beside them. And instead of, "Our family doesn't do math," the child hears: "Let's figure it out."