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Mathematics Education in the United States
The United States is a large and diverse country with considerable variation across regions, districts, and schools. Edward Liu of Rutgers University’s Graduate School of Education provided a general overview of teaching in the United States, with the caveat that descriptions may not be accurate in a given state or city.
THE HISTORY AND CONTEXT OF TEACHING
Teaching is honored in the United States, Liu said, “but in American culture it’s also somehow looked down upon. If you mention that you are a high school teacher, someone will often respond, ‘That’s terrific,’ but the next sentence out of their mouth is, ‘You must like the summer vacations off.’ So it gets a mixture of some respect and some lack of respect.” Teaching is seen as a profession in the United States, but it is a relatively low paid one and is unionized, which many other professions are not.
The U.S. education system is decentralized and fragmented. Preparation and credentialing, working conditions, and job definitions are set at the state and local levels. And there are approximately 14,500 school districts in the United States with elected local school boards that make policy.
The United States does not have a national curriculum, and because of local control, schools can undergo frequent policy or curricular changes. “You can be a veteran with lots of expertise in a math curriculum,” Liu commented. “Suddenly a new school board comes in and changes the cur
riculum or approach, and then this is all new to you. What you have learned and the lessons you have designed may no longer be as valuable or as useful. That can be very disruptive.”
The cultural context also has an influence on teaching and learning. In the United States, teaching tends to be associated with individualistic, heroic images. “Successful teachers are charismatic, they have personalities, they are dedicated; on their own they are inspiring students. If you look at a movie, you never see teachers working together or talking to one another. They’re all with their students being inspirational.”
The teaching profession itself has a culture that emphasizes autonomy and privacy. “You are the king or queen of your classroom,” described Liu. “You have a right to organize it as you feel to fit your strengths and weaknesses.” The teaching profession traditionally has resisted outside intervention from administrators and the state, though that tradition is slowly changing.
Teaching also has a culture of egalitarianism that resists distinctions based on expertise and merit. “We all are the same and have equal status, equal pay, equal say, and equal rights to teach the way we prefer.” In addition, teaching has a culture of seniority. When distinctions are made between teachers, those distinctions are usually tied to seniority rather than other criteria.
These cultural aspects of teaching have kept the profession relatively unstratified in the United States. There is little differentiation in job descriptions or pay. To gain increased responsibility and salary, teachers traditionally have had to leave the classroom and go into administration, although there have been some roles, such as department chair, that have a history of permitting teachers to stay in the classroom and take advantage of their instructional expertise.
Early career teachers have limited opportunities for apprenticeships and few entry procedures, Liu explained. New teachers are expected to start on their first day and be ready to teach a full load. “In fact, sometimes they get the most challenging course assignments, the lowest tracked students, and multiple assignments rather than the easier ones you would think would be given to a novice.” This aspect of teaching also has been undergoing gradual change in some places as professional development programs and teacher residency programs have sought to provide a more gradual and graded entry into the profession and a longerterm novice experience.
THE PREPARATION AND PROFESSIONAL DEVELOPMENT OF TEACHERS
Teachers need to be well prepared if they are to teach mathematics well. Yet, according to Maria Tatto of Michigan State University’s College of Education, the education of prospective teachers and the professional development of practicing teachers often do not provide the kinds of opportunities to learn that teachers need to be effective. “We are constantly asking teachers to teach things we have not prepared them for, and we are cheating our students of a good mathematics education.”
Tatto is the principal investigator for an international comparison of educational policy known as the first Teacher Education Study in Mathematics (TEDSM).^{1} TEDSM has just finished a systematic study of preservice mathematics preparation in 17 countries, including the United States. The study looked at prospective K–12 teachers’ characteristics and opportunities to learn, the outcomes of these opportunities, and the impact of these opportunities on novice and experienced teachers. It had three components:

Studies of teacher education policy, schooling, and social contexts at the national level

Studies of primary and lower secondary mathematics teacher education routes, institutions, programs, standards, and expectations for teacher learning

Studies of the mathematics and related teaching knowledge of future primary and lower secondary school mathematics teachers
Data collection for the study began in October 2007 and ended in June 2008. It surveyed more than 15,000 future primary teachers, more than 9,000 future lower secondary teachers, more than 4,000 teacher educators, and about 500 institutions that included units preparing future primary and lower secondary teachers. In addition to measuring background, opportunities to learn, and beliefs among teachers in each country, the study included items measuring teachers’ mathematical content and pedagogical knowledge. “We did not originally intend to test teachers, but the countries said, ‘If we’re going to do all this work, let’s develop a good test.’ And that was a good thing to do,” commented Tatto.
The results of the study were planned for release in January 2010 and
^{1} 
For more information on TEDSM, see http://teds.educ.msu.edu. 
were not available at the time of the workshop. The study also planned to release a large database of results in September 2010 for use by researchers and others.
The literature review done for the study showed that teacher education, recruitment, and pay are highly decentralized in the United States, Tatto reported. All states require certified teachers to have completed a bachelor’s degree that includes subject matter and pedagogical studies for an initial credential. Many states have additional requirements for further certification, such as additional courses or a master’s degree. But other requirements for teacher certification vary by state. Some states have provisions for alternative or emergency certification that allow people who have not met all the state requirements to teach, usually on a temporary basis.
Teacher education is provided by a wide range of organizations, including colleges, universities, school districts, state agencies, and private organizations, Tatto explained. For example, more than 1,300 colleges and universities offer teacher preparation programs in early elementary, elementary, middle, and lower secondary education. Degrees offered include bachelor’s degrees, master’s and other postbaccalaureate degrees, and 5year degrees.
As of 2007, 39 of the 50 states required 5 to 18 weeks of student teaching. These preparation programs vary widely in such factors as oversight of the selection of the cooperating teacher, the amount of contact between program faculty and field supervisors, and the links between coursework and field experience. In 2003, about one in five public school teachers was newly hired. Many alternative routes to teacher certification have been established during the past 20 years. For example, many large urban areas have approved alternative licensure programs for midcareer professionals seeking entry into teaching, and the federal government sponsors a program called Troops to Teachers to facilitate entry of former military personnel into teaching. These programs typically enable teaching candidates to begin working as fulltime teachers while they meet the licensing requirements for standard teaching licenses.
TEDSM also assessed the quality of the pool of teacher candidates using their SAT scores as a proxy. Future teachers who pursue elementary education with certification in mathematics tend to have lower SAT scores than the average college graduate. Teaching candidates who pursue secondary education licensure in specific subject content areas such as mathematics have average or higher SAT scores than other college graduates.
A factfinding study for TEDSM measured teachers’ content and pedagogical knowledge as a trial run for the assessment used in the full
study. Future teachers in the United States scored lower on most measures of mathematics content knowledge than did teachers from Bulgaria, Germany, Korea, Mexico, and Taiwan. “In the different areas of knowledge that we measured,” Tatto explained, “the United States is pretty low.” She cautioned, however, that these results are preliminary and do not include a representative sample of teachers from each country.
WHAT MATHEMATICS TEACHERS NEED TO KNOW
Comments from several of the other presenters echoed the findings offered by Tatto. Mari Muri, a senior mathematics consultant for the Project to Increase Mastery of Mathematics and Science at Wesleyan University, noted that most elementary teachers in the United States are trained as generalists and do not have much mathematics training. In most states they have taken 6 credit hours of mathematics, with that number rising to 12 credit hours in some states. “There’s not a lot of math there,” observed Muri, “and many are very uncomfortable teaching mathematics.”
Muri laid out some of the knowledge and skills that elementary teachers need to teach mathematics well. They need to have a solid grounding in mathematics and believe that mathematics is important. They also need to have a thorough understanding of pedagogy. For example, they need to know how to teach children with different learning styles and backgrounds. “Students have different interests in mathematics and different parental support, so you need to have that passion for making sure that all of them can learn.” Advanced students need to have their understanding of mathematics broadened rather than simply moving them to subjects covered in the next grade, while less advanced students need help to catch up with their peers.
To teach students with different learning styles, teachers need different ways of transmitting information. “If something doesn’t work, just saying it louder or slower does not work,” Muri commented. Teachers should explore innovative strategies such as taking students outside or on field trips, “or come dressed in some crazy outfit to motivate them.” Teachers also need to be adept at teaching students who do not speak English at home. Many states such as California already have high numbers of English language learners in classrooms, and the numbers are growing throughout the United States.
Teachers need to have a solid understanding of how to assess students and how to use that information to adjust instruction. Furthermore, assessment is closely related to the communication of mathematics, Muri
commented. “Promoting discussion in the classroom starts from an early grade, so that students are comfortable talking about mathematics and use proper mathematical terms and language.” The teacher then can use students’ verbal reflection on mathematics as formative assessments to improve instruction.
Teachers need to be able to use technology in mathematics instruction. Many new technologies are becoming available, “but that’s something that most teachers at the elementary level are not really comfortable with,” Muri described. “We need to make sure that they have that level of comfort.”
The professional development of teachers differs in important respects from teaching students. “Adult learners are not children,” she mentioned, “we need to treat them as adults.” Elementary teachers may resist learning mathematics, as may administrators. Professional development “needs to choose instruction to motivate even the teachers who come in having no mathematics background or no love of math, who are walking in the door and out almost at the same time.”
U.S. teachers do not model lessons for other teachers nearly as much as Chinese teachers do, Muri noted. Chinese teachers “are more comfortable visiting each other’s classrooms and observing a lesson.” The structure of a teacher’s day in the United States also does not permit easy collaboration. However, some districts have found ways to address this problem. For example, Javier González, a mathematics teacher at Pioneer High School in Whittier, California, noted that all of the students in his school leave at 2 p.m. on Mondays, giving teachers 1 hour to work together, and once a month they leave at 12:15, providing the teachers with 2 hours of collegial time.
However, simply providing teachers time for collaboration does not mean that they will be able to use all of that time solely to improve instruction. For example, Mary Santilli, a teacher and program leader for elementary mathematics in Trumbull, Connecticut, described some of the activities undertaken by the Connecticut Investigations Consortium, which works with prekindergarten through fifth grade teachers who use a curriculum known as “Investigations in Number, Data, and Space.” The consortium helps teachers understand and use the resources provided with the curriculum. However, the teachers also have spent considerable time rearranging the curriculum so that the order of topics covered in their classrooms matches up with the state assessments in mathematics. “Because of our state tests, it doesn’t always make sense to go in order. We had to
do some rearranging, and there was passionate debate among our group to arrive at an end product.”
CHANGING THE CULTURE OF TEACHING
“The culture of teaching has a profound effect on the daytoday activities of teachers,” commented Janine Remillard of the University of Pennsylvania’s Graduate School of Education. She noted that U.S. education is in many ways based on a production model. “We often think about education like a factory, where we have inputs and get an output. The input is the untaught student, teaching happens in the system, and children learn as a result.” That kind of model tends to emphasize efficiency, where production is maximized for a given input. It also tends to produce a disconnected workforce, where different people do different kinds of work. “It’s a very horizontal model, where there isn’t much vertical interconnection among the types of work people do.”
This horizontal model of teaching can in turn contribute to a lack of trust in teachers, Remillard commented; “We don’t put a lot of trust in the wisdom of teachers’ practice. As a result, people outside of the work of practice, like researchers or professional developers, need to provide teachers with that wisdom.” Echoing Liping Ma’s comments, Remillard described this lack of trust as one of the unseen aspects of teaching. “That’s something we struggle with in the United States,” she mentioned. “We need to think about how to foster wisdom within practice.”
Belinda Thompson, a National Board Certified Teacher with 9 years of experience teaching mathematics in grades 5 through 9, observed that attitudes vary within the United States. She described growing up in rural Kentucky, where the public schools were one of the largest employers and being a teacher meant that you were a college graduate. “In lots of rural areas and small towns, there is a different perspective on a teacher and how the community looks at a teacher.”
However, González reiterated Remillard’s observation about the lack of respect accorded to teachers. When he has visited other countries, he has been struck by the respect he received as a teacher. “In Japan, I was treated with such respect and honor, because I was a visiting teacher from the state of California.... When I go to Mexico and tell them I am a teacher, I am highly respected throughout that country, because I am a profesor. Yet in this country, for whatever reason, the teacher is not highly respected. Therefore,
it is difficult for us to produce young students who say, ‘When I grow up, I want to be a teacher.’ They want to be doctors, lawyers, other things.”
Demographic changes going on within the teaching profession may have an influence on the culture, mentioned Liu. A large group of teachers who entered the profession in the early 1970s are now retiring. “We have a large group coming in who can perhaps be reshaped by new policies. There is more interest in collaboration, and somewhat less concern about privacy. In fact, many of the new teachers I have interviewed say, ‘Yes, I wish I had more feedback; I wish more master teachers would come to my classroom.’ So this is a new generation with different expectations.” In addition, many midcareer professionals are entering teaching with work experiences and skills and life experiences from outside education. “They potentially can put some pressure on the existing system to create change.”
Jennifer BayWilliams of the University of Louisville, who is pastpresident of the Association of Mathematics Teacher Educators, also pointed to the forces of change swirling around teaching. As evidence for a renewed focus on teaching in the United States, she cited several innovative proposals made by prominent commentators, such as journalist Thomas Friedman’s call to eliminate federal income taxes for all public teachers, Secretary of Education Arne Duncan’s call to pay more to teachers in highneeds subjects like science and mathematics, and writer Malcolm Gladwell’s call for an apprenticeship system that allows candidate teachers to be rigorously evaluated. “Our country is putting a lot of effort and energy into thinking differently about teaching,” BayWilliams commented.