# Mathematics Learning Outcomes

Saint Xavier University is dedicated to providing top-quality education that is intentionally designed to develop your skills and expertise as you prepare for the next step in your education or career. The learning outcomes reflect the specific competencies that you will gain from our mathematics program, while the curriculum map portrays how these competencies will shape and prepare you for the real world.

## Learning Outcomes

### Mathematics Learning Outcomes

#### Bachelor of Science in Mathematics

Students of the mathematics program at SXU will be able to:

- Solve problems from a variety of mathematical fields, thereby displaying a breadth of knowledge of mathematics.
- Communicate results and arguments clearly, effectively and correctly, both in writing and orally.
- Use, in an appropriate and effective manner, mathematics software and technology including graphing calculators, computer algebra systems and statistical software.
- Work as a member of a problem-solving team able to critically analyze and solve mathematical problems.
- Independently research a mathematical topic and write a mathematically accurate research paper, thereby displaying a depth of knowledge.
- Model real-world problems mathematically and interpret results appropriately.

### Actuarial Science Learning Outcomes

#### Bachelor of Science in Actuarial Science

Students of the actuarial science major at SXU will be able to:

- Solve a wide variety of mathematical problems related to the actuarial science field.
- Communicate results and arguments clearly, effectively and correctly, both in writing and orally.
- Demonstrate proficiency in the fundamental concepts of financial mathematics including the theory of interests and financial derivatives.
- Write programming languages such as Java or C++ and use mathematics software and technology.
- Work as a member of a problem-solving team to critically analyze and solve mathematical problems.
- Independently research a mathematical topic on actuarial science and write a mathematically accurate research paper, thereby displaying a depth of knowledge.
- Model real-world problems mathematically and interpret results appropriately.

### Secondary Education Mathematics Learning Outcomes

#### B.S. in Math/SED (Mathematics with Secondary Education)

Students of the Mathematics with Secondary Education program at SXU will demonstrate the following competencies:

**Content Knowledge**

- Teacher candidates will demonstrate and apply knowledge of major mathematics concepts, algorithms, procedures, applications in varied contexts and connections within and among mathematical domains (number, algebra, geometry, trigonometry, statistics, probability, calculus and discrete mathematics) as outlined in the NCTM CAEP Mathematics Content for Secondary.
- Teacher candidates will independently research a mathematical topic and write a mathematically accurate research paper, thereby displaying a depth of knowledge.

**Mathematical Practices**

- Teacher candidates will use problem solving to develop conceptual understanding, make sense of a wide variety of problems, adapt and apply problem-solving strategies within the field of mathematics and other contexts, and formulate and test conjectures to frame generalizations.
- Teacher candidates will reason abstractly, reflectively and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others; represent and model generalizations using mathematics; recognize structure and express regularity in patterns of mathematical reasoning; use multiple representations to model and describe mathematics; and utilize appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others.
- Teacher candidates will formulate, represent, analyze and interpret mathematical models derived from real-world contexts or mathematical problems.
- Teacher candidates will organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences.
- Teacher candidates will demonstrate the interconnectedness of mathematical ideas and how they build on one another, and they will recognize and apply mathematical connections among mathematical ideas and across various content areas and real-world contexts.
- Teacher candidates will model how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting and representing.

**Content Pedagogy **

- Teacher candidates will apply knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains.
- Teacher candidates will analyze and consider research in planning for and leading students in rich mathematical learning experiences.
- Teacher candidates will plan lessons and units that incorporate a variety of strategies, differentiated instruction for diverse populations and mathematics-specific and instructional technologies in building all students' conceptual understanding and procedural proficiency.
- Teacher candidates will provide students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life and the workplace.
- Teacher candidates will implement techniques related to student engagement and communication including selecting high-quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies.
- Teacher candidates will be able to plan, select, implement, interpret and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students.
- Teacher candidates will monitor students' progress, make instructional decisions and measure students' mathematical understanding and ability using formative and summative assessments.

**Mathematical Learning Environment **

- Teacher candidates will exhibit knowledge of adolescent learning, development and behavior and demonstrate a positive disposition toward mathematical processes and learning.
- Teacher candidates will plan and create developmentally appropriate, sequential and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge.
- Teacher candidates will incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms and include culturally relevant perspectives to motivate and engage students.
- Teacher candidates will demonstrate equitable and ethical treatment and high expectations for all students.
- Teacher candidates will apply mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools and mathematics-specific technologies (e.g., graphing tools, interactive geometry software, computer algebra systems and statistical packages); and make sound decisions about when such tools enhance teaching and learning, recognizing both the insights to be gained and possible limitations of such tools.

**Impact on Student Learning **

- Teacher candidates will verify that secondary students demonstrate conceptual understanding; procedural fluency; the ability to formulate, represent and solve problems; logical reasoning and continuous reflection on that reasoning; productive disposition toward mathematics; and the application of mathematics in a variety of contexts within major mathematical domains.
- Teacher candidates will engage students in developmentally appropriate mathematical activities and investigations that require active engagement and include mathematics-specific technology in building new knowledge.
- Teacher candidates will be able to collect, organize, analyze and reflect on diagnostic, formative and summative assessment evidence and determine the extent to which students' mathematical proficiencies have increased as a result of their instruction.

**Professional Knowledge and Skills**

- Teacher candidates will take an active role in their professional growth by participating in professional development experiences that directly relate to the learning and teaching of mathematics.
- Teacher candidates will engage in continuous and collaborative learning that draws upon research in mathematics education to inform practice; enhance learning opportunities for all students' mathematical knowledge development; involve colleagues, other school professionals, families and various stakeholders; and advance their development as a reflective practitioner.
- Teacher candidates will be able to utilize resources from professional mathematics education organizations such as print, digital and virtual resources/collections.

**Secondary Mathematics Field Experiences and Clinical Practice**

- Teacher candidates will engage in a sequence of planned field experiences and clinical practice prior to a full-time student teaching/internship experience that include observing and participating in high school mathematics classrooms and working with a diverse range of students individually, in small groups and in large class settings under the supervision of experienced and highly qualified mathematics teachers in settings that reflect cultural, ethnic, linguistic, gender and learning differences.
- Teacher candidates will experience full-time student teaching/internship in secondary mathematics that is supervised by a highly qualified mathematics teacher and a university or college supervisor with secondary mathematics teaching experience or equivalent knowledge base.
- Teacher candidates will develop knowledge, skills and professional behaviors across high school settings; examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics; and observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment and assessment.

## Curriculum Maps

### Mathematics Curriculum Maps

If you would like to learn more about what you can expect from the programs, please review the following: