By the time the students reach the high school level, they have developed ease with several math concepts. They develop fluency in counting, comparing values, doing basic operations, and number sense. From whole numbers and integers, they move to the world of rational and irrational numbers. In fact, in every math skill, they require to explore it deeper and derive various inferences from it. That is why the math goals for high school students are more of application-oriented and inspire them to learn how mathematics is used to solve several real-world problems.
Correct approach for setting goals
Mathematics subject may become a source of worry to students who find it hard to grasp. Also, the vastness of syllabus can become overwhelming too. Teachers tend to put the onus on self-learning mode and expect them to be ready for solving math problems without much guidance. The approach may not be effective for all. It is why the process of setting goals must have the following characteristics:
- Individualized: The student’s shortcomings or the need to learn should be addressed head-on. While setting goals, the student’s gaps in learning should be in focus. It can be done by evaluating the result of the last exam taken. A discussion with the student on a one-on-one basis can also be considered.
- Timed: A student must be given ample time to learn any math topic as per the difficulty level. The goal has to be set to ensure that the student is ready for exams at appropriate time and pass it with good score.
- Contributing to skills for higher studies: Math goals should prepare high school students for the ensuing challenges waiting at college education level. If they plan to pursue college education, the goal must help them have the required competence.
- Amply challenging: The math goals should not be too easy or too difficult to achieve. In both cases, the student is likely to lose interest in studying math.
Let’s take a look at the most suitable math goals that complement the needs of high school students and help teachers have an effective lesson plan. Some states, too approve these goals.
Topic-wise math goals for high school students
Extracted from Sioux City Community Schools guide, the following math goals have been in consideration for and application at high school level:
1. Numerical ability
Moving to quantitative reasoning from calculating: The student must be able to solve the questions like how fast the city A’s population is growing if the populations at two points in time is X and Y. Which city has more population density if the sq. km areas of the two cities and their population are given.
Pure math: In pure math, the student must be able to know how to convert mixed fractions in irrational or rational numbers. They must become familiar with the way rational and irrational numbers can be converted into numbers with rational exponents.
Linear and non-linear equations: Learn how to solve linear and non-linear equations. Take challenge of solving any real-life problem by making quadratic equations from the variables and conditions provided.
Algebraic expressions and their interpretation: Be comfortable with solving algebraic expressions. Also, gain fluency in transforming algebraic expressions to solve a given problem. Such as, finding interest on loan and the resulting amount by establishing relationship between P = principal, Rate =r and term = n.
Pictorial presentations take a little advanced form at high school level as modeling. The modeling is used for estimating the occurrence of a real-life event and finding ways to solve the problems surrounding it. For example, by analyzing the data provided, students may have an overview on the situations of floods, their time of occurrence and the need for arranging food and water for stranded people.
Data evaluation: Establish relationship between data values. Find the rate at which the value changes to predict the pattern for future.
Statistics and Probability: Give justifications for conclusions and make inferences from various samples of surveys, observational studies and experimental data. Use probability in real-life situations to make predictions. For example, study and compare the probability of rain to occur from the given set of parameters such as temperature, humidity and wind direction with probability of having a plausible temperature or humidity range when it is raining.
- Learn basics of trigonometry and trigonometric functions.
- Learn and prove theorems that involve trigonometry of right triangles
- Describe geometric properties algebraically by using the coordinates and equations provided
Achieving goals – Teacher’s guide
According to Iowa Core Standards for high school’s math classes, the inclusion of learning-centric methods and facilities in classroom is essential. These standards provide an overview of methods of instructions and assessments that can help impart requisite math skills to high school students.
- Teaching methods to improve understanding and application ability: Interactive sessions, activity-based class, real-life examples, and demonstrations for building practical learning.
- Student-focused classrooms: Designing classrooms so that these ease learning and make it fun too.
- Individualized teaching: Using ways to ensure that students get individualized learning and personal attention
- Timely assessment: Assessing from time to time and creating tests to compel students to revisit learned concepts often
- Designing rich mathematical tasks: Various topics or types of problems need implementation of more than one math skill. Designing assignments so that students get to do rich mathematical tasks can improve students’ mathematical thinking. It includes problem-solving tasks, and meaningfully distributed practice.
Challenges in meeting math goals
High school math may prove difficult to learn if the learning disorders are to be managed. The curriculum may prove too overwhelming and vast. It does require teachers to be amply trained to understand the students’ difficulties and provide appropriate mode of instruction.
Lack of visualization ability is big hindrance in learning high school’s math topics. Students may crack numbers but if they find it difficult to draw inferences, they may not be able to provide solutions as expected. It arises due to little interest or limited intellectual curiosity.
Unattended weakness in some topics at elementary school stage poses a big learning gap. No assessment system enables 100% coverage of topics. The students may pass grades by solving questions related to some topics only. By leaving some topics that may be required to solve high school math problems, they show deficiency and poor confidence.
Lack of interest in subject may also manifest as difficulty in attaining math goals. The high school students may find subject too confusing. They may show signs of chronic slowness or lateness, or need of more practice to learn and apply math concepts. The timeliness in achieving goals can get affected due to this issue.
In case of middle-level school drop-outs, the lack of conceptual fluency is quite obvious. They need additional time and support or remediation to bridge the learning gap arose from the years of staying away from curriculum. It may show a negative impact on goals aimed at developing problem-solving skills.
The best way to make students sincere in learning math is that of defining goals for them. These goals work as a guide to plan the teaching lesson in class and for making personalized study schedule at home. The successful implementation depends on the study planning, active learning methods, and designing goals with an individualized approach. However, situation of drop-outs, incomplete coverage of topics in assessment, lack of interest, and learning gaps in basic skills may pose challenges. Discussion and timed assessments can significantly help in effective implementation.