Types of mathematics tools

The Academy of Math app contains videos in addition to text and formulas. Videos can be much more helpful to students who are more visual learners. To learn math, you need to know the meaning of its terms. In mathematics, the same concept applies to formulas and equations.

Studygeek can help you to understand what you are reading about and remember the meaning of each word whenever you see it. The app contains the alphabetical glossary of math terms. You can look for any term from a mathematics course and find the explanation for it. It even lets students play games when they are learning math concepts.

You can also find other tools and sites like brainybro. When incorporating tech tools like these, teachers can be more involved with students in lessons and therefore help students truly learn more. Sign in or become a BestTechie member to join the conversation. Just enter your email below to get a log in link.

Stepping Stones 2. Globatoria Young students like games so teachers often use them to make studying more interesting. Geometry Pad Geometry Pad is used as virtual graph paper.

Pattern Shapes Pattern Shapes is a tool that also helps students work with geometrical shapes, by using it, you are able to draw different shapes, fractions, and other elements of any size and height. MathPlayground MathPlayground is a gallery of games relating to mathematics, including math games, logic games, and more.

FluidMath The FluidMath platform is developed for iPads and can also be used on interactive whiteboards. Dragon Box This platform has already proven that it helps students learn hard concepts quickly.

Academy of Math This app is designed to help explain math concepts to students who are having a difficult time following along. Studygeek To learn math, you need to know the meaning of its terms. Read more posts by this author. Jake Potter. Comments Sign in or become a BestTechie member to join the conversation. Send a log in link Great! Primary among them is that assessment should be seen as an integral part of teaching and learning rather than as the culmination of the process.

With this knowledge, students and teachers can build on the understanding and seek to transform misunderstanding into significant learning. Time spent on assessment will then contribute to the goal of improving the mathematics learning of all students. The applicability of the learning principle to assessments created and used by teachers and others directly involved in classrooms is relatively straightforward.

Less obvious is the applicability of the principle to assessments created and imposed by parties outside the classroom. Tradition has allowed and even encouraged some assessments to serve accountability or monitoring purposes without sufficient regard for their impact on student learning. A portion of assessment in schools today is mandated by external authorities and is for the general purpose of accountability of the schools.

In , 46 states had mandated testing programs, as. Several researchers have studied these testing programs and judged them to be inconsistent with the current goals of mathematics education. Instruction and assessment—from whatever source and for whatever purpose—must support one another. Studies have documented a further complication as teachers are caught between the conflicting demands of mandated testing programs and instructional practices they consider more appropriate. Some have resorted to "double-entry" lessons in which they supplement regular course instruction with efforts to teach the objectives required by the mandated test.

Instructional practices may move ahead of assessment practices in some situations, whereas in other situations assessment practices could outpace instruction.

Neither situation is desirable although both will almost surely occur. However, still worse than such periods of conflict would be to continue either old instructional forms or old assessment forms in the name of synchrony, thus stalling movement of either toward improving important mathematics learning. From the perspective of the learning principle, the question of who mandated the assessment and for what purpose is not the primary issue.

Instruction and assessment—from whatever source and for whatever purpose—must be integrated so that they support one another. To satisfy the learning principle, assessment must change in ways consonant with the current changes in teaching, learning, and curriculum. In the past, student learning was often viewed as a passive process whereby students remembered what teachers told them to remember. Consistent with this view, assessment was often thought of as the end of learning.

The student was assessed on something taught previously to see if he or she remembered it. Similarly, the mathematics curriculum was seen as a fragmented collection of information given meaning by the teacher. This view led to assessment that reinforced memorization as a principal learning strategy.

As a result, students had scant oppor-. To develop mathematical competence, students must be involved in a dynamic process of thinking mathematically, creating and exploring methods of solution, solving problems, communicating their understanding—not simply remembering things.

Assessment, therefore, must reflect and reinforce this view of the learning process. This chapter examines three ways of making assessment compatible with the learning principle: ensuring that assessment directly supports student learning; ensuring that assessment is consonant with good instructional practice; and enabling teachers to become better facilitators of student learning.

Mathematics assessments can make the goals for learning real to students, teachers, parents, and the public. Assessment can play a key role in exemplifying the new types of mathematics learning students must achieve. Assessments indicate to students what they should learn. They specify and give concrete meaning to valued learning goals.

If students need to learn to perform mathematical operations, they should be assessed on mathematical operations. If they should learn to use those mathematical operations along with mathematical reasoning in solving mathematical problems, they must be assessed on using mathematical operations along with reasoning to solve mathematical problems.

In this way the nature of the assessments themselves make the goals for mathematics learning real to students, teachers, parents, and the public.

Mathematics assessments can help both students and teachers improve the work the students are doing in mathematics. Students need to learn to monitor and evaluate their progress. When students are encouraged to assess their own learning, they become more aware of what they know, how they learn, and what resources they are using when they do mathematics.

In the emerging view of mathematics education, students make their own mathematics learning individually meaningful. Important mathematics is not limited to specific facts and skills students can be trained to remember but rather involves the intellectual structures and processes students develop as they engage in activities they have endowed with meaning.

The assessment challenge we face is to give up old assessment methods to determine what students know, which are based on behavioral theories of learning and develop authentic assessment procedures that reflect current epistemological beliefs both about what it means to know mathematics and how students come to know. Current research indicates that acquired knowledge is not simply a collection of concepts and procedural skills filed in long-term memory.

Rather the knowledge is structured by individuals in meaningful ways, which grow and change over time. A close consideration of recent research on mathematical cognition suggests that in mathematics, as in reading, successful learners understand the task to be one of constructing meaning, of doing interpretive work rather than routine manipulations.

In mathematics the problem of imposing meaning takes a special form: making sense of formal symbols and rules that are often taught as if they were arbitrary conventions rather than expressions of fundamental regularities and relationships among quantities and physical entities. Modern learning theory and experience with new forms of assessment suggest several characteristics assessments should have if they are to serve effectively as learning activities.

Of particular interest is the need to provide opportunities for students to construct their own mathematical knowledge and the need to determine where students are in their acquisition of mathematical understanding. In both, the assessment must elicit important mathematics. Constructing Mathematical Knowledge Learning is a process of continually restructuring one's prior knowledge, not just adding to it.

Good education provides opportunities for students to connect what is being learned to their prior knowledge. One knows. Assessment must reflect the value of group interaction for learning mathematics. One way to provide opportunities for the construction of mathematical knowledge is through assessment tasks that resemble learning tasks 12 in that they promote strategies such as analyzing data, drawing contrasts, and making connections.

It is not enough, however, to expand mathematics assessment to take in a broader spectrum of an individual student's competence. In real-world settings, knowledge is sometimes constructed in group settings rather than in individual exploration.

Learning mathematics is frequently optimized in group settings, and assessment of that learning must reflect the value of group interaction. Some mathematics teachers are using group work in instruction to model problem solving in the real world.

They are looking for ways to assess what goes on in groups, trying to find out not only what mathematics has been learned, but also how the students have been working together. A critical issue is how to use assessments of group work in the grades they give to individual students. A recent study of a teacher who was using groups in class but not assessing the work done in groups found that her students apparently did not see such work as important.

Group work, if it is to become an integral and valued part of mathematics instruction, must be assessed in some fashion. A challenge to developers is to construct some high-quality assessment tasks that can be conducted in groups and subsequently scored fairly. Part of the construction of knowledge depends on the availability of appropriate tools, whether in instruction or assessment.

Recent experimental National Assessment of Educational Progress NAEP tasks in science use physical materials for a miniexperiment students are asked to perform by themselves. Rulers, calculators, computers, and various manipulatives are examples from mathematics of some instructional tools that should be a part of assessment. If students have been using graphing calculators to explore trigonometric functions, giving them tests on which calculators are banned greatly limits the questions they can be asked and.

Similarly, asking students to find a function that best fits a set of data by using a computer program can reveal aspects of what they know about functions that cannot be assessed by other means. Using physical materials and technology appropriately and effectively in instruction is a critical part of learning today's mathematics and, therefore, must be part of today's assessment.

Since the use of manipulatives is a critical part of today's mathematical instruction, such tools must be part of today's assessment. Reflecting Development of Competence As students progress through their schooling, it is obvious that the content of their assessments must change to reflect their growing mathematical sophistication. When students encounter new topics in mathematics, they often cannot see how the unfamiliar ideas are connected to anything they have seen before.

They resort to primitive strategies of memorization, grasping at isolated and superficial aspects of the topic.

As learning proceeds, they begin to see how the new ideas are connected to each other and to what they already know. They see regularities and uncover hidden relationships. Eventually, they learn to monitor their thinking and can choose different ways to tackle a problem or verify a solution. The example below contains a description of this growth in competence that is derived from research in cognition and that suggests the types of evidence that assessment should seek.

Coherent Knowledge. Beginners' knowledge is spotty and shallow, but as proficiency develops, it becomes structured and intergrated into prior knowledge. Principled problem solving. Novices look at the surface features of a task; proficient learners see structure of problems as they represent and solve them. Usable knowledge. Experts have knowledge that is connected to the conditions in which it can be applied effectively. They know not only what to do but when to do it.

Attention-free and efficient performance. Experts are not simply faster than novices, they are able to coordinate their automated skills with thinking processes that demand their attention. Self-regulatory skills. As people develop competence, they also develop skills for monitoring and directing their preformance.

A full portrayal of competence in mathematics demands much more than measuring how well students can perform automated skills although that is part of the picture. Assessment should also examine whether students have managed to connect the concepts they have learned, how well they can recognize underlying principles and patterns amid superficial differences, their sense of when to use processes and strategies, their grasp and command of their own understanding, and whether.

An example of how assessment results can be used to support learning comes from the Netherlands. One test for a unit on matrices contained questions about harvesting Christmas trees of various sizes in a forest. The students completed a growth matrix to portray how the sizes changed each year and were asked how the forest could be managed most profitably, given the costs of planting and cutting and the prices at which the trees were to be sold.

They also had to answer the questions when the number of sizes changed from three to five and to analyze a situation in which the forester wanted to recapture the original distribution of sizes each year. After the students handed in their solutions, the teacher scored them, noting the major errors. Given this information, the students retook the test. They had several weeks to work on it at home and were free to answer the questions however they chose, separately or in essays that combined the answers to several questions.

The second chance gave students the opportunity not simply to redo the questions on which they were unsuccessful in the first stage but, more importantly, to give greater attention to the essay questions they had little time to address. Such two-stage testing essentially formalizes what many teachers of writing do in their courses, giving students an opportunity to revise their work often more than once after the teacher or other students have read it and offered suggestions.

The extensive experience that writing teachers have been accumulating in teaching and assessing writing through extended projects can be of considerable assistance to mathematics teachers seeking to do similar work. During the two-stage testing in the Netherlands, students reflected on their work, talked with others about it, and got information from the library. Many students who had not scored well under time pressure—including many of the females—did much better under the more open conditions.

The teachers could grade the students on both the objective scores from the first stage and. The students welcomed the opportunity to show what they knew. As one put it. Usually when a timed written test is returned to us, we just look at our grade and see whether it fits the number of mistakes we made.

In the two-stage test, we learn from doing the task. We have to study the first stage carefully in order to do well on the second one. In the Netherlands, such two-stage tasks are not currently part of the national examination given at the end of secondary school, but some teachers use them in their own assessments as part of the final grade each year.

In the last year of secondary school, the teacher's assessment is merged with the score on the national examination to yield a grade for each student that is used for graduation, university admission, and job qualification. Teachers can use scoring guides to communicate the goals of improved mathematical performance. Assessment tasks that call for complex responses require scoring rubrics. Such rubrics describe what is most important about a response, what distinguishes a stronger response from a weaker one, and often what characteristics distinguish a beginning learner from one with more advanced understanding and performance.

Such information, when shared between teacher and student, has critically important implications for the learning process. Teachers can appropriately communicate the features of scoring rubrics to students as part of the learning process to illustrate the types of performance students are striving for.

Students often express mystification about what they did inadequately or what type of change would make their work stronger. Teachers can use rubrics and sample work marked according to the rubric to communicate the goals of improved mathematical explication.

When applied to actual student work, rubrics illustrate the next level of learning toward which a student may move. For example, a teacher may use a scoring rubric on a student's work and then give the student an opportunity to improve the work. In such a case, the student may use the rubric directly as a guide in the improvement process. The example on the following page illustrates how a scoring rubric can be incorporated into the student material in an assess-.

The student not only can develop a clearer sense of quality mathematics on the task at hand but can develop more facility at self-assessment. It is hoped that students can, over time, develop an inner sense of excellent performance so that they can correct their own work before submitting it to the teacher. Incorporating a Scoring Rubric Directions for students.

Today you will take part in a mathematics problem-solving assessment. This means that you will be given onen problem to solve. You will hve thirty 30 minutes to work on this problem. Please show all your work. Your paper will be read and scored by another person—someone other than your teacher. Please be sure to make it clear to the reader of your paper how you solved the problem and what you were thinking.

The person who will read your paper will be looking mainly for these things:. How well you understand the problem and the kind of math you use.

How well you can use problem-solving strategies and good reasoning. How well you can communicate your mathematical ideas and your solution. Your paper will receive a score for each of these. You will do all your work here in class on the paper provided and you may use manipulatives or a calculator ro work on your problem. I have thought about the problem carefully and feel as if I know what I'm talking about.

Mathematics also involves structure, space, and change. Mathematics can be studied as its own discipline or can be applied to other field of studies. Applied mathematics is those which are used in other sciences such as engineering, physics, chemistry, medicine, even social sciences, etc. Pure mathematics on the other hand is the theoretical study of the subject, and practical applications are discovered through its study.

Here are some of them:. Algebra is a broad division of mathematics. Algebra uses variable letters and other mathematical symbols to represent numbers in equations.

It is basically completing and balancing the parts on the two sides of the equation. It can be considered as the unifying type of all the fields in mathematics. It is the mathematics concerned with questions of shape, size, positions, and properties of space. It also studies the relationship and properties of set of points. It involves the lines, angles, shapes, and spaces formed. As its name suggests, it is the study the sides and angles, and their relationship in triangles.

Some real life applications of trigonometry are navigation, astronomy, oceanography, and architecture. Calculus is an advanced branch of mathematics concerned in finding and properties of derivatives and integrals of functions. It is the study of rates of change and deals with finding lengths, areas, and volumes.

Linear algebra is a branch of mathematics and a subfield of algebra. It studies lines, planes, and subspaces. It is concerned with vector spaces and linear mappings between those spaces. This branch of mathematics is used in chemistry, cryptography, geometry, linear programming, sociology, the Fibonacci numbers, etc.

The name combinatorics might sound complicated, but combinatorics is just different methods of counting. There are two combinatorics categories: enumeration and graph theory. Permutation, an arrangement where order matters, is often used in both of the categories. As the name suggest, differential equations are not really a branch of mathematics, rather a type of equation. It is any equation that contains either ordinary derivatives or partial derivatives. The equations define the relationship between the function, which represents physical quantities, and the derivatives, which represents the rates of change.