What Can You Build Without a Proper Foundation?

Just as houses and other buildings need strong foundations to support them, math students need strong foundations in fundamental skills to support them too. Math topics build on each other from year to year and students with weak foundational skills struggle to learn new skills that build on the old ones.

Math isn’t like social studies or history where if a student isn’t strong in, for example, American history, the student can still excel in world history. Social studies or history classes do not presume a solid working knowledge of the classes that came before.

At MATH 1-2-3®, our math tutors like to think of teaching or learning math like you would think about teaching or learning a foreign language. A student needs to master the verbs before learning how to conjugate them and to use the subjunctive mood. As with a foreign language, math concepts are at once new and cumulative. In math, a student needs to feel comfortable with the skills required for each level of math before the student can succeed at the next level. A student’s failure to become proficient in foundational concepts compromises the student’s ability to learn and understand the more advanced work that builds in the foundational skills. This affects not only performance in the classroom, but on standardized tests, including the SAT and ACT.

The skilled tutors at MATH 1-2-3® work with students of all ages, levels and abilities. Through tutoring, our experts help math students to understand the connections between new concepts they are learning to math concepts and principles they already know. This builds confidence and skill, not only for homework, class tests and classwork, but for the ACT and SAT.

Parents and math students often ask the tutors at MATH 1-2-3® whether there is such a thing as “too late” to learn foundational concepts. Our experienced tutors know that at any age, or any level of math, students with weak foundations in basic skills can always work to improve and address any deficits they may have. Weaknesses in foundational skills are sometimes only apparent when the student is called upon to use them as part of learning a new skill. That is the perfect time to call upon a highly skilled math tutor to strengthen and reinforce skills required for more advanced work.

When a math student has a solid understanding of mathematical symbols and patterns, the student can successfully connect math symbols with the concepts they represent. Once a student has that skill, the student can see patterns, math concepts, and parts of math problems in his or her head. That gives the student confidence, speeds up problem solving and makes completing homework, classroom tests and standardized tests faster. It also reduces anxiety, which is always the goal at MATH 1-2-3®. For example, knowing basic addition and subtraction facts is a necessary skill for combining like terms. Recognizing what numbers are perfect cubes often shortcuts problem solving. In eighth and ninth grade, the quick recall of multiplication tables, which are taught in elementary school, helps students more efficiently factor quadratic expressions. There are many more examples of the ways in which basic foundational concepts appear in, and affect, more complex, advanced math.

Conversely, when a student cannot recognize patterns, work out parts of math problems mentally, in whole or in part, or associate math symbols with the concepts they represent, they work more slowly. The struggle to grasp the significance of the symbols in homework and test problems and failure to recognize patterns complicates problem solving.

At MATH 1-2-3® our tutors have seen students, even advanced students, using guess and check methods, employing workarounds, counting on their fingers or relying heavily on calculators as a replacement for solid foundational skills. We believe it is always better to develop the foundational skill, rather than to develop and rely on, a substitute for it. Some math students and parents ask why it matters how the student reaches the homework or test answer. We can demonstrate that it is faster to work out parts of problems mentally, than to rely on alternate methods. In classroom tests and on standardized tests, including the SAT and ACT, working quickly and efficiently can help boost scores. Students and parents also appreciate that when a math student, whether the student is struggling, or advanced, or something in between, embraces and becomes proficient in the foundational skills, they feel more confident and more prepared. Speed and confidence help raise classroom test and standardized test scores and improve classroom and homework performance.

Successful math students in elementary, middle school, high school and college must use visual and spatial processes to think about, understand and learn new concepts. The experienced tutors at MATH 1-2-3® work with students to help them understand, develop and master the foundational visual and spatial skills they need.

Visual processing requires the understanding of symbols. On a very basic level, numerals are symbols that are used to represent quantities. At more advanced levels, algebra, geometry, statistics, logic, set theory and calculus all employ the use of different kinds of math symbols.

Math students are required to understand, use, and manipulate symbols to perform operations ranging from basic addition and subtraction to solving algebraic equations and doing calculus. Math students also employ visual and spatial representations of math processes, concepts and relationships. Students must be able to see, understand, appreciate and interpret visual and spatial information. These foundational visual skills come into play when students are presented with shapes or graphs.

Foundational visual skills also serve math students well as they help students to create mental images that correlate to mathematical concepts. For example, visualization is helpful when a student is called upon to answer questions related to proportion. Proportions and ratios are the types of relationship that are often better visualized than described in words. When elementary and middle school students can mentally picture relationships, their understanding of proportions and ratios is greatly enhanced. For example, picturing the ratio of students to teachers will help the math student understand the concept of proportion.

The foundational spatial skills are important when the math student is asked to describe the features of a shape, or to the translate graphs into usable information.

Successful math students also need to develop a strong working knowledge of math vocabulary. Not only is math taught and learned in much the way a foreign language is, but math concepts and processes also come with their own terms, terminology and vocabulary. Some math students are intimidated when presented with a glossary of unfamiliar terms. Others are overwhelmed by odd-sounding words which correspond to unfamiliar concepts. Math students at all levels, from elementary school to middle school to high school to college, are faced with words that they have never heard before and that they will not generally hear outside of the field of mathematics. At MATH 1-2-3®, our tutors are familiar with all the ways in which math vocabulary can confuse, intimidate and derail math students and are experienced in simplifying and demystifying the vocabulary of math and increasing students’ confidence and comfort with math words.

In addition to having the ability to visualize and conceptualize math principles and in addition to having a working knowledge of math vocabulary, successful math students understand well how math concepts they have already learned are related to new concepts presented to them.

Elementary school math students learn the relationship between addition and subtraction. Early math students also learn the concept of place value, which is a foundational skill which helps them to understand problems dealing with money. More advanced students learn the spatial relationship between physical objects, for example the relationship between a physical object’s size and its mass. Math students also go on to learn the relationships between math operations and the order in which they are performed.

When students become well-versed in foundational concepts, they can easily access and implement the concepts they have learned when faced with homework, test, SAT or ACT problems that require the use of multiple concepts. For example, when a student is called upon to plot information on a graph, the student will call upon concepts and skills taught at earlier levels, including collecting, evaluating and organizing information, setting up ratios, finding averages and using the coordinate system.

As students’ math skills and understanding of math concepts grows and their comfort with those skills and concepts grows, student will begin to see how math concepts apply to everyday situations. As experienced math tutors, one of our most rewarding experiences is when a student can identify the ways in which math relates to, and impacts on, the student’s daily life and activities. Strong foundations in visual and spatial concepts, math vocabulary and the connections between math concepts help math students develop from only a basic understanding of a math principle to a comfortable, working knowledge of the ways in which the principle can be applied to real-life circumstances.

To succeed in higher levels of math, students must have the necessary foundational skills, including an understanding of number concepts and symbols, a comfort with math vocabulary, a proficiency in numeric operations and the skill to apply mathematical concepts to real-life situations.

Our skilled tutors at MATH 1-2-3® empower students by showing them the connections between new material and skills they already have. When necessary, our experienced tutors re-teach or reinforce foundational math skills so students can confidently master new topics. Our expert math tutors are experienced at assessing and pinpointing where a student is less skilled, or less confident, and in providing support so that the student can strengthen foundational skills.

There is no shame in having weaker or underdeveloped foundations in certain areas. The danger is in not addressing them. Our tutors at MATH 1-2-3 pride themselves on their ability to improve a student’s foundations, to prepare the student for future math success. Call us at 1-888- MATH123 and we can get to work!