Mindy Seminario

Mindy realized she loved teaching when she began coaching swimming as a young adult. She coached all levels from swimming lessons to Junior Olympic teams. From several swim team families she also learned about homeschooling and knew she would homeschool her future children.

Mindy received her Bachelor of Arts degree in Spanish Summa Cum Laude from the University of California at Los Angeles spending a year abroad at the University of Costa Rica. She thought she would eventually teach Spanish, but fell in love with math as a homeschool mom. On a quest to learn how best to teach her children, she discovered Caleb Gattegno’s method for teaching math and began to see the subject in a whole new light. Gattegno’s method allowed her to embark on a journey of mathematical discovery along side her kids.

She is excited to be able to share this journey with students at HuckleBerry and looks forward to their many creative mathematical insights.

Algebra Before Arithmetic!

Ages: 6-9

Prerequisites: Students should be able to count to 20, and be able to write numbers and letters.

Homework: Highly recommended, and will take 15-30 minutes every week.

New students: Because this is a significantly different way of doing math that builds each week upon previous lessons, registration will not be open to new students in the Spring trimester. If you would like to sign up for winter please first contact Mindy at Mindymarissa@gmail.com.

Please note: This class is not a substitute for a full math curriculum, but rather a supplement and different approach that will help students understand core math concepts that are usually just memorized in standard math curriculum.

We spent the fall trimester getting to know the cuisenaire rods, learning how to make trains and to write basic expressions. We learned some basic operations, explored odd and even, halves and thirds, built and investigated interesting structures and had interesting discussions on the students’ own observations. We even played games and deciphered riddles.

In the winter and spring trimesters, we will build upon what we have learned and discovered. We will explore fractions, factors, and using parentheses. Using all of these and the four operations together students will see the equivalent or inverse nature of the operations and the relationships the rods share with each other.

Up until this point, we have been using letters to write our expressions. In the following trimesters, students will get to assign values to the rods. However, these values will be flexible, again emphasizing the relationships the rods share. As one rod is assigned a value, the value of the other rods will change. For more on this click here: One Can Be Anything

Homework will be recommended for the spring and winter and should take about15 to 30 minutes each week outside of class. Please reach out if help is needed! Also, because this is a significantly different way of doing math that builds each week upon previous lessons, registration will not be open to new students in the Spring trimester. If you would like to sign up for winter please first contact Mindy at Mindymarissa@gmail.com.

In this year-long class students explore the 4 basic operations (+-x ÷) plus fractions through Caleb Gattegno’s Algebra Before Arithmetic method.

Caleb Gattegno had radical beliefs about education. Founder of the Association of Teachers of Mathematics (ATM) and author of over 120 books and countless articles, he believed math wasn't just for the gifted and “that all human beings are inherently gifted with virtually limitless powers of self-learning.” For Gattegno, any student could act as a mathematician.

His method for teaching elementary school math makes the subject easily accessible using tangible colored rods as a tool. Using rods eliminates the need to rely on counting where mistakes can easily be made and cause frustration. The tactile, visual nature of the rods allows students to quickly recognize and create mathematical relationships and patterns.

But the rods are not just used as tools for calculation. Whereas traditional math classes tend to give children a set of problems expecting a determined solution: think 30 problem worksheet, Gattegno believed children could be creative mathematicians themselves. In this class students will explore creating their own patterns, equations, inequalities, and different ways of describing these mathematically. They will build structures, make mathematical discoveries and test and revise their own hypotheses (see photos at the end of this document for examples). We will use a variety of rod-based activities and games to facilitate student’s own awareness about math. However, the class will not concern itself with teaching students set procedures or algorithms to compute solutions to problems.

This is not only more engaging but also more effective. Schools that take the leap of faith (and it's quite a leap!) have students who are more competent in math, having excellent computation and problem-solving skills, and the ability to think mathematically. While the scope and sequence of the curriculum does not align with common core standards, students gain the deep understanding and mathematical reasoning called for in the standards. The Bronx Charter School for Better Learning (BBL) is a school that utilizes the Gattegno method. Although, according to greatschools, 81% of its students are from low income families, BBL still far out-performs the state average in math with most of its students at or above grade level. The school, which utilizes Gattegno’s philosophies on education and methodologies beyond the subject of math, is a great example of Gattegno’s methods in practice.

FAQs

Q. Why is the class called Algebra Before Arithmetic?

This method is sometimes referred to as Algebra Before Arithmetic because it does not use number names to describe the rods when students start out. Instead, different length rods are referred to by their colors and given a letter to represent them. This way the emphasis will be on the operations. Later, numerical work may be introduced. There are many benefits to using color names. Using color names makes mathematical expressions clearer, fractions easier to understand, helps student have greater flexibility in their thinking, and makes variables comfortable and easy for when students get to higher levels of math.

1. Will this method confuse my student when doing their regular math curriculum at home?

No, since the class will not teach set procedures to solve problems our work with the rods will only add to the math they're doing and help them understand it more deeply.

2. What are some topics this class cover?

Below is a list of topics we will likely cover in the year-long class. Because of the organic nature of the class and depending on the readiness of the individual students, we may cover more or less.

Sequences (staircases)
Odd and even
Complements (addends)
Addition and properties of addition
Subtraction and properties of subtraction
Multiplication and properties of multiplication
Division and properties of division including remainder
Fractions as operators
Equivalent fractions
Measurement using arbitrary unit values (for example if the white rod is the unit or equal to one, orange will equal 10, but if the orange Rod is the unit or equal to one then the white rod will equal 1/10)
Combining the above to create complex expressions

3. If I want to use this method in my homeschool how can I find more information?

Parents who are interested in learning more about how to use this method in their own homeschool can find lots of information and resources at the following links. Sonya Post is a homeschool mom who dedicates herself to teaching others about Gattegno’s methods. You can read her blog at https://www.arithmophobianomore.com. She also offers self paced courses at https://www.learningwellathome.com/academy/ and “Notice and Wonder Boot Camps” that you can find out about on her Facebook group. https://www.facebook.com/groups/arithmophobianomore

Hope to see you in class!

Examples of Student Discoveries, Observations and Hypotheses:

Contact

Mindy's Email: mindymarissa@aim.com