Should kindergarten learn algebraic thinking?
Is teaching Algebraic thinking in Kindergarten an overkill?
One sunny afternoon, siblings Timmy, Lucy, Max, and Lola found a bag of 24 cookies. Timmy grabbed the bag and shouted, “Cookies for everyone!” But when he poured them out, Max ended up with 8 cookies, and Lola only got 4. “Not fair!” cried Max. Lucy, the observant one, said, “Let’s share equally.” They counted and realized they should each get 6 cookies. They collected all the cookies and divided them again. Everyone got exactly 6 cookies. Max grinned, “Sharing is fun when it’s fair!” And they all munched happily ever after.
Lets dive into their Math brain 🙂
- Timmy, Lucy, Max, and Lola needed to share 24 cookies. They quickly Identified the problem situation.
- Max gets 8 cookies, and Mia gets 4, which is perceived as unfair. They assessed the initial distribution was flawed:
- Lucy recognizes that fairness means everyone should get an equal amount of cookies. Lucy initiates the need for ‘fair share’ concept.
From Logic they move deeper into Algebraic Thinking.
- Division and Equal Distribution: Total Cookies: There are 24 cookies. Number of Siblings: 4 siblings. They perform the division, 24÷4=6 Each child should get 6 cookies.
- Counting and Summing: They recount and confirm that 6 cookies each for 4 children sums up to 24 cookies.
- Balancing Equation: They ensure that 6×4=24 verifying their solution.
- Understanding Proportionality: Recognizing the initial unfair distribution (8 for Max, 4 for Mia) and understanding that this does not add up equally.
- Correcting Distribution: Collecting all cookies and redistributing them evenly shows an understanding of proportion and fairness.
- Children do this all the time. The above situation has a lot of things going for it, the problem is tactile and allows for visual perception. There is no pressure for performance or urgency for a single person to get the right answer. Its about figuring things out together as a team. The children are actively engaged. They have full freedom to ask questions, try the distribution as many times as necessary and come up with a solution! And as a bonus they get to eat cookies! If learning Algebra can be this fun in K-5, why do our children find it daunting in middle school?
Fast forward Middle school…
Lucy: slams book “I don’t get it, Mom! Algebra is like trying to speak a different language, but all I hear is gibberish!”
Mom: chuckles “I know it can feel that way, but let’s break it down. See this equation? It’s like a puzzle waiting to be solved. You’re like a math detective!”
Lucy: “It’s more like soccery, abra-cadabra-annoying algebra! “
Mom: laughs “Okay, fair point. But imagine when you crack this code, you’ll feel like a cool math witch! Plus, it’s great brain exercise.
Witches were cool! Way back in time, ‘witches’ were independant women who did not fit the family system. They were healers, widows, and elderly women, a perceived threat to the patriarchal standards of subservient women and therefore were villanized.”
Lucy: grinning “That’s crazy… It might be true, but then again, maybe they were vilianzed because they did a LOT of algebra? If I figure out algebra and turn into a witch, I’m am making Algebra vanish for good…”
Why do our kids struggle with Algebra?
Remember many of us did too?
Nobody likes to imagine going to the store to buy 53 watermelons and 96 bananas to figure out the total cost of a glass of coolaid. It feels too far fetched.
But perhaps if they were WALKING watermelons and SKATING bananas that we have to catch before they all escape and quickly make coolaid with them, kids might engage due to the wild humorous imagination!
Jokes apart, The problem is multi-fold.
- Foundational Skills: Many students enter algebra with weak foundational skills in key areas such as multiplication, fractions, and integers. For instance, a lack of fluency in multiplication can slow down problem-solving and increase errors, while difficulties with fractions and integers (positive and negative numbers) complicate the understanding and manipulation of algebraic expressions
- Teaching Methods: The way algebra is taught can also impact student understanding. Effective teaching methods that emphasize conceptual understanding over rote memorization can make a significant difference. However, not all students have access to high-quality math instruction, which can further exacerbate difficulties
- Abstract Thinking: Algebra requires a higher level of abstract thinking than arithmetic. Students must learn to manipulate variables and solve equations, which involves understanding concepts such as variables, functions, and the rules of operations on these abstract entities. This level of abstraction is a significant leap for many students
- Conceptual Shifts: Algebra represents a significant shift from arithmetic, which involves concrete numbers and straightforward operations, to a more abstract form of mathematics that uses variables and symbols to represent unknown quantities and relationships. This transition can be difficult for many students to grasp
- Problem-Solving Skills: Algebra often involves multi-step problems that require students to decode the problem, set up equations, and solve them while interpreting the results correctly. This multi-layered problem-solving process can be overwhelming for students who are not used to such complex tasks.
Algebraic thinking is more than a math equation
Algebraic thinking is more than just solving for x in a math equation; it involves recognizing patterns, understanding relationships, and developing the ability to think abstractly. Research has shown that developing algebraic thinking skills in young children significantly enhances their overall mathematical abilities and prepares them for more complex concepts later on.
We need to be deliberate in our intention to nuture a love for Math and Problem Solving from a young age in kids, much like we do with reading.
According to a study by the National Council of Teachers of Mathematics (NCTM), early exposure to algebraic thinking helps students develop a deeper understanding of numbers and operations, which is critical for success in later math education . Furthermore, the National Mathematics Advisory Panel found that students who develop algebraic thinking in elementary school are more likely to excel in high school mathematics, including algebra and calculus .
How can we help young children developing Algebraic Thinking ?
- Pattern Recognition and Creation
- Activity: Encourage children to recognize and create patterns using everyday objects like blocks, beads, or even snacks.
- Impact: A study published in the Journal of Educational Psychology found that pattern recognition activities can improve young children’s mathematical abilities by up to 15% .
- Mathematical Conversations
- Activity: Engage children in conversations about numbers, relationships, and simple equations during daily activities such as cooking, shopping, or playing games.
- Impact: The Developmental Psychology journal highlights that children who participate in math-related conversations with their parents score higher in math achievement tests .
- Interactive Games and Technology
- Activity: Utilize educational apps and games that focus on problem-solving and algebraic concepts.
- Impact: A report from the Joan Ganz Cooney Center indicates that children using math apps show a 17% improvement in their ability to solve algebraic problems .
Algebraic thinking is not just for the classroom; it is a vital part of everyday life. By fostering these skills early on, we can ensure that our children are well-equipped to tackle the challenges of the 21st century, both in their academic careers and beyond.
Here are some games that get children honing their algebraic thinking,
Practice it on a car ride, or as a quick game in every Math class, or while you are waiting at the salon or a line at the icecream shop!
1. Pattern Detective
- How to Play: One person starts a pattern using objects they see outside (e.g., red car, blue car, red car) and others have to continue it.
- Skills Developed: Pattern recognition and continuation.
2. Number Sequence Puzzle
- How to Play: Start a number sequence (e.g., 2, 4, 6, 8) and have the kids guess the next number in the sequence.
- Skills Developed: Understanding numerical relationships and sequences.
3. Algebraic I Spy
- How to Play: Say “I spy something that comes in pairs and is more than three but less than seven,” prompting kids to guess items based on the algebraic clues.
- Skills Developed: Logical reasoning and understanding inequalities.
4. Car Count Game
- How to Play: Pick a type of vehicle (e.g., trucks) and count how many you see. Then, create an equation like 2x = total number of trucks, and solve for x.
- Skills Developed: Basic algebraic equation solving.
5. Math Riddles
- How to Play: Pose algebraic riddles such as “I am thinking of a number that, when added to 5, equals 12. What is the number?”
- Skills Developed: Solving for unknowns in equations.
6. License Plate Math
- How to Play: Look at the numbers on license plates and create simple algebraic expressions (e.g., if the plate reads 478, make 4 + 7 = x, then x + 8).
- Skills Developed: Creating and solving simple equations.
7. Shape Hunt
- How to Play: Identify shapes in passing scenery (e.g., triangular road signs, rectangular billboards) and discuss their properties. Create patterns or sequences with the shapes spotted.
- Skills Developed: Geometry and pattern recognition.
8. Algebraic 20 Questions
- How to Play: Think of a number and have the kids ask up to 20 yes/no questions to figure it out (e.g., “Is it greater than 10?”).
- Skills Developed: Logical deduction and numerical reasoning.
9. What’s the Rule?
- How to Play: Create a rule for a number sequence (e.g., add 3 each time) and have the kids guess the rule based on the numbers you provide.
- Skills Developed: Understanding functions and sequences.
10. Multiplication Car Bingo
- How to Play: Create bingo cards with products of basic multiplication (e.g., 12, 15, 20). Call out multiplication problems (e.g., 3×4, 5×3), and kids mark the product if it’s on their card.
- Skills Developed: Multiplication and algebraic thinking.