Inquiry-based math at GATE

Dear GATE Families,


Great as always to see you this morning! We had a discussion focused on math that was both philosophical and practical. We covered a lot of ground so this is a long recap 


Why is self-paced math important?

• Many of our kids come to GATE from environments where they were not allowed to be accelerated in their math, they had to work in lock step with their peers. This can be incredibly frustrating for gifted kids!
  
• Data shows that student-centered learning (which includes self-pacing) increases motivation and achievement while decreasing anxiety related to learning.
  

How does student-centered, inquiry-based math at GATE work?

• At GATE, student-centered learning in math means the students work at their own pace and receive one-on-one help from a teacher when they need assistance.
  
  • While math facts and vocabulary have their place in our program, we encourage the students to engage in inquiry while working through and thinking about math.
    
  • What does inquiry-based math look like at GATE?
    
    • When a student gets stuck on a problem and asks for help from the teacher, they usually want the teacher to tell them the next step or even give them a clear path to the answer. Instead we ask the students questions!
      
      • One of the first questions would be - did you read the directions? You will not be shocked to hear that the answer is often no!
        
      • We also ask, what concept are you learning about in your book right now? This helps the kids center themselves in the concept and approach the problem through the lens of the skills related to that specific concept.
        
      • Another question is - what have you tried so far? This question triggers the student to walk the teacher through their problem solving strategy and frequently provides a lightbulb moment for the students. Some kids need to verbalize to aid in processing thoughts.
        
      • We also ask kids to try to think of a real life scenario in which the problem could be applicable. Many times when students draw pictures or diagrams they are better able to think their way to a solution.
        
      • Another good question - have you solved a problem like this before? If so, how is this problem the same/different?
        
      • We also encourage students to talk to their peers about problems that are perplexing to them. Peer support provides encouragement and a different perspective, both of which can be useful when puzzling through a tough problem. While GATE employs this strategy in math class, some students who have a greater need for verbal processing may benefit from additional math support outside of GATE. Ms. H and Ms. S both offer after school study halls/tutoring that could be great for these types of kiddos!
        
    • At GATE the overall goal is to aid the math student in thinking through their problem. Applying past knowledge and utilizing intuition and creative thinking are all critical in math. Plus, thinking critically is much more fun compared to drilling for rote memorization!
      
    • In an interview in Quanta magazine, mathematician David Bessis explains that becoming a great mathematician hinges on the willingness to constantly question and refine intuitions. The concept of refining intuitions as they relate to math is so interesting! Embracing instinct over logic when solving a problem could uncover a novel path, one that you may not find under the constraints of pure logic. Bessis says that math requires “tapping into a childlike state and embracing one’s imagination, including the mistakes that come with it.” This is inquiry-based learning with a growth mindset - a powerful combination!
      
    • The AoPS/Beast Academy curriculum is a great facilitator of inquiry-based learning in math. The curriculum focuses on deep conceptual understanding and the students learn advanced problem solving skills. This helps students practice critical thinking and develop resilience in the face of challenging problems.
      
    • What does GATE do for kids that are not enthusiastic about math and/or have a hard time pacing themselves?
      
      • GATE is not a pressure cooker school. We do not place pressure on the kids to complete a specific math book by a certain time. However, some kids may not be as internally motivated to work to their potential in terms of pacing.
        • In our experience, this usually happens for three reasons. 1) Lack of the executive functioning skills required for self-pace, 2) Low math confidence, 3) Need for verbal processing (as described above).
        • Giving the kids agency in their math progress helps tremendously. This looks like:
          • Helping the kids set goals.
          • Teaching them to advocate for themselves and receive the help they need in class.
          • Setting timers for kids that have the propensity to perseverate on problems.

Grade scales at GATE

• Our GATE progress reports are coded in three colors, green, yellow, and red. Green signifies an above average performance in the A to B range.
• In the 7th and 8th grade students receive actual letter graded transcripts.
• If your student is receiving green checks you can expect them to earn As or Bs on their transcripts.
• Our As and Bs do not translate to grading in traditional school settings, all of our students are accelerated.
  • Most Bay Area schools are familiar with GATE and its accelerated, rigorous curriculum. This is also reflected in our letters of recommendation where the rigor of our curriculum is explained for admissions staff. Schools call me to learn more about our program if they are not familiar with GATE.

What math should my child do in high school? Do they have to take Calculus?

• Don't worry if they do not take Calculus in high school! They will likely have to take Calculus again in college anyway!
• Kids starting Algebra 1 in I5 of their 7th grade year should have no problem completing the required curriculum before GATE graduation.
  • Remember, the AoPS curriculum is much more rigorous compared to traditional math programs.
  • Several of the chapters in the AoPS advanced math books (algebra, geometry) have concepts that are not covered in high school and are therefore not on the placement tests.
    • Therefore, it is not imperative that GATE students finish the entire book.
• Please do not worry if your child does not finish pre-algebra, algebra, or geometry before graduating from GATE. Your student has received a solid foundation in math from Beast Academy, they are very prepared to take on the appropriate level of high school math!

What to do with kids that have an insatiable appetite for math?

• Let them daydream and play with math! These two articles are great stories about how amazing math discoveries can be made when ordinary people allow themselves to play with and ponder shapes.
  
• Play games with them! I found this website with a bunch of math games that you can play with your kids at home. Also, a GATE parent shared a card game with us that he used to help his kids learn multiplication tables. Set up a stack of cards and have the kids turn cards over two at a time and yell out the product of the number of the two cards. Time your kids as they do this and they can play again and again while trying to best their previous times.
  
• This site, developed by Stanford mathematics professor Jo Boaler, has a lot of fun math activities, many centered around data science.
  
• Help your student come up with a math project. Two years ago we had a student that was interested in answering impossible questions proposed by other GATE Academy students for his Heart’s Desire Project. One question was “How many pennies (assuming pre-1982 for simplicity) would you need to cover the entire surface area of the sun with copper, and therefore make sunlight invisible to humans on earth?” You can see how a question like this can lead to many lines of inquiry. Simple questions like, "what is the surface area of a penny?" quickly lead to questions like, "how many pennies would the US need to mint in order to achieve this feat?" or "how many lumens of light actually reach the earth from the sun?" and "will a penny block the light or will the heat generated from the pennies transmit its own light?" The questions are endless - this is inquiry!