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Geneva 304 Elementary Math Frequently Asked Questions

What are the Illinois Learning Standards?
The Illinois Learning Standards are designed to ensure that students graduating from high school are prepared to enter credit bearing entry courses in two or four year college programs or enter the workforce. The standards are clear and concise to ensure that parents, teachers, and students have a deeper understanding of the expectations in reading, writing, speaking and listening, language and mathematics in school.
 
What makes the Illinois Learning Standards different than previous standards? 
In simple terms, the Illinois Learning Standards represent a shift from computational to conceptual, and are constructed upon the three foundational notions of: Focus, Coherence, and Rigor. A brief overview of these concepts and how they differ from previous standards follows.
  • FOCUS
    A typical critique of contemporary American math curricula is that it is ‘a mile wide and an inch deep’. Traditional math curricula followed a ‘scaffold-ed’ approach whereby many subjects were repeatedly touched-on over the course of a student’s academic career. In such a scenario many educators and parents found that their students were never provided with an opportunity to gain deep, meaningful understanding of a particular topic. The focused approach of the Illinois Learning Standards addresses this challenge by introducing fewer topics per year and providing students with extensive opportunities to engage meaningfully with those topics.

  • COHERENCE
    The ‘mile wide inch deep’ phenomenon is further addressed in the Illinios Learning Standards by the concept of coherence. In traditional math curricula, not only were many subjects taught in all grades but there was often no rhyme or reason to the order in which such subjects were introduced and taught. Thus a third grade math book may have started with geometry, shifted to telling time, and transitioned into multiplication facts. The Illinois Learning Standards are purposefully constructed to ensure that current learning is much more coherently connected to previous learning.

  • RIGOR
    As noted above, prior to the adoption of the Illinois Learning Standards more traditional math curricula was constructed around the concept of computational accuracy. Students were taught mathematical formulas, or algorithms, as the primary means of solving problems and then expected to ‘plug and chug’ to find the correct answer. The rigor of the standards calls for students to acquire deep conceptual understanding of concepts like addition or division before learning the traditional formula. 
Will students learn how to do addition, subtraction, multiplication, or division ‘the old way’?
In fancy math speak, ‘the old way’ is known as ‘the traditional algorithm’. An algorithm is a structure or formula that is used to compute a given problem and yes, in this approach to mathematics instruction the traditional algorithms that we were taught as children are still taught to students. However, in many cases the traditional algorithms have been shifted to later grades to provide students with extensive opportunities to gain deeper understanding of the concepts before the ‘short cut’ of the algorithm is taught.
 
I’ve heard that in the Illinois Learning Standards students are not required to find the correct answer. Is this true? 
No this is not true, and in fact, quite the opposite. The Illinois Learning Standards are constructed upon 8 Mathematical Practices that provide a foundation for deep and meaningful understanding of math concepts. One of those practices, Attending to Precision, emphasizes the discrete, explicit nature of math and requires that students take care to focus on their work and be precise in solving problems. While we hope that the deep conceptual understanding that lies at the heart of the Illinois Learning Standards provides students with the tools to discover multiple ways to solve a problem, it is important to recognize that it is the approaches that can differ, not the answers.
 
Will students still be required to learn their ‘math facts’?
Yes, as noted above, the Illinois Learning Standards provide a more focused, coherent, and rigorous approach to math and are constructed around 8 important Mathematical Practices. Such an approach requires that students are able to focus on a complex problem and not need to ‘step out of a problem’ to compute basic facts. In other words, memorization of facts is important in that it allows students to focus their mental energy on deeper conceptual meaning of mathematics. The critical difference in this approach is that students will be taught multiple strategies to use in learning the facts before they are expected to memorize them.
 
What can I do at home to support the Illinois Learning Standards? 
First and foremost, support and encourage your children and their teachers as they work to increase their already impressive skills in new and exciting ways. In addition, it is important to help our kids know that struggling through a challenging problem is often the best way to grow as a learner. Shortcuts are great if you truly understand the underlying principles, but shortcuts can also inhibit more meaningful understanding. To that end, encourage your children to explain how they determined their answers, ask them questions about the concepts they are learning, and challenge them to find different ways to solve complex problems. Furthermore, try to bring math authentically into your conversations of daily life, as when you are paying your bill at the grocery store. The more authentic interactions our children have with numbers and math, the stronger their conceptual understanding will be.
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