Thank you. I'm happy to provide a little more color, and please feel free to ask me if you have additional follow up questions.
*direct instruction vs. inquiry
Please see the instructional hierarchy diagram - EI in Step #1, inquiry in Step #s 3/4.
I deliberately use the term "explicit instruction" instead of direct instruction. The National Math Advisory Panel stated the following: "By the term explicit instruction, the Panel means that teachers provide clear models for solving a problem type using an array of examples, that students receive extensive practice in use of newly learned strategies and skills, that students are provided with opportunities to think aloud (i.e., talk through the decisions they make and the steps they take), and that students are provided with extensive feedback."
*disadvantaged vs. non-disadvantaged
In ed policy, disadvantaged demographics typically refer to students from low-income families, those with lower parental education levels, single-parent households, Students with Disabilities (SWDs), English language learners (ELs), or students from underrepresented minority groups who often face larger opportunity gaps.
I would argue that any grade-level elementary school that does full SWD inclusion and EL inclusion will likely have a not insignificant amount of disadvantaged students by default.
*early-stage vs. late-stage inquiry
I think this webpage explains it the best, citing Paul Kirschner and Carl Hendrick:
"Deciding whether a student needs explicit instruction or inquiry-based instruction depends on where the student lies on the novice-to-expert continuum for a particular concept or skill. Learners who are in the process of developing foundational knowledge greatly benefit from explicit instruction as their minds concentrate on absorbing and structuring new information. This group includes both students who have faced difficulties in mathematics and those who are exploring these concepts and skills for the first time. Techniques like clear explanations, step-by-step instruction, and worked examples help reduce cognitive load, enabling them to process and retain core concepts (Kirschner & Hendrick, 2024).
On the other hand, learners who have already developed a strong understanding of the subject thrive with inquiry-based instruction. Their brains are primed for deeper exploration, creative problem-solving, and connecting ideas in meaningful ways (Kirschner & Hendrick, 2024)."
I appreciated your cogent analysis, but it seems to conflate three dimensions at once:
* direct instruction vs Inquiry
* disadvantaged vs “normal”
* early stage vs late-stage inquiry.
Could you please entangle them for us?
Thank you :-)
Thank you. I'm happy to provide a little more color, and please feel free to ask me if you have additional follow up questions.
*direct instruction vs. inquiry
Please see the instructional hierarchy diagram - EI in Step #1, inquiry in Step #s 3/4.
I deliberately use the term "explicit instruction" instead of direct instruction. The National Math Advisory Panel stated the following: "By the term explicit instruction, the Panel means that teachers provide clear models for solving a problem type using an array of examples, that students receive extensive practice in use of newly learned strategies and skills, that students are provided with opportunities to think aloud (i.e., talk through the decisions they make and the steps they take), and that students are provided with extensive feedback."
*disadvantaged vs. non-disadvantaged
In ed policy, disadvantaged demographics typically refer to students from low-income families, those with lower parental education levels, single-parent households, Students with Disabilities (SWDs), English language learners (ELs), or students from underrepresented minority groups who often face larger opportunity gaps.
I would argue that any grade-level elementary school that does full SWD inclusion and EL inclusion will likely have a not insignificant amount of disadvantaged students by default.
*early-stage vs. late-stage inquiry
I think this webpage explains it the best, citing Paul Kirschner and Carl Hendrick:
https://www.ldatschool.ca/an-introduction-to-the-science-of-math/
"Deciding whether a student needs explicit instruction or inquiry-based instruction depends on where the student lies on the novice-to-expert continuum for a particular concept or skill. Learners who are in the process of developing foundational knowledge greatly benefit from explicit instruction as their minds concentrate on absorbing and structuring new information. This group includes both students who have faced difficulties in mathematics and those who are exploring these concepts and skills for the first time. Techniques like clear explanations, step-by-step instruction, and worked examples help reduce cognitive load, enabling them to process and retain core concepts (Kirschner & Hendrick, 2024).
On the other hand, learners who have already developed a strong understanding of the subject thrive with inquiry-based instruction. Their brains are primed for deeper exploration, creative problem-solving, and connecting ideas in meaningful ways (Kirschner & Hendrick, 2024)."
Much appreciated, thank you.