In my recent posts, I addressed the topics:

• Do the standards require Algebra 2?
• What can we do for HS students who are not “ready?”

Some educators may think I am in or not in favor of all students taking Algebra 2.  Disclaimer: Algebra 2 is being used to represents a third year HS course of HS standards that are not previously covered in the course sequence. This could also could be Integrated 3.

Before we get to that, lets first consider some “facts” that most educators will agree with.

• More mathematical understanding will not harm students.
• The rate of change of the world is greater than today than any other time in history.
• Students will not need less mathematical understanding for tomorrow’s world than they need for today’s world.
• There is a correlation between the level of mathematical understanding and the amount of money a person may make in a life time.
• To truly prepare students for post-secondary success (knowing many will need to re-train), mathematical understanding should not be a barrier.
• Mathematical understanding is acting like a filter to students out of careers they are interested in.
• The number of STEM careers are increasing and mathematical understanding should act like a pump for interested students into these careers.
• There is a correlation between the number of remedial mathematics courses and if a person will finish their program or degree.

We know some things about the current system:

• It is designed to filter students out who do not have a mathematical understanding of algebra.
• A student’s understanding of numbers impacts their ability to access and develop algebra understanding.
• In many districts, the “top” level achievers or two of students are removed from the grade level mathematics instruction and placed in accelerated tracks.
• The freshman level math course contains students who have previously failed the course and students who are not “top” level achievers.
• Many students passing freshman mathematics take remedial mathematics post-secondary.
• Freshman level mathematics course has one of the highest failure rates.

So, let us get back to the question at hand. Should all students take Algebra 2?  Yes!

Here is why:

• Students who take Algebra 2 will have more access to mathematics instruction than students who do not.
• Algebra 2 reviews Algebra 1 concepts by applying them to more rigorous content.
• Students are two years older and there is a big difference between a freshman and a junior.
• Algebra skills are not post-secondary developed after Algebra 1.
• A second chance at Algebra will only decrease the number of remedial courses a student will take post-secondary which increases my chances of success.
• No one really knows what the future looks like and how much mathematics will be needed, what jobs will be, etc.

Finally, what is a better alternative or evidence that there is one yet?

I am often asked, “What can we do for high school students who are not “ready?”  I think the question educators are trying to ask is “What can we do when students have unfinished learning?”  This, is a great question because we know this may impact a students’ ability to access the mathematics learning at high levels.  I think the bigger question is, “What can we do when students have unfinished learning so students can have access to mathematics learning at high levels?”

Remember: The point of the first Shift of Focus is to spend the majority of time on the most important high school content to increase college and career readiness.

We can use the HS Focus document to focus instructional time on the especially and relatively important high school content and widely applicable prerequisite for a range of college majors, postsecondary programs and careers.  The focused instructional time can be used to provide scaffolding to increase access to mathematics learning at high levels.  This does not change the content or duration of a high school course. It redistributes the instructional time to focus on the especially and relatively important high school content.  This shifts the content coverage to an inch-wide and a mile-deep approach.

Below are tips to help implement Focus at the high school level.

Increase these:

1. Access to high school mathematics standards *
2. Focusing on the especially and relatively important high school domains, clusters, and standards
3. Problem solving and communicating reasoning focused on widely applicable prerequisites
4. Access to the teachers with the most experience or perceived to be most-effective
5. Scaffolding instruction

Decrease these:

1. Below grade level mathematics standards *
2. Covering the standards in a “checklist” approach lacking focus
3. Problem solving and communicating reasoning applied to complex high school content
4. Access to the least experience or perceived to be least-effective
5. Stretching content over two years for the sake of slowing it down

What about data science, statistics and probability? While I agree, these are highly applicable and relevant content and courses, they are just not the current gatekeeper contents, it’s algebra.  We cannot replace algebra content courses with non-algebra content and hope to increase the college and career readiness for our students.

What about an equivalent course to algebra 2?  Schools are able to place the standards (content) in the high school course as they locally determine. Content is content.  Especially and relatively important high school domains, clusters, and standards emphasis can be differentiated within a course to locally meet the needs of students as well as teaching approach such as a discrete vs integrated approach.  The student learning is the desired outcome.  The only guidance about time we are given in the high school standards is to spend the majority of time on the most important content.

It is often tempting to lower the expectations for students with unfinished learning because we want to put them on a certain career “pathway.”  I hear it all the time, “but “these” students can’t or they are never going to…”  However, this approach and mind-set does not increase their college and career readiness. We do not know what a students’ future holds or what the world will look like in 10, 20 or 30 years.  Many of our students will have to re-train at some point and we do not mathematics to be the barrier.

I know first-hand what this looks, I was one of “those students.” I began my life in a foster home, was returned to a teenage mom, labeled “at-risk,” had chronic absenteeism (47 days my 7^th grade year), put in short-hand and typing classes in hopes I would at least be employable as a secretary. And I was never denied access to mathematics learning at high levels?

While I never used the shorthand, I have found the typing classes to be most helpful in my current role, which no one would have ever predicted for me. But I joined the military for six years, had access to options like education and basic needs, found my inner strength and self-esteem, and now hold a bachelor of science in mathematics.

It was because I had access to “mathematics learning at high levels” in school that mathematics was not a barrier when I returned back to school. I went to school in New York under the Regents program and had access to mathematics learning at high levels”  We should not judge a students’ exit from our schools by their entrance into our schools.

Schools should refrain from student tracking, teacher tracking, and ensure students have access to mathematics learning at high levels.  We want to equip our students with the high school content they will need to pursue their dreams without their K-12 mathematics learning being a barrier that keeps them from realizing their fullest potential.  Want to make a difference in the life of a student in poverty, give them access to mathematics learning at high levels.  Mathematics learning at high levels allowed me to leave a life of generational poverty. Don’t we want that to be the story for all of our students in Iowa?

In my next blog, I will connect this topic to the 2nd Shift of Coherence and share resources, tools and strategies that can be used.

* the mathematics standards contain additional standards denoted by (+) and are not intended for all students.

This is likely the question I receive the most.  According to the Iowa Core Mathematics Standards and Standards for Mathematical Practice, there is not a mention of a required Algebra 2 course, or any other high school course for that matter.  Yet, we are talking about this topic more than ever in Iowa and across the country.  I think this is the wrong question. Instead, I am suggesting we reframe the question and ask, “What is required for College and Career Readiness in mathematics.”  In this blog post, I am going to attempt to answer this question.  Disclaimer: Capitalization and other notation may be used grammatically wrong for emphasis.

The Iowa Core Mathematics Standards and Standards for Mathematical Practice are intended to be ALL standards for ALL students. When we look at the high school standards, some standards have (+)s and these are NOT for all students.  The high school standards are sorted by Domains such as Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability.  Domains are further broken down by Clusters and they may contain one or many standards.  The standards were not intended to create courses or specific approaches such as Algebra 1, Geometry, and Algebra 2 or Integrated. It was the intention to give ACCESS to All students to learn high school mathematics when they are in high school each and every year.

It is up to schools locally to create courses, pathways, etc. This flexibility helps schools promote ACCESS for ALL without lowering expectations and while meeting the needs of students.  This is known as the first Shift for Mathematics, Focus.  Focus means where we are going to spend the majority of our instructional time.  It takes the approach of a mile wide and an inch deep of the past and translates it to the inch wide and mile deep focusing time on the most critical content.

How much instructional time? Up to 85% on the content highlighted in the Focus documents and 15%  for the rest of the standards.

What domain, cluster and standards? We can use the High School Focus document by Student Achievement Partners, www.achievethecore.org, provides guidance distinguishing between especially important, relatively important and widely applicable. For more on Focus, please see Iowa Math Chats

• Number and Quantity: N-RN, Real Numbers:
  • Both clusters in this domain contain widely applicable prerequisites.
  • N-Q, Quantities: Every standard in this domain is a widely applicable prerequisite.
  • Note, this domain is especially important in the high school content standards overall as a widely applicable prerequisite.
• Algebra: Every domain in this category contains widely applicable prerequisites.
  • Note, the A-SSE domain is especially important in the high school content standards overall as a widely applicable prerequisite.
• Functions: F-IF, Interpreting Functions:
  • Every cluster in this domain contains widely applicable prerequisites.
  • Additionally, standards F-BF.1 and F-LE.1 are relatively important within this category as widely applicable prerequisites.
• Geometry: 
  • The following standards and clusters are relatively important within this category as widely applicable prerequisites: G-CO.1 G-CO.9 G-CO.10 G-SRT.B G-SRT.C
  • Note, the above standards in turn have learning prerequisites within the Geometry category, including: G-CO.A G-CO.B G-SRT.A
• Statistics and Probability: 
  • The following standards are relatively important within this category as widely applicable prerequisites: S-ID.2 S-ID.7 S-IC.1
  • Note, the above standards in turn have learning prerequisites within 6-8. SP.
• Applying Key Takeaways from Grades 6–8**: Solving problems at a level of sophistication appropriate to high school by:
  • Applying ratios and proportional relationships.
  • Applying percentages and unit conversions, e.g., in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3 , acre-feet, etc.).
  • Applying basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.
  • Applying concepts and skills of geometric measurement e.g., when analyzing a diagram or schematic.
  • Applying concepts and skills of basic statistics and probability (see 6-8.SP). ·
  • Performing rational number arithmetic fluently.

This means there is flexibility so ALL students can have access to the high school mathematics instruction they need. Some students may need more time on especially important, relatively important and widely applicable standards and practices. Some students may need up to 85% of instructional time focused on number and algebra (at the high school level) instead of spending large amounts of times on other standards that are not as important for their college and career readiness.

We want our students to be able to pursue their dreams without mathematics being a barrier.  We know the fewer remedial mathematics courses they take post-secondary, then the more likely it seems they are to persevere with completing programs and degrees. The world we live in becomes more technical each and every day whether in engineering, health care, farming, mechanics, etc., or the military.   Mathematics needs to be the pump into options for our students and not the filter.  We need to remember that it is NOT about courses but about learning.  Learning that will better prepare our students for their future, whatever they may choose.

The main role I have is to help educators in Iowa implement the mathematics standards with fidelity.  It seems like it should be an easy task but it is not. There is so much information out there to sort through, it is hard to know what is the best information to use for where you may be at.   Plus, as educators, we are not all in the same place so what is right for one may not be right for another, whew!

I have thought a great deal over the last few years and wondered how I could help Iowa educators to have access to the information that they may find useful. And how do I make all of the information that I have access to accessible to Iowa educators.  So, I have come up with all but an original idea to “knowledge transfer” what I have access to to others. Iowa Math Chats – 5 minute video chats where I share everything I know about a topic.  I have wanted to do it for a while and finally I just went for it.

These Iowa Math Chats are designed for IOWA mathematics educators of any type. I say this because the context is for Iowa and where the work and conversation is. If you are in another state, most of the information is still helpful but know that it was designed for Iowans.

The first series is a series of what ALL educators need to understand about the 1st Shift of FOCUS. You can read more about all three SHIFTS here. BUT if you don’t have FOCUS  then it is really super difficult to have any  of the other SHIFTS and the Standards of Mathematical Practices. (Capitals are being used intentionally to show emphasis).

Why these topics on FOCUS? These topics are the most misunderstood when I talk to educators.  Here is why:

1. Many try to implement the standards without paying attention to the Clusters – Clusters – Super Important!

• Math Standards – I explain about Domains, Clusters, and Standards and why Clusters are so important! Focus Documents

2. If the different types of Clusters are not tended to – then the grade level proficiencies will not happen.

• Focus Documents (Part 1) Clusters – I explain about the different types of clusters in the math standards and why it matters to instruction and learning. Focus Documents

3. If we keep acting like this is new math – the standards are exactly the same math we have always had –  that was the point of the standards – to get rid of all the pneumonics and tricks!! No more “butterfly” math.

• Focus Documents (Part 2) Clusters & College & Career Readiness (CCR) – I explain what the non-negotiable mathematics is for Iowa students to be CCR.
  Bonus – I DEBUNK the MYTH it is “NEW MATH!” Focus Documents

4. The Fluencies and the major Clusters make up the Major Work of the Grade – where we should be spending up to 85% of our instructional time on.

• Focus Documents (Part 3) How the Fluencies and Grade Clusters Connect to Lead to the Major Work of the Grade – I explain how the Fluencies and Clusters Connect to the Major Work of the Grade! Focus Documents

5. There are Major Clusters that are a priority and the number of standards vary – prioritizing standards could lead to prioritizing only part of the standards that need to work together in a Cluster and lead to non-proficiency.

• Focus Documents (Part 4) Priority Standards and the Iowa Core Math Standards –  I explain the “priority” standards for K-8 mathematics. Focus Documents

Stay tuned for the next series on Coherence! This information is also available on Facebook. Remember to subscribe so you get updates.