Do the standards require Algebra 2?

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.

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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.

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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.

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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.

 

Have the Standards Been Implemented w/ Fidelity?

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!

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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.

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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.

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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).

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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!

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

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.

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.

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.

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

What to use for a math intervention?

This has been a really popular question lately as we are well into the school year. What to use for a math intervention? Sometimes educators are looking for a strategy, sometimes a process and sometimes a thing.  I always assure them that if there was a “magic” mathematics anything, I would know about it and be sure to tell them but there isn’t. There are some better rabbit holes for us to go down as we try to find what helps our students learn mathematics and what educators can use to help students “get it,” or get “caught up.” Let us just agree, that those terms in quotes are ambiguous at best.  In  this blog I am going to help you find  a few rabbit holes you may want to explore.

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In previous blogs, I have shared about Number Sense and Learning Trajectories.  I first learned of Learning Trajectories directly from Doug Clements at math SCASS (Math State Collaborative on Assessment and Student Standards), which is the mechanism nationally or how people who have my job get “smart” together about the good stuff to bring back to our individual states. It is put on by CCSSO (Council of Chief State Officers). The same group that brought us the mathematics standards.

Anyways, I didn’t “get it.”  It wasn’t that Doug did a bad job of teaching me, it was  because I had a secondary mathematics background and I didn’t know what I didn’t know.  Which the experience made me realize, I do not know what I need to know about K-5 mathematics. I needed to get “smart” about K-5 mathematics and quick. So I asked some of the AEA consultants, how do I get smart about what I need to know about K-5, and they said take Number Sense from Christina Tondevold.

After taking the Number Sense training, then and only then did I “get it.” Eureka, I understood that I had not had Number Sense myself!  No wonder I didn’t understand the Learning Trajectories I didn’t even understand the 4 early Number Concepts and the 4 Number Relationships (subitizing, verbal counting, object counting, cardinality, spatial relations, 1/2 more/less, benchmarks of 5 & 10, part-part-whole.)  This was the reason that I didn’t understand the Learning Trajectories and how to use them to help students.  But by connecting the  Number Sense learning with the research based Learning Trajectories activities, I realized how powerful they could be to use with students.

This brings us to the topic at hand. Can they be used as a math intervention? An intervention is a combination of program elements or strategies designed to produce behavior changes or improve health status among individuals or an entire population. Educators learning more about Number Sense  and then using Learning Trajectories, to give students experiences to increase their Number Sense  along research based Learning Trajectories could help teachers take students from where they are at to where we want them to be more quickly than perhaps what we are currently doing.

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Example: A student still counting on their fingers may need more subitizing. (I know this because I understand the information in Number Sense .)  I know I need to give the student experiences so I go to the Learning Trajectories and select subitizing and I can get close to where I think the student is at and then work them forward along the subitizing trajectory.  See the screencast here.

A few last tidbits. Number Sense is closing for purchasing individual accounts on October 28, 2019 and will not re-open for a year. Schools purchasing multiple accounts can do so at any time.  The Learning Trajectories are open sourced and you just have to create an account.  I encourage you to watch the video  snippets.  Lastly, for those who are looking for Learning Trajectories more bells and whistle or sophistication in computer program, diagnostics, intervention, be sure to check out Building Blocks or Number Worlds which packages the work of the Learning Trajectories.

I share this information as a potential rabbit hole that you may want to explore. Will we do a better teaching and learning with increase Number Sense ? Yes.  Will we have researched based activities to use with students if we use Learning Trajectories ? Yes. Could this help teachers love to teach math, help students love learning math and help them learn more math? You be the judge. Let me know your thoughts in the comments.

 

How to count HS mathematics?

I receive several questions about how to count high school mathematics.  Years, courses, standards, etc.  Students need three years of mathematics and all of the standards. In Iowa, we have local control which means high schools can decide how to “bundle” standards into courses.  Which can be confusing to count.  We know counting matters.  So, let’s think about counting in regards to standards.

Again, how schools bundle the mathematics standards is up to them in high school.  The mathematics standards do not designate specific courses.  If you count the high school mathematics standards, you will find there are over 150 of them.  For simplicity, we will just say 150 standards.  Next, I am going to say something that will surprise many – the number of the high school mathematics standards does not matter.  That’s right – it does not matter how many there are.

 

This is because, they are not the same things or the same size. Just like the ducks and pizzas. They cannot be counted together because they are not the same.  What I mean by this, is the fact that there are 150 standards means just that, there are 150 standards.  Some of them are big and some of them are smaller.  If most of them are small, then they do not amount to very much.  But we all know that even if they are all small, there is still a lot of high school mathematics content so we must have Focus which is usually missed in implementing the standards.  (I explain this further below.)

The bigger question I get asked is about counting courses of different length that contains the same number of standards.  So, let’s do some math.  If all students have to take three years of mathematics and all students need all of the standards, then most would say, it would be a good idea to divide them into three equal parts and handle it that way.  But when if we take the standards and divide them into 1/3’s and stretch that over two years, that still leaves 2/3’s of the standards to fit into the last year. Which does not seem feasible because if it takes me two years to get through 1/3 of the standards, then getting through (hopefully learning) 2/3’s of the standards in half the time seems like it would not work.

How is this all supposed to work?  It comes down to Focus.

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All standards for all students bundled in a way that that honors the “importance,” the “weighting,” or the Focus of the standards.  Since high school was structured differently than K-8, then many miss the Focus Documents for high school.  To say it another way, most of the time in high school mathematics should be spent on the standards that matter the most to prepare students for the futures they want.  Take a look at the Focus Documents, notice that it doesn’t say we are skipping any standards.  It says, spend most of the time on algebra and functions because if student can solve some things and graph some things, it will serve them well.  Perhaps an algebra heavy geometry would be the right path for some students.

When students do not get an opportunity to learn all of the standards, are “we” becoming the deciding factor for their future? Is this an access and equity issue? Are students belonging to a certain sub-group more likely to end up not getting all the standards? Is this contributing to the achievement gap? Are we able to predict which students will not get access to all of the standards?  What are the solutions besides not giving students access?

Lastly, the (+) are the additional standards and are not intended for all students.

Let me know your thoughts and questions.