diff --git a/packages/doenetml-worker/src/components/MathInput.js b/packages/doenetml-worker/src/components/MathInput.js
index a7bec2a08..77e592ed0 100644
--- a/packages/doenetml-worker/src/components/MathInput.js
+++ b/packages/doenetml-worker/src/components/MathInput.js
@@ -147,6 +147,7 @@ export default class MathInput extends Input {
         sugarInstructions.push({
             replacementFunction: returnWrapNonLabelsSugarFunction({
                 wrappingComponentType: "math",
+                wrapSingleIfNotWrappingComponentType: true,
             }),
         });
 
diff --git a/packages/doenetml-worker/src/components/MathList.js b/packages/doenetml-worker/src/components/MathList.js
index b17691e2e..65ce2e8f0 100644
--- a/packages/doenetml-worker/src/components/MathList.js
+++ b/packages/doenetml-worker/src/components/MathList.js
@@ -277,7 +277,6 @@ export default class MathList extends CompositeComponent {
         };
 
         stateVariableDefinitions.maths = {
-            public: true,
             shadowingInstructions: {
                 createComponentOfType: "math",
             },
diff --git a/packages/doenetml-worker/src/components/Text.js b/packages/doenetml-worker/src/components/Text.js
index 8ec308677..bc1e9908d 100644
--- a/packages/doenetml-worker/src/components/Text.js
+++ b/packages/doenetml-worker/src/components/Text.js
@@ -169,9 +169,48 @@ export default class Text extends InlineComponent {
                 dependencyValues,
             }) {
                 let numChildren = dependencyValues.textLikeChildren.length;
+
                 if (numChildren > 1) {
+                    // if have multiple children, then we could still update them if
+                    // 1. all children come from a single composite with asList set to true, and
+                    // 2. the desired value is a comma-separated list with the number of entries
+                    //    matching the number of children.
+                    // In that case, we will attempt to update each child to the corresponding entry
+                    // from the desired value.
+
+                    // Check if all text children are from a composite with asList set to true
+                    let foundAllFromListComposite = false;
+                    for (let range of dependencyValues.textLikeChildren
+                        .compositeReplacementRange) {
+                        if (
+                            range.asList &&
+                            range.firstInd === 0 &&
+                            range.lastInd === numChildren - 1
+                        ) {
+                            foundAllFromListComposite = true;
+                        }
+                    }
+
+                    if (foundAllFromListComposite) {
+                        // Check if desired value is a comma-separated list with the same number of entries as children
+                        let splitValues = desiredStateVariableValues.value
+                            .split(",")
+                            .map((v) => v.trim());
+
+                        if (splitValues.length === numChildren) {
+                            // All conditions are met, so we attempt to update the children
+                            let instructions = splitValues.map((v, i) => ({
+                                setDependency: "textLikeChildren",
+                                desiredValue: v,
+                                childIndex: i,
+                                variableIndex: 0,
+                            }));
+                            return { success: true, instructions };
+                        }
+                    }
                     return { success: false };
                 }
+
                 if (numChildren === 1) {
                     return {
                         success: true,
diff --git a/packages/doenetml-worker/src/components/TextInput.js b/packages/doenetml-worker/src/components/TextInput.js
index bd2c4b624..8f801059e 100644
--- a/packages/doenetml-worker/src/components/TextInput.js
+++ b/packages/doenetml-worker/src/components/TextInput.js
@@ -101,6 +101,7 @@ export default class Textinput extends Input {
         sugarInstructions.push({
             replacementFunction: returnWrapNonLabelsSugarFunction({
                 wrappingComponentType: "text",
+                wrapSingleIfNotWrappingComponentType: true,
             }),
         });
 
diff --git a/packages/doenetml-worker/src/test/tagSpecific/boolean.test.ts b/packages/doenetml-worker/src/test/tagSpecific/boolean.test.ts
index 549a14acd..26188e1e2 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/boolean.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/boolean.test.ts
@@ -1009,7 +1009,7 @@ describe("Boolean tag tests", async () => {
                 isSupersetCaseInsensitive: false,
             },
             {
-                set1: "<extract prop='listItems'><text>a, c</text></extract>",
+                set1: "<extract prop='list'><text>a, c</text></extract>",
                 set2: "<sequence type='letters' from='a' to='e' step='2' />",
                 isSubset: true,
                 isSubsetCaseInsensitive: true,
diff --git a/packages/doenetml-worker/src/test/tagSpecific/callAction.test.ts b/packages/doenetml-worker/src/test/tagSpecific/callAction.test.ts
index 924bec46a..4d6910e7d 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/callAction.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/callAction.test.ts
@@ -5,7 +5,6 @@ import {
     updateBooleanInputValue,
     updateMathInputValue,
 } from "../utils/actions";
-import me from "math-expressions";
 
 const Mock = vi.fn();
 vi.stubGlobal("postMessage", Mock);
@@ -18,7 +17,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let [ind, num] of numbers.entries()) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -42,7 +41,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -54,7 +53,7 @@ describe("callAction tag tests", async () => {
     it("resample random numbers", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" >
       <label>roll dice</label>
     </callAction></p>
@@ -373,7 +372,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -424,7 +423,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -436,7 +435,7 @@ describe("callAction tag tests", async () => {
     it("chained actions", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" >
       <label>roll dice and add point</label>
     </callAction></p>
@@ -461,7 +460,7 @@ describe("callAction tag tests", async () => {
     it("chained actions, unnecessary $", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" >
       <label>roll dice and add point</label>
     </callAction></p>
@@ -488,7 +487,7 @@ describe("callAction tag tests", async () => {
             doenetML: `
     <map assignNames="set1 set2">
     <template newNamespace>
-      <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+      <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
       <p><callAction target="s" actionName="resample" name="rs" >
         <label>roll dice and add point</label>
       </callAction></p>
@@ -525,7 +524,7 @@ describe("callAction tag tests", async () => {
             let numbers = stateVariables[`/set${ind}/nums`].stateValues.text
                 .split(",")
                 .map(Number);
-            expect(numbers.length).eq(5);
+            expect(numbers.length).eq(7);
             for (let num of numbers) {
                 expect(Number.isInteger(num)).be.true;
                 expect(num).gte(1);
@@ -579,7 +578,7 @@ describe("callAction tag tests", async () => {
                 .split(",")
                 .map(Number);
 
-            expect(numbers2.length).eq(5);
+            expect(numbers2.length).eq(7);
             for (let num of numbers2) {
                 expect(Number.isInteger(num)).be.true;
                 expect(num).gte(1);
@@ -592,7 +591,7 @@ describe("callAction tag tests", async () => {
     it("chained actions on multiple sources", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" >
       <label>roll dice and add point</label>
     </callAction></p>
@@ -626,7 +625,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -679,7 +678,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -744,7 +743,7 @@ describe("callAction tag tests", async () => {
     </graph>
     $P.coords{assignNames="P2"}
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" triggerWhen="$(P.x)>0 and $(P.y)>0" >
       <label>roll dice</label>
     </callAction></p>
@@ -758,7 +757,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -822,7 +821,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -901,7 +900,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -936,7 +935,7 @@ describe("callAction tag tests", async () => {
     </graph>
     $P.coords{assignNames="P2"}
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" triggerWhenObjectsClicked="P" >
       <label>roll dice</label>
     </callAction></p>
@@ -950,7 +949,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -993,7 +992,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1032,7 +1031,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1068,7 +1067,7 @@ describe("callAction tag tests", async () => {
         <point name="P">(-1,2)</point>
       </graph>
       $P.coords{assignNames="P2"}
-      <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+      <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
       <p><callAction target="s" actionName="resample" name="rs" triggerWhenObjectsClicked="P" >
         <label>roll dice</label>
       </callAction></p>
@@ -1097,7 +1096,7 @@ describe("callAction tag tests", async () => {
             let numbers = stateVariables[numsName].stateValues.text
                 .split(",")
                 .map(Number);
-            expect(numbers.length).eq(5);
+            expect(numbers.length).eq(7);
             for (let num of numbers) {
                 expect(Number.isInteger(num)).be.true;
                 expect(num).gte(1);
@@ -1140,7 +1139,7 @@ describe("callAction tag tests", async () => {
                 .split(",")
                 .map(Number);
 
-            expect(numbers2.length).eq(5);
+            expect(numbers2.length).eq(7);
             for (let num of numbers2) {
                 expect(Number.isInteger(num)).be.true;
                 expect(num).gte(1);
@@ -1181,7 +1180,7 @@ describe("callAction tag tests", async () => {
                 .split(",")
                 .map(Number);
 
-            expect(numbers2.length).eq(5);
+            expect(numbers2.length).eq(7);
             for (let num of numbers2) {
                 expect(Number.isInteger(num)).be.true;
                 expect(num).gte(1);
@@ -1219,7 +1218,7 @@ describe("callAction tag tests", async () => {
     </graph>
     $P.coords{assignNames="P2"}
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" triggerWhenObjectsFocused="P" >
       <label>roll dice</label>
     </callAction></p>
@@ -1233,7 +1232,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1276,7 +1275,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1315,7 +1314,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1350,7 +1349,7 @@ describe("callAction tag tests", async () => {
     </graph>
     $P.coords{assignNames="P2"}
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs"  triggerWith="addPoint" >
       <label>roll dice and add point</label>
     </callAction></p>
@@ -1377,7 +1376,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1447,7 +1446,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1537,7 +1536,7 @@ describe("callAction tag tests", async () => {
             .split(",")
             .map(Number);
 
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1575,7 +1574,7 @@ describe("callAction tag tests", async () => {
 
     $P.coords{assignNames="P2"}
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs"  triggerWith="addPoint" triggerWhen="$(P.x)<0 and $(P.y)<0" >
       <label>roll dice and add point</label>
     </callAction></p>
@@ -1601,7 +1600,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1628,7 +1627,7 @@ describe("callAction tag tests", async () => {
         let numbers2 = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1719,7 +1718,7 @@ describe("callAction tag tests", async () => {
         numbers2 = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1800,7 +1799,7 @@ describe("callAction tag tests", async () => {
 
     <p>points from graph: <collect componentTypes="point" target="g" prop="coords" assignNames="p1 p2 p3" /></p>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet name="tset" >
       <label>perform actions</label>
@@ -1827,7 +1826,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1879,7 +1878,7 @@ describe("callAction tag tests", async () => {
         let numbers2 = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1897,7 +1896,7 @@ describe("callAction tag tests", async () => {
 
     <p>points from graph: <collect componentTypes="point" target="g" prop="coords" assignNames="p1 p2 p3" /></p>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <p>Enter x: <answer name="ans">x</answer></p>
 
@@ -1942,7 +1941,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -1994,7 +1993,7 @@ describe("callAction tag tests", async () => {
         let numbers2 = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -2009,7 +2008,7 @@ describe("callAction tag tests", async () => {
     it("chaining with updateValue", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" >
       <label>roll dice and more</label>
     </callAction></p>
@@ -2043,7 +2042,7 @@ describe("callAction tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -2096,7 +2095,7 @@ describe("callAction tag tests", async () => {
         let numbers2 = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers2.length).eq(5);
+        expect(numbers2.length).eq(7);
         for (let num of numbers2) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -2110,7 +2109,7 @@ describe("callAction tag tests", async () => {
     it("math in label", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="rs" ><label>Hi <m>\\sum_{i=1}^5x_i</m></label></callAction></p>
     `,
         });
@@ -2124,7 +2123,7 @@ describe("callAction tag tests", async () => {
     it("label is name", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="resample" name="resample_numbers" labelIsName /></p>
     `,
         });
@@ -2138,7 +2137,7 @@ describe("callAction tag tests", async () => {
     it("case insensitive action name", async () => {
         let core = await createTestCore({
             doenetML: `
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
     <p><callAction target="s" actionName="reSamplE" name="rs"><label>roll dice</label></callAction></p>
     <p>Sum: <number name="sum"><sum>
       <map>
diff --git a/packages/doenetml-worker/src/test/tagSpecific/mathlist.test.ts b/packages/doenetml-worker/src/test/tagSpecific/mathlist.test.ts
index 5b5549cd0..7c9f72eb9 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/mathlist.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/mathlist.test.ts
@@ -1589,4 +1589,45 @@ describe("MathList tag tests", async () => {
             "Latex: \\frac{x}{y}, a^{b}",
         );
     });
+
+    it("definition and inverse based on shadowed value from a mathList prop", async () => {
+        let core = await createTestCore({
+            doenetML: `
+
+    <matchesPattern excludeMatches="a b" name="mp" />
+
+    <p name="p">$mp.excludeMatches{assignNames="ml"}</p>
+
+    <mathInput name="mi">$mp.excludeMatches</mathInput>
+
+    `,
+        });
+
+        const stateVariables = await returnAllStateVariables(core);
+
+        let x1 = "a",
+            x2 = "b";
+        await test_mathList({
+            core,
+            name: "/ml",
+            maths: [x1, x2],
+            pName: "/p",
+            text: `${x1}, ${x2}`,
+        });
+
+        x1 = "c";
+        x2 = "d";
+        await updateMathInputValue({
+            latex: `${x1}, ${x2}`,
+            componentName: "/mi",
+            core,
+        });
+        await test_mathList({
+            core,
+            name: "/ml",
+            maths: [x1, x2],
+            pName: "/p",
+            text: `${x1}, ${x2}`,
+        });
+    });
 });
diff --git a/packages/doenetml-worker/src/test/tagSpecific/numberlist.test.ts b/packages/doenetml-worker/src/test/tagSpecific/numberlist.test.ts
index 6267a2de5..1303dcde9 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/numberlist.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/numberlist.test.ts
@@ -1,6 +1,9 @@
 import { describe, expect, it, vi } from "vitest";
 import { createTestCore, returnAllStateVariables } from "../utils/test-core";
-import { updateMathInputValue } from "../utils/actions";
+import {
+    updateBooleanInputValue,
+    updateMathInputValue,
+} from "../utils/actions";
 
 const Mock = vi.fn();
 vi.stubGlobal("postMessage", Mock);
@@ -17,7 +20,7 @@ describe("NumberList tag tests", async () => {
         name?: string;
         pName?: string;
         text?: string;
-        numbers?: any[];
+        numbers?: number[];
     }) {
         const stateVariables = await returnAllStateVariables(core);
 
@@ -517,6 +520,94 @@ describe("NumberList tag tests", async () => {
         await check_items(max1, max2);
     });
 
+    it("always merge math lists when have one math child", async () => {
+        let core = await createTestCore({
+            doenetML: `
+    <p name="p1"><numberList name="nl1">
+      <math>1,2,3,4,5</math>
+    </numberList></p>
+
+    <p name="p2">Third number: $nl1[3]</p>
+    <p name="p3">Fifth number: $nl1[5]</p>
+
+    <p>Change values:
+      <mathInput name="mi1">$nl1[1]</mathInput>
+      <mathInput name="mi2">$nl1[2]</mathInput>
+      <mathInput name="mi3">$nl1[3]</mathInput>
+      <mathInput name="mi4">$nl1[4]</mathInput>
+      <mathInput name="mi5">$nl1[5]</mathInput>
+    </p>
+    `,
+        });
+
+        async function check_items(vals: number[]) {
+            await test_numberList({
+                core,
+                name: `/nl1`,
+                numbers: vals,
+                pName: `/p1`,
+                text: vals.join(", "),
+            });
+
+            const stateVariables = await returnAllStateVariables(core);
+
+            expect(stateVariables["/p2"].stateValues.text).eq(
+                `Third number: ${vals[2]}`,
+            );
+            expect(stateVariables["/p3"].stateValues.text).eq(
+                `Fifth number: ${vals[4]}`,
+            );
+        }
+
+        let vals = [1, 2, 3, 4, 5];
+
+        await check_items(vals);
+
+        vals = [6, 7, 8, 9, 10];
+        for (let [i, v] of vals.entries()) {
+            await updateMathInputValue({
+                latex: v.toString(),
+                componentName: `/mi${i + 1}`,
+                core,
+            });
+        }
+        await check_items(vals);
+    });
+
+    it("maxNumber with when have one math child", async () => {
+        let core = await createTestCore({
+            doenetML: `
+    <p name="p1"><numberList maxNumber="3" name="nl">
+      <math name="m">1,2,3,4,5</math>
+    </numberList></p>
+
+    <p name="p2">Copied math: $m</p>
+
+    <p name="p3">Copied numberList: $nl</p>
+
+    `,
+        });
+
+        let vals = [1, 2, 3, 4, 5];
+
+        await test_numberList({
+            core,
+            name: `/nl`,
+            numbers: vals.slice(0, 3),
+            pName: `/p1`,
+            text: vals.slice(0, 3).join(", "),
+        });
+
+        let stateVariables = await returnAllStateVariables(core);
+
+        expect(stateVariables["/p2"].stateValues.text).eq(
+            `Copied math: ${vals.join(", ")}`,
+        );
+        expect(stateVariables["/p3"].stateValues.text).eq(
+            `Copied numberList: ${vals.slice(0, 3).join(", ")}`,
+        );
+    });
+
     it("maxNumber with mathList or numberList child", async () => {
         let core = await createTestCore({
             doenetML: `
@@ -1042,4 +1133,44 @@ describe("NumberList tag tests", async () => {
         expect(stateVariables["/pText"].stateValues.text).eq("Text: 7, -8");
         expect(stateVariables["/pLatex"].stateValues.text).eq("Latex: 7, -8");
     });
+
+    it("definition and inverse based on shadowed value from a numberList prop", async () => {
+        let core = await createTestCore({
+            doenetML: `
+
+    <regionBetweenCurves boundaryValues="-5 8" name="rbc" />
+
+    <p name="p">$rbc.boundaryValues{assignNames="nl"}</p>
+    <mathInput name="mi">$rbc.boundaryValues</mathInput>
+
+    `,
+        });
+
+        const stateVariables = await returnAllStateVariables(core);
+
+        let n1 = -5,
+            n2 = 8;
+        await test_numberList({
+            core,
+            name: "/nl",
+            numbers: [n1, n2],
+            pName: "/p",
+            text: `${n1}, ${n2}`,
+        });
+
+        n1 = 3;
+        n2 = 6;
+        await updateMathInputValue({
+            latex: `${n1}, ${n2}`,
+            componentName: "/mi",
+            core,
+        });
+        await test_numberList({
+            core,
+            name: "/nl",
+            numbers: [n1, n2],
+            pName: "/p",
+            text: `${n1}, ${n2}`,
+        });
+    });
 });
diff --git a/packages/doenetml-worker/src/test/tagSpecific/text.test.ts b/packages/doenetml-worker/src/test/tagSpecific/text.test.ts
index d21faae80..b17938379 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/text.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/text.test.ts
@@ -981,13 +981,13 @@ describe("Text tag tests", async () => {
         ]);
     });
 
-    it("numListItems and listItems", async () => {
+    it("numListItems and list", async () => {
         let core = await createTestCore({
             doenetML: `
     <p><text name="t">Hello there, friend!</text>!</p>
 
     <p name="p2">Number of list items is $t.numListItems.</p>
-    <p name="p3">list items: $t.listItems.</p>
+    <p name="p3">list items: $t.list.</p>
     `,
         });
 
@@ -1001,7 +1001,7 @@ describe("Text tag tests", async () => {
         );
 
         expect(stateVariables["/t"].stateValues.numListItems).eq(2);
-        expect(stateVariables["/t"].stateValues.listItems).eqls([
+        expect(stateVariables["/t"].stateValues.list).eqls([
             "Hello there",
             "friend!",
         ]);
diff --git a/packages/doenetml-worker/src/test/tagSpecific/textinput.test.ts b/packages/doenetml-worker/src/test/tagSpecific/textinput.test.ts
index c4f21b5ee..49caa7c30 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/textinput.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/textinput.test.ts
@@ -1585,7 +1585,7 @@ describe("TextInput tag tests", async () => {
     <p name="p4">Number of words is $ti.numWords.</p>
     <p name="p5">Words: $ti.words.</p>
     <p name="p6">Number of list items is $ti.numListItems.</p>
-    <p name="p7">List items: $ti.listItems.</p>
+    <p name="p7">List: $ti.list.</p>
      `,
         });
 
@@ -1601,11 +1601,11 @@ describe("TextInput tag tests", async () => {
             const words = string.trim().split(/\s+/);
             const numWords = words.length;
 
-            const listItems = string
+            const list = string
                 .trim()
                 .split(",")
                 .map((s) => s.trim());
-            const numListItems = listItems.length;
+            const numListItems = list.length;
 
             const stateVariables = await returnAllStateVariables(core);
 
@@ -1625,7 +1625,7 @@ describe("TextInput tag tests", async () => {
                 `Number of list items is ${numListItems}.`,
             );
             expect(stateVariables["/p7"].stateValues.text).eq(
-                `List items: ${listItems.join(", ")}.`,
+                `List: ${list.join(", ")}.`,
             );
 
             expect(stateVariables["/ti"].stateValues.numCharacters).eq(
@@ -1639,7 +1639,7 @@ describe("TextInput tag tests", async () => {
             expect(stateVariables["/ti"].stateValues.numListItems).eq(
                 numListItems,
             );
-            expect(stateVariables["/ti"].stateValues.listItems).eqls(listItems);
+            expect(stateVariables["/ti"].stateValues.list).eqls(list);
         }
 
         let string = "";
diff --git a/packages/doenetml-worker/src/test/tagSpecific/textlist.test.ts b/packages/doenetml-worker/src/test/tagSpecific/textlist.test.ts
index eb45a21df..9b2333276 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/textlist.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/textlist.test.ts
@@ -642,4 +642,44 @@ describe("TextList tag tests", async () => {
             "Text: apple, banana",
         );
     });
+
+    it("definition and inverse based on shadowed value from a textList prop", async () => {
+        let core = await createTestCore({
+            doenetML: `
+
+    <math functionSymbols="a b" name="m" />
+
+    <p name="p">$m.functionSymbols{assignNames="tl"}</p>
+
+
+    <textInput name="ti">$m.functionSymbols</textInput>
+
+    `,
+        });
+
+        let x1 = "a",
+            x2 = "b";
+        await test_textList({
+            core,
+            name: "/tl",
+            texts: [x1, x2],
+            pName: "/p",
+            text: `${x1}, ${x2}`,
+        });
+
+        x1 = "c";
+        x2 = "d";
+        await updateTextInputValue({
+            text: `${x1}, ${x2}`,
+            componentName: "/ti",
+            core,
+        });
+        await test_textList({
+            core,
+            name: "/tl",
+            texts: [x1, x2],
+            pName: "/p",
+            text: `${x1}, ${x2}`,
+        });
+    });
 });
diff --git a/packages/doenetml-worker/src/test/tagSpecific/triggerset.test.ts b/packages/doenetml-worker/src/test/tagSpecific/triggerset.test.ts
index eb05c837b..284e0b660 100644
--- a/packages/doenetml-worker/src/test/tagSpecific/triggerset.test.ts
+++ b/packages/doenetml-worker/src/test/tagSpecific/triggerset.test.ts
@@ -25,7 +25,7 @@ describe("TriggerSet tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
@@ -113,7 +113,7 @@ describe("TriggerSet tag tests", async () => {
       <point name="P">(1,2)</point>
     </graph>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet name="tset">
       <label>perform updates and actions</label>
@@ -145,7 +145,7 @@ describe("TriggerSet tag tests", async () => {
       <point name="P">(1,2)</point>
     </graph>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet name="tset">
       <label>perform updates and actions</label>
@@ -178,7 +178,7 @@ describe("TriggerSet tag tests", async () => {
       <point name="P">(1,2)</point>
     </graph>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet name="tset">
       <label>perform updates and actions</label>
@@ -216,7 +216,7 @@ describe("TriggerSet tag tests", async () => {
       <point name="P">(1,2)</point>
     </graph>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet name="tset">
       <label>perform updates and actions</label>
@@ -705,7 +705,7 @@ describe("TriggerSet tag tests", async () => {
     <p>Say hello: <text name="hello"></text></p>
     <p>Count: <number name="n">1</number></p>
 
-    <p name="nums"><aslist><sampleRandomNumbers name="s" numSamples="5" type="discreteUniform" from="1" to="6" /></aslist></p>
+    <p name="nums"><sampleRandomNumbers name="s" numSamples="7" type="discreteUniform" from="1" to="6" /></p>
 
     <triggerSet triggerWhen="$(P.x)>0 and $(P.y)>0">
       <label>perform updates</label>
@@ -737,7 +737,7 @@ describe("TriggerSet tag tests", async () => {
         let numbers = stateVariables["/nums"].stateValues.text
             .split(",")
             .map(Number);
-        expect(numbers.length).eq(5);
+        expect(numbers.length).eq(7);
         for (let num of numbers) {
             expect(Number.isInteger(num)).be.true;
             expect(num).gte(1);
diff --git a/packages/doenetml-worker/src/utils/label.js b/packages/doenetml-worker/src/utils/label.js
index cb7782683..89a7699d0 100644
--- a/packages/doenetml-worker/src/utils/label.js
+++ b/packages/doenetml-worker/src/utils/label.js
@@ -3,6 +3,7 @@ export function returnWrapNonLabelsSugarFunction({
     createAttributeOfType,
     onlyStringOrMacros = false,
     customWrappingFunction,
+    wrapSingleIfNotWrappingComponentType = false,
 }) {
     return function ({ matchedChildren, componentInfoObjects }) {
         if (matchedChildren.length === 0) {
@@ -84,9 +85,11 @@ export function returnWrapNonLabelsSugarFunction({
             if (
                 (childrenToWrap.length === 1 &&
                     typeof childrenToWrap[0] !== "string" &&
-                    !componentInfoObjects.isCompositeComponent({
-                        componentType: childrenToWrap[0].componentType,
-                    })) ||
+                    (!wrapSingleIfNotWrappingComponentType ||
+                        componentInfoObjects.componentIsSpecifiedType(
+                            childrenToWrap[0],
+                            wrappingComponentType,
+                        ))) ||
                 childrenToWrap.length === 0
             ) {
                 return { success: false };