diff --git a/runtime/scripts/jme.js b/runtime/scripts/jme.js
index 470945258..191535ece 100644
--- a/runtime/scripts/jme.js
+++ b/runtime/scripts/jme.js
@@ -2201,10 +2201,13 @@ Scope.prototype = /** @lends Numbas.jme.Scope.prototype */ {
      *
      * @param {string} name
      */
-    deleteVariable: function(name) {
+    deleteVariable: function(name, options) {
+        options = options || {};
         name = jme.normaliseName(name, this);
         this.deleted.variables[name] = true;
-        this.deleted.constants[name] = true;
+        if(options.delete_constant !== false) {
+            this.deleted.constants[name] = true;
+        }
     },
     /** Mark the given function name as deleted from the scope.
      *
@@ -2544,7 +2547,7 @@ Scope.prototype = /** @lends Numbas.jme.Scope.prototype */ {
         var s = new Scope([this]);
         if(defs.variables) {
             defs.variables.forEach(function(v) {
-                s.deleteVariable(v);
+                s.deleteVariable(v, {delete_constant: false});
             });
         }
         if(defs.functions) {
diff --git a/runtime/scripts/parts/jme.js b/runtime/scripts/parts/jme.js
index 48021ecbe..9015dea1c 100644
--- a/runtime/scripts/parts/jme.js
+++ b/runtime/scripts/parts/jme.js
@@ -288,6 +288,7 @@ JMEPart.prototype = /** @lends Numbas.JMEPart.prototype */
         if(!tree && this.marks>0) {
             this.error('part.jme.answer missing');
         }
+        scope = scope.unset(this.question.local_definitions);
         var expr = jme.display.treeToJME(tree,{plaindecimal: true},scope);
         settings.correctVariables = jme.findvars(jme.compile(expr),[],scope);
         settings.correctAnswer = jme.display.simplifyExpression(